an_introduction_to_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d83da440",
   "metadata": {},
   "source": [
    "# Defining a Statistical Model\n",
    "\n",
    "In the most general sense, the goal of statistics is understand the world around us.  Often times, to do this, we come up with a mental model of the world, from data.  If our data is of a high quality and is an accurate reflection of the world around us, the model we come up with can possibly be an accurate reflection of the world, rather than meaningless symbols or \"just notation\".  \n",
    "\n",
    "With a well informed model, we can simulate the underlying phenomenon we captured data on, either extrapolating into the future what might happen in the real world, understanding what's happening now, even if we can't directly observe it, or being able to automate away an extremely hard task.  \n",
    "\n",
    "Statistical models allow us to ask - \n",
    "\n",
    "* What if?\n",
    "* What's happening now?\n",
    "* Why is it happening?\n",
    "* What will happen?\n",
    "* What happened?\n",
    "\n",
    "And actually come up with answers that might be reasonable!  \n",
    "\n",
    "Additionally, statistical models allow us to automate tasks that appear like science fiction; we can teach robots to simulate processes of cognition like sight, hearing, and speech.  \n",
    "\n",
    "In order to understand how these models work, we'll need quite a bit of mathematical rigour, but the pay off will be the ability to simulate and understand the world around us through computation.\n",
    "\n",
    "# Maximum Likelihood Estimation\n",
    "\n",
    "Before we start introducing statistical models, we need the right mental model of what a statistical model is and does.  For this we turn to maximum likelihood estimation.  You may recall from last time that maximum likelihood estimation can be used to find the shape parameters of a distribution.  Recall that the shape parameters are merely the associated measures of center, spread, skew, kurtosis and higher order terms that allow us to easily define an accurate description of the underlying data through a process that generates data similar to the distribution of values seen.\n",
    "\n",
    "Realize, that given the above description, we've already seen our first statistical model - the process (or mathematical formula) that generates a distribution of data via sampling.\n",
    "\n",
    "Let's review with a few examples to see this in action:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5eb0c86a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "data = np.random.normal(0, 1, size=10000)\n",
    "center, spread = stats.norm.fit(data)\n",
    "simulated_data = np.random.normal(center, spread, size=10000)\n",
    "\n",
    "f, axes = plt.subplots(1, 2, figsize=(10, 4), sharex=True)\n",
    "sns.distplot( data , color=\"green\", ax=axes[0])\n",
    "sns.distplot( simulated_data , color=\"blue\", ax=axes[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd6701fe",
   "metadata": {},
   "source": [
    "As you can see here there is very little difference between the simulated data and or original source!  This is because we made a few assumptions:\n",
    "\n",
    "1. we assumed a normal distribution when simulating our data\n",
    "2. we assumed we had enough original data to come up with reasonable shape parameters\n",
    "\n",
    "In general, this leads us to a conclusion - we can think of the underlying distribution that our most closely resembles as sort of a mental model for our real world phenomenon.  By understanding the underlying distribution that creates our process, in this case a normal distribution, we can simulate accurate representations of our underlying process, by only knowing the center and spread of the data!\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Use the following function to test the given data set, and then simulate new data.  Check your conclusion by plotting the two datasets, your simulated one and the original, as well as looking at the answer.  Do this for 10 separate runs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "33e1e3d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def get_random_dataset():\n",
    "    dists = [\"normal\", \"exponential\", \"gamma\", \"poisson\"]\n",
    "    method = random.choice(dists)\n",
    "    \n",
    "    if method == \"exponential\":\n",
    "        scale = random.randint(0, 500)\n",
    "        return method, np.random.exponential(\n",
    "            scale=scale, \n",
    "            size=500\n",
    "        )\n",
    "    if method == \"gamma\":\n",
    "        scale = random.randint(0, 500)\n",
    "        shape = random.randint(0, 5)\n",
    "        return method, np.random.gamma(\n",
    "            shape=shape,\n",
    "            scale=scale, \n",
    "            size=500\n",
    "        )\n",
    "    if method == \"normal\":\n",
    "        scale = random.randint(0, 15)\n",
    "        loc = random.randint(0, 500)\n",
    "        return method, np.random.normal(\n",
    "            loc=loc,\n",
    "            scale=scale,\n",
    "            size=500\n",
    "        )\n",
    "    if method == \"poisson\":\n",
    "        lam = random.randint(1, 6)\n",
    "        return method, np.random.poisson(\n",
    "            lam=lam,\n",
    "            size=500\n",
    "        )\n",
    "    \n",
    "answer, data = get_random_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a38d63f",
   "metadata": {},
   "source": [
    "## The Connection Between Likelihood and Probability\n",
    "\n",
    "Before we leave our high level discussion, there is an important point to make - \n",
    "\n",
    "$$ Likelihood(data | \\mu, \\sigma) \\neq Probability(\\mu, \\sigma | data) $$\n",
    "\n",
    "This is because with the likelihood we ask, what are the most likely shape parameters that could have generated this data?  With the probability we ask, given these shape parameters what is the probability we saw this data?\n",
    "\n",
    "So we can think of these as two sides of the same coin for estimation purposes.\n",
    "\n",
    "Let's see what the probability would look like in python:\n",
    "\n",
    "Source: https://towardsdatascience.com/probability-concepts-explained-maximum-likelihood-estimation-c7b4342fdbb1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "436dd8f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.88026944877706"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def probability(mu, sigma, data):\n",
    "    simulated_data = np.random.normal(mu, sigma, size=len(data))\n",
    "    return stats.ttest_ind(simulated_data, data)[1]\n",
    "\n",
    "data = np.random.normal(0, 1, size=10000)\n",
    "mu_guess = 0\n",
    "sigma_guess = 1\n",
    "probability(mu_guess, sigma_guess, data)\n",
    "# probability that given these shape parameters we saw this data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99c7c36c",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Use the student's t-test to calculate the probability that you were able to recover the shape parameters for a given distribution.  Do this 10 times with the following function.  You can check the true answer.  Be sure to figure out which distribution you are working with first, then figure out the shape parameters using maximum likelihood estimation, then calculate the t-test to get the probability.  After that simulate out the data, like in the previous exercise, and compare your simulated data with the original, does the simulated data look similar with the original?  Run a ks-2sample test to make sure.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ec2177ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "def get_random_dataset():\n",
    "    dists = [\"normal\", \"exponential\", \"gamma\", \"poisson\"]\n",
    "    method = random.choice(dists)\n",
    "    \n",
    "    if method == \"exponential\":\n",
    "        scale = random.randint(0, 500)\n",
    "        return method, np.random.exponential(\n",
    "            scale=scale, \n",
    "            size=500\n",
    "        ), [scale]\n",
    "    \n",
    "    if method == \"gamma\":\n",
    "        scale = random.randint(0, 500)\n",
    "        shape = random.randint(0, 5)\n",
    "        return method, np.random.gamma(\n",
    "            shape=shape,\n",
    "            scale=scale, \n",
    "            size=500\n",
    "        ), [shape, scale]\n",
    "    \n",
    "    if method == \"normal\":\n",
    "        scale = random.randint(0, 15)\n",
    "        loc = random.randint(0, 500)\n",
    "        return method, np.random.normal(\n",
    "            loc=loc,\n",
    "            scale=scale,\n",
    "            size=500\n",
    "        ), [loc, scale]\n",
    "    \n",
    "    if method == \"poisson\":\n",
    "        lam = random.randint(1, 6)\n",
    "        return method, np.random.poisson(\n",
    "            lam=lam,\n",
    "            size=500\n",
    "        ), [lam]\n",
    "    \n",
    "answer, data, shape_parameters = get_random_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9109040",
   "metadata": {},
   "source": [
    "## Linear Regression \n",
    "\n",
    "Linear Regression is one of the simplest and most interpretable models there is.  Before we dive into it's specifics, let's first see how it relates to maximum likelihood estimation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1852c841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 600x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.random.normal(0, 10, size = 100)\n",
    "y = x*2 + 5 + np.random.normal(0, 15, size = 100)\n",
    "sns.jointplot(x=x, y=y, kind=\"reg\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b08ab77",
   "metadata": {},
   "source": [
    "Here we see the joint distribution of the data.  By looking at the blue shaded line we see the joint simulated distribution from the relationship between the shape parameters of the shared distribution.  Additionally, we see the point estimate - the maximum likelihood estimation - the dark blue line cutting through the data.\n",
    "\n",
    "The reason why a distribution like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1291c3b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "data = np.random.normal(0, 1, size=10000)\n",
    "sns.distplot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b513254f",
   "metadata": {},
   "source": [
    "is simple - it's because the maximum point estimate for this distribution is where the majority of the top of the theoretical curve that represents the shape of the distribution.  In other words, the MLE takes the highest point of the distribution.  In two dimensional space, this is represented as a line as the above picture shows.\n",
    "\n",
    "\"One might even say as maximum likelihood estimation of a vector x, given linear measurements corrupted by Gaussian measurement errors.\"\n",
    "\n",
    "stolen from http://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf this line is beautiful and I need think of my own way of saying it.\n",
    "\n",
    "## The Ordinary Least Squares Algorithm\n",
    "\n",
    "The Ordinary Least Squares Algorithm is probably the simplest thing you could think of - Here is the psuedo code for the algorithm:\n",
    "\n",
    "1. start with a line cutting through the data (perhaps pick two random points in the space and draw a line through them)\n",
    "2. look at the difference between all the points and the line\n",
    "3. update the line such that the sum of the squared differences is made smaller\n",
    "4. repeat until the sum of squared differences is as small as possible\n",
    "\n",
    "There are lots of ways to implement this, we'll look at a few methods here:\n",
    "\n",
    "### A Brief Digression - Newton - Raphson's Method\n",
    "\n",
    "Before we go through Stochastic Gradient Descent, let's start by looking at a simplier method for approximating values.\n",
    "\n",
    "Newton-Raphson's Method is based on the notion that we can guess and check our way to the solution of a minimization or maximization problem through iteration.  \n",
    "\n",
    "This method can be used to approximate the roots of any real valued function.\n",
    "\n",
    "The way the method works is as follows:\n",
    "\n",
    "1. Initialize a guess root $x_{0}$\n",
    "2. Calculate the derivative with respect to the function\n",
    "3. Update our guess by $x_{i} = x_{i-1} - \\frac{f(x_{i-1})}{f'(x_{i-1})}$\n",
    "4. Once the change between $x_{i}$ and $x_{i-1}$ is neglible then we quit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "31d2ff80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"NewtonIteration_Ani.gif\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('<img src=\"NewtonIteration_Ani.gif\">')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c38f9dad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from hackthederivative import complex_step_finite_diff as differentiate\n",
    "from functools import partial\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import pylab\n",
    "%matplotlib inline\n",
    "\n",
    "def newton_raphson_method(x_0, f, tolerance=1e-10, max_iter=1e5):\n",
    "    fprime = partial(differentiate, f)\n",
    "    x_cur = 100000000000\n",
    "    x_prev = x_0\n",
    "    count = 0\n",
    "    error = []\n",
    "    while True:\n",
    "        x_cur = x_prev - (f(x_prev) / fprime(x_prev))\n",
    "        error.append(abs(x_prev - x_cur))\n",
    "        if abs(x_prev - x_cur) < tolerance:\n",
    "            break\n",
    "        x_prev = x_cur\n",
    "        count += 1\n",
    "        if count > max_iter:\n",
    "            break\n",
    "    return x_cur, error\n",
    "    \n",
    "root, error = newton_raphson_method(1000, lambda x: x**2 - 9)\n",
    "plt.plot(error)\n",
    "pylab.xlabel('number of steps')\n",
    "pylab.ylabel(\"error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1dd90162",
   "metadata": {},
   "source": [
    "While the method we will use for ordinary least squares is somewhat different in how it's computed, two conceptual themes will remain consistent - we can use a derivative to drive our model closer to an optimum.  And second, as our model updates, we will (hopefully) reduce the amount of error in our guess.\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Find the zeros for the following equations using calculus (differentiate and then set the derivative equal to zero, then solve for x), then verify your solution using newton raphson.\n",
    "\n",
    "### Equation 1\n",
    "\n",
    "$$ x^{3} + x^{2} + 1 $$\n",
    "\n",
    "### Equation 2\n",
    "\n",
    "$$ x^{2} + 1 $$\n",
    "\n",
    "### Equation 3\n",
    "\n",
    "$$ 4x^{4} + 8 $$\n",
    "\n",
    "### Equation 4\n",
    "\n",
    "$$ 16x^{5} + 12x^{2} + 4 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41ff2bfe",
   "metadata": {},
   "source": [
    "## Gradient Descent\n",
    "\n",
    "Gradient Descent, like Newton-Raphson can be used to guess values that optimize some problem.  The general problem Gradient Descent solves is that of maximum likelihood estimation.  \n",
    "\n",
    "There are two main ways the algorithm can be implemented:\n",
    "\n",
    "1. Via Linear Algebra\n",
    "2. Via Calculus \n",
    "\n",
    "Of the two methods above typically the Linear Algebra solution is used in practice, but is far harder to understand than it's Calculus equivalent.  Let's look at the Calculus version below:\n",
    "\n",
    "Gradient Descent requires a cost function.  The cost function used will give us the gradients that we will use to do our updating of our model parameters.  Generally speaking, a cost function is answering the question of how far apart our model prediction is from what was actually seen in the data?  This means, cost functions are typically described in terms of total distance from our predictions to the observed values from the data.  Thus in general our Gradient Descent algorithm looks like this:\n",
    "\n",
    "1. Initialize our model parameters with random values\n",
    "2. Calculate the gradient by summing the partial derivatives of the cost function for each parameter\n",
    "3. Update each parameter by subtracting off the partial derivative with respect to that parameter \n",
    "4. Continue until error is minimized with respect to all parameters\n",
    "\n",
    "Notice the similarities between this method and Newton-Raphson, these are the steps of the two algorithms in general:\n",
    "\n",
    "1. initialize with some random guess\n",
    "2. calculate a derivative\n",
    "3. update based on that derivative\n",
    "4. continue until the error becomes neglible\n",
    "\n",
    "Now let's look at how to implement gradient descent for ordinary least squares:\n",
    "\n",
    "\n",
    "Reference:\n",
    "\n",
    "[ML Cheatsheet](https://ml-cheatsheet.readthedocs.io/en/latest/gradient_descent.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "51134d59",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random\n",
    "\n",
    "def update_weights(m, b, X, Y, learning_rate):\n",
    "    m_deriv = 0\n",
    "    b_deriv = 0\n",
    "    N = len(X)\n",
    "    for i in range(N):\n",
    "        # Calculate partial derivatives w.r.t to equation (y - (mx + b))^2\n",
    "        # remember we use the chain rule here.\n",
    "        # -2x(y - (mx + b))\n",
    "        m_deriv += -2*X[i] * (Y[i] - (m*X[i] + b))\n",
    "\n",
    "        # -2(y - (mx + b))\n",
    "        b_deriv += -2*(Y[i] - (m*X[i] + b))\n",
    "\n",
    "    # We subtract because the derivatives point in direction of steepest ascent\n",
    "    m -= (m_deriv / N) * learning_rate\n",
    "    b -= (b_deriv / N) * learning_rate\n",
    "    \n",
    "    return m, b\n",
    "\n",
    "def cost_function(m, b, X, y):\n",
    "    N = len(X)\n",
    "    total_cost = 0\n",
    "    for i in range(N):\n",
    "        total_cost += math.pow((y[i] - (m*X[i] + b)), 2)\n",
    "    return total_cost / N\n",
    "\n",
    "def gradient_descent(X, y, learning_rate=0.001, tolerance=1e-2, max_iter=1e5):\n",
    "    m = 0\n",
    "    b = 0\n",
    "    error = []\n",
    "    count = 0\n",
    "    while True:\n",
    "        m, b = update_weights(m, b, X, y, learning_rate)\n",
    "        cur_cost = cost_function(m, b, X, y)\n",
    "        error.append(cur_cost)\n",
    "        count += 1\n",
    "        if cur_cost < tolerance:\n",
    "            break\n",
    "        if count > max_iter:\n",
    "            break\n",
    "    return m, b, error\n",
    "    \n",
    "X = [random.randint(1, 10)+random.random()*10 for _ in range(1000)]\n",
    "y = [4 + 3*X[i] + random.random() for i in range(len(X))]\n",
    "m, b, error = gradient_descent(X, y)\n",
    "y_predict = [m*X[i]+b for i in range(len(X))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "764d48ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y_predict,'r-')\n",
    "plt.plot(X,y,'b.')\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "92df53e9",
   "metadata": {},
   "source": [
    "Aside:\n",
    "\n",
    "We can also use linear algebra to do stochastic gradient descent without explicitly computing a gradient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cfdfc34f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 5.0, 6.0, 40.0)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def linear_regression(X, y):\n",
    "    X_b = np.c_[np.ones((len(X),1)), X]\n",
    "    x_transpose_times_x = X_b.T.dot(X_b)\n",
    "    inverse = np.linalg.inv(x_transpose_times_x)\n",
    "    return inverse.dot(X_b.T).dot(y)\n",
    "    \n",
    "optimal_theta = linear_regression(X, y)\n",
    "X_new = np.array([[0],[5]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]\n",
    "y_predict = X_new_b.dot(optimal_theta)\n",
    "y_predict\n",
    "\n",
    "plt.plot(X_new,y_predict,'r-')\n",
    "plt.plot(X,y,'b.')\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0,5,6,40])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b16b788",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e906df61",
   "metadata": {},
   "source": [
    "As we can see, our algorithm does quiet well!\n",
    "\n",
    "# Exercise\n",
    "\n",
    "Carry out the derivation of the derivatives for the equation: \n",
    "\n",
    "$$ (y - (mx + b))^{2} $$\n",
    "\n",
    "w.r.t. m and then b.\n",
    "\n",
    "Notice, the final answer is provided in the code above.  Your goal is to work through the steps and show your work."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e35b44b",
   "metadata": {},
   "source": [
    "## Working With Libraries\n",
    "\n",
    "\n",
    "Now let's look at an example using a library (which you'll usually do) to do linear regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b80e8b51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>chol</th>\n",
       "      <th>stab.glu</th>\n",
       "      <th>hdl</th>\n",
       "      <th>ratio</th>\n",
       "      <th>glyhb</th>\n",
       "      <th>location</th>\n",
       "      <th>age</th>\n",
       "      <th>gender</th>\n",
       "      <th>height</th>\n",
       "      <th>weight</th>\n",
       "      <th>frame</th>\n",
       "      <th>bp.1s</th>\n",
       "      <th>bp.1d</th>\n",
       "      <th>bp.2s</th>\n",
       "      <th>bp.2d</th>\n",
       "      <th>waist</th>\n",
       "      <th>hip</th>\n",
       "      <th>time.ppn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1000</td>\n",
       "      <td>203.0</td>\n",
       "      <td>82</td>\n",
       "      <td>56.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>4.31</td>\n",
       "      <td>Buckingham</td>\n",
       "      <td>46</td>\n",
       "      <td>female</td>\n",
       "      <td>62.0</td>\n",
       "      <td>121.0</td>\n",
       "      <td>medium</td>\n",
       "      <td>118.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>29.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>720.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1001</td>\n",
       "      <td>165.0</td>\n",
       "      <td>97</td>\n",
       "      <td>24.0</td>\n",
       "      <td>6.9</td>\n",
       "      <td>4.44</td>\n",
       "      <td>Buckingham</td>\n",
       "      <td>29</td>\n",
       "      <td>female</td>\n",
       "      <td>64.0</td>\n",
       "      <td>218.0</td>\n",
       "      <td>large</td>\n",
       "      <td>112.0</td>\n",
       "      <td>68.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>46.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>360.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1002</td>\n",
       "      <td>228.0</td>\n",
       "      <td>92</td>\n",
       "      <td>37.0</td>\n",
       "      <td>6.2</td>\n",
       "      <td>4.64</td>\n",
       "      <td>Buckingham</td>\n",
       "      <td>58</td>\n",
       "      <td>female</td>\n",
       "      <td>61.0</td>\n",
       "      <td>256.0</td>\n",
       "      <td>large</td>\n",
       "      <td>190.0</td>\n",
       "      <td>92.0</td>\n",
       "      <td>185.0</td>\n",
       "      <td>92.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>180.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1003</td>\n",
       "      <td>78.0</td>\n",
       "      <td>93</td>\n",
       "      <td>12.0</td>\n",
       "      <td>6.5</td>\n",
       "      <td>4.63</td>\n",
       "      <td>Buckingham</td>\n",
       "      <td>67</td>\n",
       "      <td>male</td>\n",
       "      <td>67.0</td>\n",
       "      <td>119.0</td>\n",
       "      <td>large</td>\n",
       "      <td>110.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>33.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1005</td>\n",
       "      <td>249.0</td>\n",
       "      <td>90</td>\n",
       "      <td>28.0</td>\n",
       "      <td>8.9</td>\n",
       "      <td>7.72</td>\n",
       "      <td>Buckingham</td>\n",
       "      <td>64</td>\n",
       "      <td>male</td>\n",
       "      <td>68.0</td>\n",
       "      <td>183.0</td>\n",
       "      <td>medium</td>\n",
       "      <td>138.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>44.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>300.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     id   chol  stab.glu   hdl  ratio  glyhb    location  age  gender  height  \\\n",
       "0  1000  203.0        82  56.0    3.6   4.31  Buckingham   46  female    62.0   \n",
       "1  1001  165.0        97  24.0    6.9   4.44  Buckingham   29  female    64.0   \n",
       "2  1002  228.0        92  37.0    6.2   4.64  Buckingham   58  female    61.0   \n",
       "3  1003   78.0        93  12.0    6.5   4.63  Buckingham   67    male    67.0   \n",
       "4  1005  249.0        90  28.0    8.9   7.72  Buckingham   64    male    68.0   \n",
       "\n",
       "   weight   frame  bp.1s  bp.1d  bp.2s  bp.2d  waist   hip  time.ppn  \n",
       "0   121.0  medium  118.0   59.0    NaN    NaN   29.0  38.0     720.0  \n",
       "1   218.0   large  112.0   68.0    NaN    NaN   46.0  48.0     360.0  \n",
       "2   256.0   large  190.0   92.0  185.0   92.0   49.0  57.0     180.0  \n",
       "3   119.0   large  110.0   50.0    NaN    NaN   33.0  38.0     480.0  \n",
       "4   183.0  medium  138.0   80.0    NaN    NaN   44.0  41.0     300.0  "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"diabetes.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9be3be61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "medium    184\n",
       "small     104\n",
       "large     103\n",
       "Name: frame, dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"frame\"].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3881da47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2257.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 17 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>3.17e-264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:30:32</td>     <th>  Log-Likelihood:    </th>          <td> -1997.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   386</td>      <th>  AIC:               </th>          <td>   4003.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   382</td>      <th>  BIC:               </th>          <td>   4019.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>    1.0795</td> <td>    0.110</td> <td>    9.788</td> <td> 0.000</td> <td>    0.863</td> <td>    1.296</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>    6.2453</td> <td>    1.019</td> <td>    6.127</td> <td> 0.000</td> <td>    4.241</td> <td>    8.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>   -0.1856</td> <td>    0.102</td> <td>   -1.817</td> <td> 0.070</td> <td>   -0.386</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th>  <td>    3.9590</td> <td>    0.575</td> <td>    6.883</td> <td> 0.000</td> <td>    2.828</td> <td>    5.090</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>37.566</td> <th>  Durbin-Watson:     </th> <td>   1.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  58.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.642</td> <th>  Prob(JB):          </th> <td>2.15e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.406</td> <th>  Cond. No.          </th> <td>    92.0</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.959\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.959\n",
       "Method:                 Least Squares   F-statistic:                              2257.\n",
       "Date:                Thu, 17 Nov 2022   Prob (F-statistic):                   3.17e-264\n",
       "Time:                        19:30:32   Log-Likelihood:                         -1997.7\n",
       "No. Observations:                 386   AIC:                                      4003.\n",
       "Df Residuals:                     382   BIC:                                      4019.\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            1.0795      0.110      9.788      0.000       0.863       1.296\n",
       "glyhb          6.2453      1.019      6.127      0.000       4.241       8.249\n",
       "weight        -0.1856      0.102     -1.817      0.070      -0.386       0.015\n",
       "waist          3.9590      0.575      6.883      0.000       2.828       5.090\n",
       "==============================================================================\n",
       "Omnibus:                       37.566   Durbin-Watson:                   1.968\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               58.335\n",
       "Skew:                           0.642   Prob(JB):                     2.15e-13\n",
       "Kurtosis:                       4.406   Cond. No.                         92.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fa062bd",
   "metadata": {},
   "source": [
    "## T-Tests and F-Tests\n",
    "\n",
    "Let's start by understanding what the \"t-test\" and the \"f-test\" mean in this context.  If you recall from last time, in general the t-test is used to test whether or not two different samples come from the same distribution.  In this case the \"t-test\" tests the null hypothesis that the given independent variable is different from zero.  So if we reject the null hypothesis, in this case, it is different than zero.\n",
    "\n",
    "Likewise for the \"F-test\", in general it tests if 2 or more variables come from the same population.  In this case, the null hypothesis states that all the variables jointly equal zero or in otherwords, contribute nothing to the explaination of the y variable.\n",
    "\n",
    "\n",
    "To be specific, in the above example with respect to the t-tests:\n",
    "\n",
    "We reject the null hypothesis 3 out of 4 times, therefore all but the weight we strongly reject as being zero.  However, since the pvalue is close to 0.05 and given our own semantic knowledge about diabetes, we will choose to keep diabetes in our model.\n",
    "\n",
    "We also reject the null hypothesis that the variables jointly are zero and therefore the model does have statistical meaning.\n",
    "\n",
    "Source: https://stats.stackexchange.com/questions/59250/how-to-interpret-the-output-of-the-summary-method-for-an-lm-object-in-r\n",
    "\n",
    "## Goodness of fit measures\n",
    "\n",
    "The next two measures we will look at are Akaike Information Criterion and Bayesian Information Criterion, but first we will look at the algorithm that underlies them both: KL - Divergence\n",
    "\n",
    "### Digression - KL-Divergence\n",
    "\n",
    "Kullback Liebler divergence is, like many other things in statistics a way of measuring how different two distributions are.  But the way it asks the question and the uses of KL-Divergence are surprisingly rich.  Checkout this quote from wikipedia:\n",
    "\n",
    "\"Expressed in the language of Bayesian inference, ${\\displaystyle D_{\\text{KL}}(P\\parallel Q)}$  is a measure of the information gained when one revises one's beliefs from the prior probability distribution Q to the posterior probability distribution P.  In other words, it is the amount of information lost when Q is used to approximate P.  In applications, P typically represents the \"true\" distribution of data, observations, or a precisely calculated theoretical distribution, while Q typically represents a theory, model, description, or approximation of P.  In order to find a distribution Q that is closest to P, we can minimize KL divergence and compute an information projection.\"\n",
    "\n",
    "Source: https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence\n",
    "\n",
    "While this feels like a restatement of ks_2sample with fewer guarantees:\n",
    "\n",
    "1. it's assymetric => ${\\displaystyle D_{\\text{KL}}(P\\parallel Q)} \\neq {\\displaystyle D_{\\text{KL}}(Q\\parallel P)}$\n",
    "\n",
    "2. there is no guarantee that comparisons between different paired distributions will have an ordering:\n",
    "\n",
    "I.E. if we have: \n",
    "\n",
    "${\\displaystyle D_{\\text{KL}}(P\\parallel Q)} = 5$\n",
    "\n",
    "${\\displaystyle D_{\\text{KL}}(Q\\parallel R)} = 7$\n",
    "\n",
    "It is not the case that:\n",
    "\n",
    "${\\displaystyle D_{\\text{KL}}(P\\parallel Q)} \\lt {\\displaystyle D_{\\text{KL}}(Q\\parallel R)}$\n",
    "\n",
    "And further more:\n",
    "\n",
    "${\\displaystyle D_{\\text{KL}}(P\\parallel R)} \\neq 12$\n",
    "\n",
    "And yet!\n",
    "\n",
    "KL-Divergence is **_powerful_**.  To summarize, once of the ways we can use it:\n",
    "\n",
    "* compare the divergence between two distributions _regardless_ of distribution shape.\n",
    "\n",
    "Consider the following case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "86cde092",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "normal_dist = np.random.normal(0, 1, size=10000)\n",
    "exponential_dist = np.random.exponential(1.9, size=10000)\n",
    "sns.distplot( exponential_dist , color=\"blue\")\n",
    "sns.distplot( normal_dist , color=\"green\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49e0b4f2",
   "metadata": {},
   "source": [
    "We can use KL-Divergence to measure how different these really are!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "2b1ff52f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "import numpy as np\n",
    "t1 = stats.norm(0, 1)\n",
    "t2 = stats.expon(1.9)\n",
    "\n",
    "# domain to evaluate PDF on\n",
    "x = np.linspace(-5, 5, 100)\n",
    "stats.entropy(t1.pdf(x), t2.pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ab3d9ef",
   "metadata": {},
   "source": [
    "Perhaps surprisingly, the divergence is infinite!  Despite these two distributions appearing very similar, they are definitely different!  This gives us more reason to believe that we shouldn't always trust, even precise pictures.\n",
    "\n",
    "Another important use of KL-Divergence is telling you by how much you are off from a theoretical optimum.  In other words, if we have enough information, it tells us how much we don't know.  \n",
    "\n",
    "The interested, there are even more examples found here: \n",
    "    \n",
    "https://www.programcreek.com/python/example/62037/scipy.stats.entropy\n",
    "        \n",
    "## Akaike Information Criterion && Bayesian Information Criterion\n",
    "\n",
    "The AIC is another one of those tools that helps assess how well the model does.  It is an application of KL-divergence.  The way it does this is by looking at the overall goodness of fit of the model.  The smaller the AIC, the better the model fits the data.  And if a model has lots of parameters the score will always be higher, so this is a way of assessing goodness of fit, while avoiding overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4b771a5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.955</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.955</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   4198.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 17 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>3.03e-268</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:43:02</td>     <th>  Log-Likelihood:    </th>          <td> -2092.5</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   400</td>      <th>  AIC:               </th>          <td>   4189.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   398</td>      <th>  BIC:               </th>          <td>   4197.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>   <td>    1.1357</td> <td>    0.110</td> <td>   10.281</td> <td> 0.000</td> <td>    0.918</td> <td>    1.353</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th> <td>    3.9302</td> <td>    0.153</td> <td>   25.633</td> <td> 0.000</td> <td>    3.629</td> <td>    4.232</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>62.760</td> <th>  Durbin-Watson:     </th> <td>   1.897</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 161.768</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.765</td> <th>  Prob(JB):          </th> <td>7.46e-36</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.714</td> <th>  Cond. No.          </th> <td>    5.28</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.955\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.955\n",
       "Method:                 Least Squares   F-statistic:                              4198.\n",
       "Date:                Thu, 17 Nov 2022   Prob (F-statistic):                   3.03e-268\n",
       "Time:                        19:43:02   Log-Likelihood:                         -2092.5\n",
       "No. Observations:                 400   AIC:                                      4189.\n",
       "Df Residuals:                     398   BIC:                                      4197.\n",
       "Df Model:                           2                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            1.1357      0.110     10.281      0.000       0.918       1.353\n",
       "waist          3.9302      0.153     25.633      0.000       3.629       4.232\n",
       "==============================================================================\n",
       "Omnibus:                       62.760   Durbin-Watson:                   1.897\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              161.768\n",
       "Skew:                           0.765   Prob(JB):                     7.46e-36\n",
       "Kurtosis:                       5.714   Cond. No.                         5.28\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9d41b445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.954</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.954</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2691.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 17 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>7.90e-258</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:43:48</td>     <th>  Log-Likelihood:    </th>          <td> -2029.9</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   388</td>      <th>  AIC:               </th>          <td>   4066.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   385</td>      <th>  BIC:               </th>          <td>   4078.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>    1.4347</td> <td>    0.102</td> <td>   14.062</td> <td> 0.000</td> <td>    1.234</td> <td>    1.635</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>    8.7908</td> <td>    1.004</td> <td>    8.755</td> <td> 0.000</td> <td>    6.817</td> <td>   10.765</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>    0.4709</td> <td>    0.039</td> <td>   12.173</td> <td> 0.000</td> <td>    0.395</td> <td>    0.547</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>12.704</td> <th>  Durbin-Watson:     </th> <td>   2.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.002</td> <th>  Jarque-Bera (JB):  </th> <td>  14.920</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.338</td> <th>  Prob(JB):          </th> <td>0.000576</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.683</td> <th>  Cond. No.          </th> <td>    82.0</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.954\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.954\n",
       "Method:                 Least Squares   F-statistic:                              2691.\n",
       "Date:                Thu, 17 Nov 2022   Prob (F-statistic):                   7.90e-258\n",
       "Time:                        19:43:48   Log-Likelihood:                         -2029.9\n",
       "No. Observations:                 388   AIC:                                      4066.\n",
       "Df Residuals:                     385   BIC:                                      4078.\n",
       "Df Model:                           3                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            1.4347      0.102     14.062      0.000       1.234       1.635\n",
       "glyhb          8.7908      1.004      8.755      0.000       6.817      10.765\n",
       "weight         0.4709      0.039     12.173      0.000       0.395       0.547\n",
       "==============================================================================\n",
       "Omnibus:                       12.704   Durbin-Watson:                   2.003\n",
       "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               14.920\n",
       "Skew:                           0.338   Prob(JB):                     0.000576\n",
       "Kurtosis:                       3.683   Cond. No.                         82.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2ed1a53",
   "metadata": {},
   "source": [
    "In the above example we look at two competing models for explaining the total cholesterol in diabetes patients.  The first model uses two parameters, hdl and waist. The AIC is lower than in the second model which uses hdl, glyhb and weight.  And so we can say with confidence that the first model is definitely a better representation than the second - it has a higher AIC than the second.  \n",
    "\n",
    "The only real substantiative difference between AIC and BIC is the AIC is less likely to find the true model than BIC.  In fact it was shown that asymptotically, BIC will eventually find the true model, while AIC doesn't always.  It was however shown that AIC often does find good models, even if they aren't the theoretical \"best\".  Other than that, they are basically the same.  They just penalize extra parameters differently, in that AIC penalizes them more heavily than BIC does.\n",
    "\n",
    "Source: https://en.wikipedia.org/wiki/Akaike_information_criterion#Comparison_with_BIC\n",
    "\n",
    "## R-Squared\n",
    "\n",
    "The next goodness of fit measure we will look at is $R^{2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3578373c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def r_squared(true_y, pred_y):\n",
    "    y_bar = np.mean(true_y)\n",
    "    total_sum_of_squares = sum((true_y - y_bar)**2)\n",
    "    residual_sum_of_squares = sum((true_y - pred_y)**2)\n",
    "    return 1 - (residual_sum_of_squares/total_sum_of_squares)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d600a88c",
   "metadata": {},
   "source": [
    "The $R^{2}$ measure returns a float between 0 and 1 which gives a notion of how well the model fits the observed (or sometimes called the dependent) variable.  The closer to 1 the better the model fits the data.\n",
    "\n",
    "Essentially, $R^{2}$ is the ratio of variance explained by the model compared with total variance in the observed variable.  It's important to note - $R^{2}$ is only true for linear models.  If you try to use it for non-linear models you can end up with values less than 0 or greater than 1, which make no sense. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "537b8ee1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2257.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Thu, 17 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>3.17e-264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>19:47:25</td>     <th>  Log-Likelihood:    </th>          <td> -1997.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   386</td>      <th>  AIC:               </th>          <td>   4003.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   382</td>      <th>  BIC:               </th>          <td>   4019.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>    1.0795</td> <td>    0.110</td> <td>    9.788</td> <td> 0.000</td> <td>    0.863</td> <td>    1.296</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>    6.2453</td> <td>    1.019</td> <td>    6.127</td> <td> 0.000</td> <td>    4.241</td> <td>    8.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>   -0.1856</td> <td>    0.102</td> <td>   -1.817</td> <td> 0.070</td> <td>   -0.386</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th>  <td>    3.9590</td> <td>    0.575</td> <td>    6.883</td> <td> 0.000</td> <td>    2.828</td> <td>    5.090</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>37.566</td> <th>  Durbin-Watson:     </th> <td>   1.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  58.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.642</td> <th>  Prob(JB):          </th> <td>2.15e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.406</td> <th>  Cond. No.          </th> <td>    92.0</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.959\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.959\n",
       "Method:                 Least Squares   F-statistic:                              2257.\n",
       "Date:                Thu, 17 Nov 2022   Prob (F-statistic):                   3.17e-264\n",
       "Time:                        19:47:25   Log-Likelihood:                         -1997.7\n",
       "No. Observations:                 386   AIC:                                      4003.\n",
       "Df Residuals:                     382   BIC:                                      4019.\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            1.0795      0.110      9.788      0.000       0.863       1.296\n",
       "glyhb          6.2453      1.019      6.127      0.000       4.241       8.249\n",
       "weight        -0.1856      0.102     -1.817      0.070      -0.386       0.015\n",
       "waist          3.9590      0.575      6.883      0.000       2.828       5.090\n",
       "==============================================================================\n",
       "Omnibus:                       37.566   Durbin-Watson:                   1.968\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               58.335\n",
       "Skew:                           0.642   Prob(JB):                     2.15e-13\n",
       "Kurtosis:                       4.406   Cond. No.                         92.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa3b8f2",
   "metadata": {},
   "source": [
    "Here we see the $R^{2}$ is 0.959 which is a pretty good measure of fit!  So we can say between this and the AIC being quiet low (lower than the case when we had fewer explaintory variables) we are doing pretty well.\n",
    "\n",
    "## Mean Squared Error and Mean Absolute Error\n",
    "\n",
    "The problems with $R^{2}$ are well documented but there are other measures which don't suffer from the same issues.  We'll look at two such measures here:\n",
    "\n",
    "Mean Squared Error is simply the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6c5d8d3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1831.720447577852"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "def mse(y_true, y_pred):\n",
    "    return np.mean((y_true - y_pred)**2)\n",
    "\n",
    "\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "mse(diabetes[\"chol\"].values, result.fittedvalues)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ac435b6",
   "metadata": {},
   "source": [
    "But what does the number 1831.72 mean? One way you can make sense of this is by normalizing the result based on the range of values, but what's the right value to normalize by? We could take the absolute difference between the largest and smallest predicted values. But even such a transformation still doesn't answer the question of what Mean Squared Error means.\n",
    "\n",
    "The truth is, it's context specific. So it depends on the units of the dependent variable. In this case, we are saying we are off by about 1831.72 milligrams of cholesterol per deciliter of blood. Is that a lot? It depends on the context we are working in and the requirements of stringency we have placed infront of us.\n",
    "\n",
    "Unfortunately there is no objective general rule about Mean Squared Error, all of it is context specific. But the nice thing about Mean Squared Error is it is a true measure. So for optimization problems its a great tool. The only main issue I found is, it's far too sensitive to bad cases. This is in part because it is squared and in part because it is a mean, both of which will overstate any individual cases in which the errors are extreme, even if the model does very well fitting most cases.\n",
    "\n",
    "If outliers are important to your model, then we can say that mean squared error is a good measure to use. If outliers are extremely rare, or unimportant to attempt to fit, you are better off simply either choosing a different metric or throwing out those cases and retraining your model.\n",
    "\n",
    "However, it's important that the outliers need not be extreme only with respect to model fit, but must be extreme compared to the rest of the dependent and/or independent values in the dataset.\n",
    "\n",
    "## Mean Absolute Error\n",
    "The Mean Absolute Error functions much the same way as the Mean Squared Error. The only difference is a different distance function is used to calculate the final error measure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "67914f30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33.5060761358191"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "def mae(y_true, y_pred):\n",
    "    return np.mean(abs(y_true - y_pred))\n",
    "\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "mae(diabetes[\"chol\"].values, result.fittedvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df9483a0",
   "metadata": {},
   "source": [
    "Note that the Mean Absolute Error is smaller than the Mean Squared Error or even the Root Mean Squared Error, this is because the absolute value is a different distance function.\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Use the Cardiac Catheterization Diagnostic data to replicate the above analysis - \n",
    "\n",
    "Come up with a model that best fits Cholesterol.  You may as many or as few of the other values as you deem appropriate.  Interpret the coeficients and the pvalues associated.  Additionally, look at the MSE, MAE, $R^{2}$, AIC and BIC to support your findings.  If your initial model is bad, come up with a second one or even a third until you find a model that fits the data to a satisfactory amount."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6db49d6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sex</th>\n",
       "      <th>age</th>\n",
       "      <th>cad_dur</th>\n",
       "      <th>choleste</th>\n",
       "      <th>sigdz</th>\n",
       "      <th>tvdlm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>73</td>\n",
       "      <td>132</td>\n",
       "      <td>268.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>68</td>\n",
       "      <td>85</td>\n",
       "      <td>120.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>54</td>\n",
       "      <td>45</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>58</td>\n",
       "      <td>86</td>\n",
       "      <td>245.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>56</td>\n",
       "      <td>7</td>\n",
       "      <td>269.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sex  age  cad_dur  choleste  sigdz  tvdlm\n",
       "0    0   73      132     268.0      1    1.0\n",
       "1    0   68       85     120.0      1    1.0\n",
       "2    0   54       45       NaN      1    0.0\n",
       "3    1   58       86     245.0      0    0.0\n",
       "4    1   56        7     269.0      0    0.0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acath_df = pd.read_stata(\"acath.dta\")\n",
    "\n",
    "acath_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41c1908e",
   "metadata": {},
   "source": [
    "# Exploratory Data Analysis Meets Modeling\n",
    "\n",
    "In what follows we will show you how to take the things we learned during the exploratory phase and apply them in the modeling phase.  \n",
    "\n",
    "For instance, if our independent variables and our dependent variable both follow a normal distribution then we'd use a linear-linear model, as we'll see now.\n",
    "\n",
    "Throughout what remains consider the distribution of the variables that you learned during the exploratory phase and use them as a guide for what model you use in the modeling phase.\n",
    "\n",
    "## Parameter Interpretation\n",
    "\n",
    "The practice of parameter interpretation is the art within the science of statistics.  The goal here is to understand how the world works through the lense of the statistical model and try to understand what the data is telling you.  Mathematical modeling is about statistical testing and rigour, but it is also about story telling.  \n",
    "\n",
    "For the tools we are looking at in this section, it is worth noting that none of them modify the parameters of the model.  So we are still doing linear regression, even if we apply a transform to the columns of the data.  It is imperative that we be linear in our parameters, not linear in our relationships.\n",
    "\n",
    "### linear - linear model\n",
    "\n",
    "Linear - linear means that the variables and output variable are in their original form and we assume a linear relationship between input and output.\n",
    "\n",
    "So in the following model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a4b11161",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.959</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2257.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 21 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>3.17e-264</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:01:25</td>     <th>  Log-Likelihood:    </th>          <td> -1997.7</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   386</td>      <th>  AIC:               </th>          <td>   4003.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   382</td>      <th>  BIC:               </th>          <td>   4019.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>    1.0795</td> <td>    0.110</td> <td>    9.788</td> <td> 0.000</td> <td>    0.863</td> <td>    1.296</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>    6.2453</td> <td>    1.019</td> <td>    6.127</td> <td> 0.000</td> <td>    4.241</td> <td>    8.249</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>   -0.1856</td> <td>    0.102</td> <td>   -1.817</td> <td> 0.070</td> <td>   -0.386</td> <td>    0.015</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th>  <td>    3.9590</td> <td>    0.575</td> <td>    6.883</td> <td> 0.000</td> <td>    2.828</td> <td>    5.090</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>37.566</td> <th>  Durbin-Watson:     </th> <td>   1.968</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  58.335</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.642</td> <th>  Prob(JB):          </th> <td>2.15e-13</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 4.406</td> <th>  Cond. No.          </th> <td>    92.0</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.959\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.959\n",
       "Method:                 Least Squares   F-statistic:                              2257.\n",
       "Date:                Mon, 21 Nov 2022   Prob (F-statistic):                   3.17e-264\n",
       "Time:                        16:01:25   Log-Likelihood:                         -1997.7\n",
       "No. Observations:                 386   AIC:                                      4003.\n",
       "Df Residuals:                     382   BIC:                                      4019.\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            1.0795      0.110      9.788      0.000       0.863       1.296\n",
       "glyhb          6.2453      1.019      6.127      0.000       4.241       8.249\n",
       "weight        -0.1856      0.102     -1.817      0.070      -0.386       0.015\n",
       "waist          3.9590      0.575      6.883      0.000       2.828       5.090\n",
       "==============================================================================\n",
       "Omnibus:                       37.566   Durbin-Watson:                   1.968\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               58.335\n",
       "Skew:                           0.642   Prob(JB):                     2.15e-13\n",
       "Kurtosis:                       4.406   Cond. No.                         92.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23269cbd",
   "metadata": {},
   "source": [
    "Here we are saying in general:\n",
    "\n",
    "$$ Chol \\approx \\theta_{1}*hdl + \\theta_{2}*glyhb + \\theta_{3}*weight + \\theta_{4}*waist $$\n",
    "\n",
    "And we are saying in particular we are saying that:\n",
    "\n",
    "$$ \\theta_{1} = 1.0795 $$\n",
    "$$ \\theta_{2} = 6.2453 $$\n",
    "$$ \\theta_{3} = -0.1856 $$\n",
    "$$ \\theta_{4} = 3.9590 $$\n",
    "\n",
    "Which translates to:\n",
    "\n",
    "$$ Chol \\approx 1.0795*hdl + 6.2453*glyhb  - 0.1856*weight + 3.9590*waist $$\n",
    "\n",
    "Therefore, holding all other variables constant, an increase of hdl by 1 milligram per deciliter of blood will lead to an increase of 1.0795 in the milligrams of cholesterol per deciliter of blood on average.\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Use the Cardiac Catheterization Diagnostic data to replicate the above analysis - \n",
    "\n",
    "Interpret the results of your model for each variable and state whether the variables are statistically significant or not."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ab1641c",
   "metadata": {},
   "source": [
    "### log - linear model\n",
    "\n",
    "One of the major challenges of statistical analysis with linear regression is our data is rarely normally distributed.  That said, it can often times be made approximately normally distributed through transformation.  One of the hallmark transformations is making use of the logarithm.  \n",
    "\n",
    "This is because it takes things that are multiplicative:\n",
    "\n",
    "$$ log(a*b) = log(a) + log(b) $$\n",
    "\n",
    "And makes them additive!  This allows us to force data into the linear class of models.  However it means our interpretations will absolutely change.  Let's see how!\n",
    "\n",
    "With anything logarithmic we look at the percentage of the variable.  Let's look at an example for the log-linear case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1d692e92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.988</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.988</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   7677.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 21 Nov 2022</td> <th>  Prob (F-statistic):</th>           <td>  0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:08:52</td>     <th>  Log-Likelihood:    </th>          <td> -343.70</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   386</td>      <th>  AIC:               </th>          <td>   695.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   382</td>      <th>  BIC:               </th>          <td>   711.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>    0.0225</td> <td>    0.002</td> <td>   14.789</td> <td> 0.000</td> <td>    0.019</td> <td>    0.025</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>    0.0601</td> <td>    0.014</td> <td>    4.282</td> <td> 0.000</td> <td>    0.033</td> <td>    0.088</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>   -0.0055</td> <td>    0.001</td> <td>   -3.940</td> <td> 0.000</td> <td>   -0.008</td> <td>   -0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th>  <td>    0.1257</td> <td>    0.008</td> <td>   15.868</td> <td> 0.000</td> <td>    0.110</td> <td>    0.141</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>26.154</td> <th>  Durbin-Watson:     </th> <td>   1.790</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  29.892</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.621</td> <th>  Prob(JB):          </th> <td>3.23e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.562</td> <th>  Cond. No.          </th> <td>    92.0</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.988\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.988\n",
       "Method:                 Least Squares   F-statistic:                              7677.\n",
       "Date:                Mon, 21 Nov 2022   Prob (F-statistic):                        0.00\n",
       "Time:                        16:08:52   Log-Likelihood:                         -343.70\n",
       "No. Observations:                 386   AIC:                                      695.4\n",
       "Df Residuals:                     382   BIC:                                      711.2\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl            0.0225      0.002     14.789      0.000       0.019       0.025\n",
       "glyhb          0.0601      0.014      4.282      0.000       0.033       0.088\n",
       "weight        -0.0055      0.001     -3.940      0.000      -0.008      -0.003\n",
       "waist          0.1257      0.008     15.868      0.000       0.110       0.141\n",
       "==============================================================================\n",
       "Omnibus:                       26.154   Durbin-Watson:                   1.790\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               29.892\n",
       "Skew:                          -0.621   Prob(JB):                     3.23e-07\n",
       "Kurtosis:                       3.562   Cond. No.                         92.0\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]]\n",
    "ols = sm.OLS(np.log(diabetes[\"chol\"].values), measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ed32730",
   "metadata": {},
   "source": [
    "Here we are saying in general:\n",
    "\n",
    "$$ Log(Chol) \\approx \\theta_{1}*hdl + \\theta_{2}*glyhb + \\theta_{3}*weight + \\theta_{4}*waist $$\n",
    "\n",
    "And we are saying in particular we are saying that:\n",
    "\n",
    "$$ \\theta_{1} = 1.0795 $$\n",
    "$$ \\theta_{2} = 6.2453 $$\n",
    "$$ \\theta_{3} = -0.1856 $$\n",
    "$$ \\theta_{4} = 3.9590 $$\n",
    "\n",
    "Which translates to:\n",
    "\n",
    "$$ Log(Chol) \\approx 1.0795*hdl + 6.2453*glyhb  - 0.1856*weight + 3.9590*waist $$\n",
    "\n",
    "Therefore, holding all other variables constant, an increase of hdl by 1 milligram per deciliter of blood will lead to an increase of 1.0795% in the milligrams of cholesterol per deciliter of blood on average.\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Take the log of the dependent variable in the Cardiac Catheterization Diagnostic data and rerun your analysis and interpretation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5d305eb",
   "metadata": {},
   "source": [
    "### linear - log model\n",
    "\n",
    "Let's look at what happens when we transform the $X_{i}$'s:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c295c0cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared (uncentered):</th>      <td>   0.962</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared (uncentered):</th> <td>   0.962</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>          <td>   2417.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 21 Nov 2022</td> <th>  Prob (F-statistic):</th>          <td>1.05e-269</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:21:08</td>     <th>  Log-Likelihood:    </th>          <td> -1985.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   386</td>      <th>  AIC:               </th>          <td>   3978.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>   382</td>      <th>  BIC:               </th>          <td>   3994.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     4</td>      <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>              <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "     <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>hdl</th>    <td>   28.0979</td> <td>    5.290</td> <td>    5.311</td> <td> 0.000</td> <td>   17.696</td> <td>   38.500</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>glyhb</th>  <td>   38.9181</td> <td>    7.169</td> <td>    5.429</td> <td> 0.000</td> <td>   24.823</td> <td>   53.013</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>weight</th> <td>  -17.7311</td> <td>   17.721</td> <td>   -1.001</td> <td> 0.318</td> <td>  -52.573</td> <td>   17.111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>waist</th>  <td>   34.7496</td> <td>   26.137</td> <td>    1.330</td> <td> 0.184</td> <td>  -16.641</td> <td>   86.140</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>69.191</td> <th>  Durbin-Watson:     </th> <td>   2.038</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td> 143.127</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.950</td> <th>  Prob(JB):          </th> <td>8.32e-32</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 5.300</td> <th>  Cond. No.          </th> <td>    112.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] R² is computed without centering (uncentered) since the model does not contain a constant.<br/>[2] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                                 OLS Regression Results                                \n",
       "=======================================================================================\n",
       "Dep. Variable:                      y   R-squared (uncentered):                   0.962\n",
       "Model:                            OLS   Adj. R-squared (uncentered):              0.962\n",
       "Method:                 Least Squares   F-statistic:                              2417.\n",
       "Date:                Mon, 21 Nov 2022   Prob (F-statistic):                   1.05e-269\n",
       "Time:                        16:21:08   Log-Likelihood:                         -1985.0\n",
       "No. Observations:                 386   AIC:                                      3978.\n",
       "Df Residuals:                     382   BIC:                                      3994.\n",
       "Df Model:                           4                                                  \n",
       "Covariance Type:            nonrobust                                                  \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "hdl           28.0979      5.290      5.311      0.000      17.696      38.500\n",
       "glyhb         38.9181      7.169      5.429      0.000      24.823      53.013\n",
       "weight       -17.7311     17.721     -1.001      0.318     -52.573      17.111\n",
       "waist         34.7496     26.137      1.330      0.184     -16.641      86.140\n",
       "==============================================================================\n",
       "Omnibus:                       69.191   Durbin-Watson:                   2.038\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              143.127\n",
       "Skew:                           0.950   Prob(JB):                     8.32e-32\n",
       "Kurtosis:                       5.300   Cond. No.                         112.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] R² is computed without centering (uncentered) since the model does not contain a constant.\n",
       "[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# data source: https://hbiostat.org/data/\n",
    "# data dictionary: https://hbiostat.org/data/repo/Cdiabetes.html\n",
    "# glyhb is Glycosolated Hemoglobin\n",
    "diabetes = pd.read_csv(\"diabetes.csv\")\n",
    "diabetes = diabetes.dropna(subset=[\"hdl\", \"glyhb\", \"weight\", \"waist\"])\n",
    "measures = np.log(diabetes[[\"hdl\", \"glyhb\", \"weight\", \"waist\"]])\n",
    "ols = sm.OLS(diabetes[\"chol\"].values, measures)\n",
    "result = ols.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48efaddc",
   "metadata": {},
   "source": [
    "Here we are saying in general:\n",
    "\n",
    "$$ Log(Chol) \\approx \\theta_{1}*hdl + \\theta_{2}*glyhb $$\n",
    "\n",
    "And we are saying in particular we are saying that:\n",
    "\n",
    "$$ \\theta_{1} = 28.0979 $$\n",
    "$$ \\theta_{2} = 38.9181 $$\n",
    "\n",
    "Which translates to:\n",
    "\n",
    "$$ Log(Chol) \\approx 28.0979*hdl + 38.9181*glyhb $$\n",
    "\n",
    "Therefore, holding all other variables constant, an increase of hdl by 1% milligram per deciliter of blood will lead to an increase of 28.0979% in the milligrams of cholesterol per deciliter of blood on average.  \n",
    "\n",
    "What's more interesting is now weight and waist don't matter.\n",
    "\n",
    "## Exercise\n",
    "\n",
    "Take the log of the dependent variable in the Cardiac Catheterization Diagnostic data and rerun your analysis and interpretation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73e1a2e6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}