linear_regression Version 0.1

• Installing The Package
• Purpose of Package
• Comparison with scipy.stats.linregress
• Using The Package
• Linear Regression Mathematical Equations
• Plans for Version 0.2

Installing the Package

From the command line:

pip install linear_regression

Also available at https://pypi.python.org/pypi?name=linear-regression&version=0.1&:action=display

Purpose of Package

The purpose of this package is to make it simple to perform simple least squares regression analysis on two sets of measurements. The scipy.stats module contains a function 'linregress' that can quickly perform regression analysis on two sets of measurements, but it does not have the option to force the best fit line to intercept the origin (i.e. to have a y intercept of 0). It also lacks other options, as demonstrated in the comparison below.

Comparison Between scipy.stats.linregress and the linear_regression package:

Best Fit Line (BFL) Attributes and Options	linear_regression v0.1	scipy.stat.linregress
slope	Yes	Yes
std. error of slope	Yes	Yes
y-intercept	Yes	Yes
r (correlation coefficient)	Yes	Yes
r-squared	Yes	No
p-value	No	Yes
std. error of y-intercept	Yes	No
slope of BFL through origin	Yes	No
std. error of slope of BFL through origin	Yes	No
r for BFL through origin	Yes	No
r-squared for BFL through origin	Yes	No
Returns Regression Results As	Pandas DataFrame or String	Tuple
Option To Return Results For BFL, BFL through origin, or both simultaneously	Yes	No

Using The Package

Version 0.1 of this package only contains a single module, lr.py, which contains a simple class named lr.

Load The lr class

from linear_regression.lr import lr

Store the x and y coordinates from you dataset into seperate array-like object (arrays, np arrays, lists, tuples...)

Example: My dataset contains the following (x,y) data points:

(1.0,2.2), (1.8,3.8),(4.5,6.3), (5.2, 9.3)

I then create a list for the x coordinates and a list for the y coordinates below:

x = [1.0,1.8,4.5,4.7,5.0]
y = [2.2,3.8,6.4,7.2,9.3]

Create an instance object of the lr class using the x and y variables are instance arguments.

I'll name my object data. I will use this object throughout the tutorial.

data = lr(x,y)

lr Object Methods

results

parameters:

• zero_intercept: (default value is False) if set to True, returns DataFrame for the best fit line through the origin.

• both: (default value is False) if set to True, returns DataFrame both the best fit line and the best fit line through the origin (both overrides zero_intercept if both is set to True).

returns:

• DataFrame contaning slope, y-intercept, std.error of slope, std. error of y intercept, r, and r-squared for either the regular best fit line, the best fit line through the origin, or both the regular best fit line + the best fit line through the origin.

Examples:

regression_results = data.results() #No parameters specified, so by default returns 
                                    #DataFrame with values for the regular best fit line 
print(regression_results)

        Slope  Intercept  Std. Error, Slope  Std. Error, Intercept         r  \
BFL  1.445573   0.865051           0.257081               0.972703  0.955689   

     r-squared  
BFL   0.913341  

print(data.results(zero_intercept = True)) #Retuns DataFrame with results for the best fit line through the origin

                     Slope  Intercept  Std. Error, Slope         r  r-squared
BFL Through (0,0)  1.65102        0.0           0.109809  0.991269   0.982613

print(data.results(both = True)) #Returns DataFrame with values for both the regular best 
                          # fit line and the best fit line through the origin

                      Slope  Intercept  Std. Error, Slope  \
BFL                1.445573   0.865051           0.257081   
BFL Through (0,0)  1.651020   0.000000           0.109809   

                   Std. Error, Intercept         r  r-squared  
BFL                             0.972703  0.955689   0.913341  
BFL Through (0,0)                    NaN  0.991269   0.982613  

Printing the object

If you print your lr object, it will return a string with the regression results for both the best fit line and the best fit line through the origin.

Example using the data lr object:

print(data)

LINEAR LEAST-SQUARES REGRESSION ANALYSIS

BEST FIT LINE:
slope = 1.44557329463
intercept = 0.865050798258
std. error, slope = 0.257080665506
std. error, intercept = 0.972703011277
r = 0.955688839522
r-squared = 0.913341157987
number of data points = 5

BEST FIT LINE THROUGH THE ORIGIN, (0,0):
slope = 1.65101983794
intercept = 0.0
std. error, slope = 0.109809386014
r = 0.991268534449
r-squared = 0.982613307389
number of data points = 5

lr Object Attributes

slope - returns the slope of the best fit line.

print(data.slope)

1.44557329463

slope00 - returns the slope of the best fit line through the origin

print(data.slope00)

1.65101983794

intercept - returns the y-intercept of the best fit line

print(data.intercept)

0.865050798258

slope_std_error - returns the std. error of the slope of the best fit line

print(data.slope_std_error)

0.257080665506

slope_std_error00 - returns the std. error of the slope of the best fit line through the origin

print(data.slope_std_error00)

0.109809386014

intercept_std_error - returns the std. error of the intercept of the best fit line

print(data.intercept_std_error)

0.972703011277

r - returns the correlation coefficient

print(data.r)

0.955688839522

r00 - returns the correlation coefficient for the BFL through the origin

print(data.r00)

0.991268534449

Linear Regression Mathematical Equations

The least squares regression mathematical equations that I used can be found at https://github.com/DRosenman/linear_regression/blob/master/leastsquaresmath.pdf

Plans for Version 0.2

• Add module for creating various regression plots.

• Add p-value for BFL and BFL through origin