Predict_Roughness_of_3D_Print_Material.ipynb

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      "source": [
        "# Importing the libraries\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "%matplotlib inline"
      ],
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      "execution_count": 16,
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      "source": [
        "printer = pd.read_csv('/content/3DPrinting_data.csv')"
      ],
      "metadata": {
        "id": "wChMZ4OB4rth"
      },
      "execution_count": 17,
      "outputs": []
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      "cell_type": "code",
      "source": [
        "printer['infill_pattern'].replace(['grid','honeycomb'], [0,1], inplace = True)\n",
        "printer['material'].replace(['abs','pla'], [0,1], inplace = True)"
      ],
      "metadata": {
        "id": "nEzNuQ9H5XNu"
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      "execution_count": 18,
      "outputs": []
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      "source": [
        "# Model 1 : Predicting roughness based on 9 features.\n",
        "- Here we will be **building** a **multiple linear regression** model to **predict** `roughness` based on all the 9 features from `layer_height` to `fan_speed`"
      ]
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      "source": [
        "# Defining features and labels\n",
        "X = printer.drop(['roughness','tension_strength','elongation'], axis = 1)\n",
        "y = printer['roughness']"
      ]
    },
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              "   layer_height  wall_thickness  infill_density  infill_pattern  \\\n",
              "0          0.02               8              90               0   \n",
              "1          0.02               7              90               1   \n",
              "2          0.02               1              80               0   \n",
              "3          0.02               4              70               1   \n",
              "4          0.02               6              90               0   \n",
              "\n",
              "   nozzle_temperature  bed_temperature  print_speed  material  fan_speed  \n",
              "0                 220               60           40         0          0  \n",
              "1                 225               65           40         0         25  \n",
              "2                 230               70           40         0         50  \n",
              "3                 240               75           40         0         75  \n",
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      "source": [
        "#importing statsmodels library\n",
        "import statsmodels.api as sm"
      ]
    },
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      "source": [
        "# let's define a function for the multiple regression\n",
        "\n",
        "def linear_Regression(x,y):\n",
        "    \n",
        "    x = sm.add_constant(x)\n",
        "    \n",
        "    #defining the model, fitting the model and printing the results\n",
        "    multiple_model = sm.OLS(y,x).fit()\n",
        "    print(multiple_model.summary())"
      ]
    },
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          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:              roughness   R-squared:                       0.875\n",
            "Model:                            OLS   Adj. R-squared:                  0.851\n",
            "Method:                 Least Squares   F-statistic:                     35.95\n",
            "Date:                Mon, 14 Nov 2022   Prob (F-statistic):           3.83e-16\n",
            "Time:                        16:08:26   Log-Likelihood:                -248.19\n",
            "No. Observations:                  50   AIC:                             514.4\n",
            "Df Residuals:                      41   BIC:                             531.6\n",
            "Df Model:                           8                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "======================================================================================\n",
            "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
            "--------------------------------------------------------------------------------------\n",
            "const                 -0.9534      0.159     -6.006      0.000      -1.274      -0.633\n",
            "layer_height        1269.4449     87.648     14.483      0.000    1092.437    1446.453\n",
            "wall_thickness         2.3342      2.189      1.066      0.293      -2.087       6.756\n",
            "infill_density        -0.0423      0.234     -0.181      0.857      -0.515       0.430\n",
            "infill_pattern        -0.1255     11.280     -0.011      0.991     -22.907      22.656\n",
            "nozzle_temperature    15.0562      2.529      5.953      0.000       9.948      20.164\n",
            "bed_temperature      -55.6225      9.279     -5.995      0.000     -74.362     -36.883\n",
            "print_speed            0.6496      0.206      3.153      0.003       0.233       1.066\n",
            "material             298.4514     58.364      5.114      0.000     180.582     416.321\n",
            "fan_speed              7.8989      1.238      6.379      0.000       5.398      10.399\n",
            "==============================================================================\n",
            "Omnibus:                        1.107   Durbin-Watson:                   1.467\n",
            "Prob(Omnibus):                  0.575   Jarque-Bera (JB):                0.749\n",
            "Skew:                           0.300   Prob(JB):                        0.688\n",
            "Kurtosis:                       3.018   Cond. No.                     3.59e+18\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
            "[2] The smallest eigenvalue is 2.48e-31. This might indicate that there are\n",
            "strong multicollinearity problems or that the design matrix is singular.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
            "  x = pd.concat(x[::order], 1)\n"
          ]
        }
      ],
      "source": [
        "#calling the linear regression function\n",
        "linear_Regression(X,y)"
      ]
    },
    {
      "cell_type": "markdown",
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      "source": [
        "### Inference from model\n",
        "1. The **R-squared** value is **0.875 ot 87.5%** which states that **about 87.5%** of proportion of **variability** in data can be **explained** by this **linear regression model**. The **r-squared** is the most **important parameter** for a **model evaluation**. higher the value, better is the fit.\n",
        "\n",
        "2. The **p-value** is an **important measure** for evaluating the various **variables**. **Closer** is the **p-value to 1**, the **lesser** is that **feature variable** has to do with the **label variable**. In our model, **wall thickness, infill_density and infill_pattern** are all close to 1 meaning they **don't** play **much role** in roughness.\n",
        "\n",
        "3. Finally, the **expression** for this model can be written from the **coefficients** as follows\n",
        "\n",
        "`Roughness = -0.9534 + 1269.4449*layer_height + 2.3342*wall_thickness - 0.0423*infill_density - 0.1255*infill_pattern + 15.0562*nozzle_temperature - 55.6225*bbed_temperature + 0.6496*print_speed + 298.4514*material + 7.8989*fan_speed`\n",
        "\n",
        "4. The coefficients suggest the following\n",
        "   - In the **absence** of all the **parameters**, the **roughness decreases** by **0.9534 micro metre** by the constant term. This may be **due** to **other factors** like **ambient temperature** which are **not considered** for the model.\n",
        "   - A **positive coefficient value** states that an **increase in wall thickness** (example) by 1 mm results in **increase in roughness** by 2.3342 micro metre.\n",
        "   - Similarly, **a negative coefficient value** states that an **increase in bed temperature** by a degree C causes **55.6225 micro metre decrease** in roughness."
      ]
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      "source": [
        "### Now let's eliminate `wall thickness`, `infill density` and `infill pattern` and build the model to see if there's any improvement."
      ]
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          "height": 270
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          "data": {
            "text/plain": [
              "   layer_height  wall_thickness  infill_density  infill_pattern  \\\n",
              "0          0.02               8              90               0   \n",
              "1          0.02               7              90               1   \n",
              "2          0.02               1              80               0   \n",
              "3          0.02               4              70               1   \n",
              "4          0.02               6              90               0   \n",
              "\n",
              "   nozzle_temperature  bed_temperature  print_speed  material  fan_speed  \n",
              "0                 220               60           40         0          0  \n",
              "1                 225               65           40         0         25  \n",
              "2                 230               70           40         0         50  \n",
              "3                 240               75           40         0         75  \n",
              "4                 250               80           40         0        100  "
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
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              "          dataTable['output_type'] = 'display_data';\n",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "#check X\n",
        "X.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "execution": {
          "iopub.execute_input": "2022-07-07T12:50:37.858777Z",
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          "status": "completed"
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        "id": "90ce523f"
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      "outputs": [],
      "source": [
        "X = X.drop(['wall_thickness','infill_density','infill_pattern'], axis = 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 26,
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          "status": "completed"
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        "id": "cac01282",
        "outputId": "e7b8ef36-a074-4f0a-fa41-35fcc2e8a9c1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
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      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   layer_height  nozzle_temperature  bed_temperature  print_speed  material  \\\n",
              "0          0.02                 220               60           40         0   \n",
              "1          0.02                 225               65           40         0   \n",
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              "3          0.02                 240               75           40         0   \n",
              "4          0.02                 250               80           40         0   \n",
              "\n",
              "   fan_speed  \n",
              "0          0  \n",
              "1         25  \n",
              "2         50  \n",
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              "4        100  "
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              "                                                     [key], {});\n",
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              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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        "X.head()"
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    {
      "cell_type": "code",
      "execution_count": 27,
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        "id": "6a0a79f2",
        "outputId": "c68c4b0c-f027-4eaf-9f5e-8cd587033a76",
        "colab": {
          "base_uri": "https://localhost:8080/"
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:              roughness   R-squared:                       0.872\n",
            "Model:                            OLS   Adj. R-squared:                  0.857\n",
            "Method:                 Least Squares   F-statistic:                     59.78\n",
            "Date:                Mon, 14 Nov 2022   Prob (F-statistic):           1.67e-18\n",
            "Time:                        16:08:26   Log-Likelihood:                -248.88\n",
            "No. Observations:                  50   AIC:                             509.8\n",
            "Df Residuals:                      44   BIC:                             521.2\n",
            "Df Model:                           5                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "======================================================================================\n",
            "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
            "--------------------------------------------------------------------------------------\n",
            "const                 -0.9307      0.151     -6.172      0.000      -1.235      -0.627\n",
            "layer_height        1246.5353     83.178     14.986      0.000    1078.901    1414.169\n",
            "nozzle_temperature    14.7774      2.398      6.163      0.000       9.945      19.610\n",
            "bed_temperature      -54.3045      8.815     -6.160      0.000     -72.070     -36.539\n",
            "print_speed            0.5538      0.180      3.070      0.004       0.190       0.917\n",
            "material             294.1610     56.159      5.238      0.000     180.981     407.341\n",
            "fan_speed              7.6993      1.177      6.542      0.000       5.328      10.071\n",
            "==============================================================================\n",
            "Omnibus:                        0.850   Durbin-Watson:                   1.367\n",
            "Prob(Omnibus):                  0.654   Jarque-Bera (JB):                0.720\n",
            "Skew:                           0.285   Prob(JB):                        0.698\n",
            "Kurtosis:                       2.857   Cond. No.                     3.59e+18\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
            "[2] The smallest eigenvalue is 2.37e-31. This might indicate that there are\n",
            "strong multicollinearity problems or that the design matrix is singular.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
            "  x = pd.concat(x[::order], 1)\n"
          ]
        }
      ],
      "source": [
        "#calling the linear regression function\n",
        "linear_Regression(X,y)"
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    },
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        "## Inference\n",
        "1. The **R-squared** value decreases to **87.2%** which is **not much decrease**.\n",
        "2. The **p-values** of all the **considered features** do play an **important role** in predicting the label.\n",
        "3. We can **improve** the **model** further by considering **interaction terms** based on the **correlation heatmap**.\n",
        "4. The various interaction terms are as follows\n",
        "    - Material and nozzle temperature (-0.78)\n",
        "    - Bed temperature and nozzle temperature (0.6)\n",
        "    - Fan speed and nozzle temperatue (0.6)\n",
        "    - Fan speed and bed temperature (1)"
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              "   layer_height  nozzle_temperature  bed_temperature  print_speed  material  \\\n",
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        "#get the interaction terms by multiplying values\n",
        "\n",
        "inter_mn = X['material']*X['nozzle_temperature']\n",
        "inter_bn = X['bed_temperature']*X['nozzle_temperature']\n",
        "inter_fn = X['fan_speed']*X['nozzle_temperature']\n",
        "inter_fb = X['fan_speed']*X['bed_temperature']"
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            "text/plain": [
              "   layer_height  nozzle_temperature  bed_temperature  print_speed  material  \\\n",
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              "7         50         210        14700        10500         3500  \n",
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              "      <th></th>\n",
              "      <th>layer_height</th>\n",
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              "      <th>bed_temperature</th>\n",
              "      <th>print_speed</th>\n",
              "      <th>material</th>\n",
              "      <th>fan_speed</th>\n",
              "      <th>interct_mn</th>\n",
              "      <th>interact_bn</th>\n",
              "      <th>interact_fn</th>\n",
              "      <th>interact_fb</th>\n",
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              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.02</td>\n",
              "      <td>220</td>\n",
              "      <td>60</td>\n",
              "      <td>40</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>13200</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02</td>\n",
              "      <td>225</td>\n",
              "      <td>65</td>\n",
              "      <td>40</td>\n",
              "      <td>0</td>\n",
              "      <td>25</td>\n",
              "      <td>0</td>\n",
              "      <td>14625</td>\n",
              "      <td>5625</td>\n",
              "      <td>1625</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02</td>\n",
              "      <td>230</td>\n",
              "      <td>70</td>\n",
              "      <td>40</td>\n",
              "      <td>0</td>\n",
              "      <td>50</td>\n",
              "      <td>0</td>\n",
              "      <td>16100</td>\n",
              "      <td>11500</td>\n",
              "      <td>3500</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.02</td>\n",
              "      <td>240</td>\n",
              "      <td>75</td>\n",
              "      <td>40</td>\n",
              "      <td>0</td>\n",
              "      <td>75</td>\n",
              "      <td>0</td>\n",
              "      <td>18000</td>\n",
              "      <td>18000</td>\n",
              "      <td>5625</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.02</td>\n",
              "      <td>250</td>\n",
              "      <td>80</td>\n",
              "      <td>40</td>\n",
              "      <td>0</td>\n",
              "      <td>100</td>\n",
              "      <td>0</td>\n",
              "      <td>20000</td>\n",
              "      <td>25000</td>\n",
              "      <td>8000</td>\n",
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              "      <td>0.02</td>\n",
              "      <td>200</td>\n",
              "      <td>60</td>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>200</td>\n",
              "      <td>12000</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.02</td>\n",
              "      <td>205</td>\n",
              "      <td>65</td>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>25</td>\n",
              "      <td>205</td>\n",
              "      <td>13325</td>\n",
              "      <td>5125</td>\n",
              "      <td>1625</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.02</td>\n",
              "      <td>210</td>\n",
              "      <td>70</td>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>50</td>\n",
              "      <td>210</td>\n",
              "      <td>14700</td>\n",
              "      <td>10500</td>\n",
              "      <td>3500</td>\n",
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              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>0.02</td>\n",
              "      <td>215</td>\n",
              "      <td>75</td>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>75</td>\n",
              "      <td>215</td>\n",
              "      <td>16125</td>\n",
              "      <td>16125</td>\n",
              "      <td>5625</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>0.02</td>\n",
              "      <td>220</td>\n",
              "      <td>80</td>\n",
              "      <td>40</td>\n",
              "      <td>1</td>\n",
              "      <td>100</td>\n",
              "      <td>220</td>\n",
              "      <td>17600</td>\n",
              "      <td>22000</td>\n",
              "      <td>8000</td>\n",
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          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "#adding these interaction terms to dataset using .concat() function of pandas\n",
        "#we will call this dataset as interaction\n",
        "\n",
        "interaction = pd.concat([X,inter_mn,inter_bn,inter_fn,inter_fb], axis = 1)\n",
        "\n",
        "#chenge column names of this interaction terms\n",
        "interaction = interaction.rename(columns = {0:'interct_mn', 1:'interact_bn', 2:'interact_fn',\n",
        "                             3:'interact_fb'})\n",
        "\n",
        "interaction.head(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "execution": {
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          "base_uri": "https://localhost:8080/"
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      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:              roughness   R-squared:                       0.925\n",
            "Model:                            OLS   Adj. R-squared:                  0.910\n",
            "Method:                 Least Squares   F-statistic:                     63.22\n",
            "Date:                Mon, 14 Nov 2022   Prob (F-statistic):           1.31e-20\n",
            "Time:                        16:08:26   Log-Likelihood:                -235.45\n",
            "No. Observations:                  50   AIC:                             488.9\n",
            "Df Residuals:                      41   BIC:                             506.1\n",
            "Df Model:                           8                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "======================================================================================\n",
            "                         coef    std err          t      P>|t|      [0.025      0.975]\n",
            "--------------------------------------------------------------------------------------\n",
            "const                 -1.0735      0.923     -1.163      0.252      -2.938       0.791\n",
            "layer_height        1246.5353     65.870     18.924      0.000    1113.508    1379.562\n",
            "nozzle_temperature     0.0050      0.004      1.146      0.259      -0.004       0.014\n",
            "bed_temperature      -57.8032     50.004     -1.156      0.254    -158.788      43.182\n",
            "print_speed            0.5538      0.143      3.877      0.000       0.265       0.842\n",
            "material            5516.1791   2836.453      1.945      0.059    -212.153    1.12e+04\n",
            "fan_speed             33.0427     27.526      1.200      0.237     -22.546      88.632\n",
            "interct_mn           -25.7036     12.956     -1.984      0.054     -51.869       0.462\n",
            "interact_bn            0.2588      0.227      1.138      0.262      -0.201       0.718\n",
            "interact_fn           -0.2032      0.174     -1.169      0.249      -0.554       0.148\n",
            "interact_fb            0.1662      0.138      1.206      0.235      -0.112       0.444\n",
            "==============================================================================\n",
            "Omnibus:                        0.934   Durbin-Watson:                   1.345\n",
            "Prob(Omnibus):                  0.627   Jarque-Bera (JB):                0.333\n",
            "Skew:                           0.132   Prob(JB):                        0.847\n",
            "Kurtosis:                       3.300   Cond. No.                     4.80e+20\n",
            "==============================================================================\n",
            "\n",
            "Notes:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
            "[2] The smallest eigenvalue is 9.58e-32. This might indicate that there are\n",
            "strong multicollinearity problems or that the design matrix is singular.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
            "  x = pd.concat(x[::order], 1)\n"
          ]
        }
      ],
      "source": [
        "# NOw let's fit this model to the linear regression function\n",
        "\n",
        "linear_Regression(interaction,y)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "execution": {
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          "shell.execute_reply.started": "2022-07-07T04:58:59.887863Z"
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        },
        "tags": [],
        "id": "851ff072"
      },
      "source": [
        "## Model Summary\n",
        "- Alright now, we have an increased R-squared of 92.5% or 0.925 which is very high.\n",
        "- We will stop here and declare this model as the most suitable for predicting roughness"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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          "status": "completed"
        },
        "tags": [],
        "id": "ff027989"
      },
      "source": [
        "## Similarly we will fit models for predicting tension strength and elongation as well. I will reduce the explanations here. The procedure is absolutely same starting with all features and then tuning for better results."
      ]
    }
  ]
}