{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[33mDEPRECATION: Python 3.4 support has been deprecated. pip 19.1 will be the last one supporting it. Please upgrade your Python as Python 3.4 won't be maintained after March 2019 (cf PEP 429).\u001b[0m\n", "Requirement already satisfied: statsmodels in /home/megan.owen/.local/lib/python3.4/site-packages (0.9.0)\n", "Requirement already satisfied: patsy in /home/megan.owen/.local/lib/python3.4/site-packages (from statsmodels) (0.5.1)\n", "Requirement already satisfied: six in /usr/local/lib/python3.4/site-packages (from patsy->statsmodels) (1.11.0)\n", "Requirement already satisfied: numpy>=1.4 in /home/megan.owen/.local/lib/python3.4/site-packages (from patsy->statsmodels) (1.16.0)\n" ] } ], "source": [ "# if you need to install the statsmodel library\n", "!pip install --user statsmodels" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# if you need to install scikit-learn\n", "!pip install --user sklearn" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 6 - Review of linear regression\n", "\n", "A linear relationship between two variables is one in which the scatterplot of them looks roughly like a line. *Linear regression* is a method for modelling how a *dependent variable* linearly depends on one or more *independent variables*. The dependent variable (also called a *response variable* and many other things) is what we are trying to model or predict, and is usually denoted $Y$. The independent variables (also called *explanatory* or *input variables*) are the information we are using to make the predictiong, and are usually denoted $X_1, X_2, ...$.\n", "\n", "The linear relationship is: $$Y = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ... + \\beta_n X_n + \\epsilon$$\n", "where $\\epsilon$ represents the error.\n", "\n", "Here, $Y, X_1, X_2, ..., X_n$ are *random variables* which is what mathematical variables that can take different values with different probabilities are called.\n", "\n", "Linear regression finds the coefficients $\\beta_0, \\beta_1, ..., \\beta_n$ so that the sum of the squares of the error term for each data observation is minimized (as small as possible).\n", "\n", "In this lab, we will look at a classic dataset used for studying regression containing data about Boston housing prices in the 1970s (?)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "import statsmodels.formula.api as smf\n", "import seaborn as sns\n", "import numpy as np\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the dataset from the sci-kit learn package." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from sklearn.datasets import load_boston\n", "boston_dict = load_boston()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the variable `boston_dict`:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'DESCR': \".. _boston_dataset:\\n\\nBoston house prices dataset\\n---------------------------\\n\\n**Data Set Characteristics:** \\n\\n :Number of Instances: 506 \\n\\n :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\\n\\n :Attribute Information (in order):\\n - CRIM per capita crime rate by town\\n - ZN proportion of residential land zoned for lots over 25,000 sq.ft.\\n - INDUS proportion of non-retail business acres per town\\n - CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\\n - NOX nitric oxides concentration (parts per 10 million)\\n - RM average number of rooms per dwelling\\n - AGE proportion of owner-occupied units built prior to 1940\\n - DIS weighted distances to five Boston employment centres\\n - RAD index of accessibility to radial highways\\n - TAX full-value property-tax rate per $10,000\\n - PTRATIO pupil-teacher ratio by town\\n - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\\n - LSTAT % lower status of the population\\n - MEDV Median value of owner-occupied homes in $1000's\\n\\n :Missing Attribute Values: None\\n\\n :Creator: Harrison, D. and Rubinfeld, D.L.\\n\\nThis is a copy of UCI ML housing dataset.\\nhttps://archive.ics.uci.edu/ml/machine-learning-databases/housing/\\n\\n\\nThis dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\\n\\nThe Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\\nprices and the demand for clean air', J. Environ. Economics & Management,\\nvol.5, 81-102, 1978. Used in Belsley, Kuh & Welsch, 'Regression diagnostics\\n...', Wiley, 1980. N.B. Various transformations are used in the table on\\npages 244-261 of the latter.\\n\\nThe Boston house-price data has been used in many machine learning papers that address regression\\nproblems. \\n \\n.. topic:: References\\n\\n - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\\n - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. 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] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "boston = pd.DataFrame(boston_dict .data, columns = boston_dict.feature_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display the new dataframe. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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506 rows × 13 columns

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" ], "text/plain": [ " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", "0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n", "1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n", "2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n", "3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n", "4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n", "5 0.02985 0.0 2.18 0.0 0.458 6.430 58.7 6.0622 3.0 222.0 \n", "6 0.08829 12.5 7.87 0.0 0.524 6.012 66.6 5.5605 5.0 311.0 \n", "7 0.14455 12.5 7.87 0.0 0.524 6.172 96.1 5.9505 5.0 311.0 \n", "8 0.21124 12.5 7.87 0.0 0.524 5.631 100.0 6.0821 5.0 311.0 \n", "9 0.17004 12.5 7.87 0.0 0.524 6.004 85.9 6.5921 5.0 311.0 \n", "10 0.22489 12.5 7.87 0.0 0.524 6.377 94.3 6.3467 5.0 311.0 \n", "11 0.11747 12.5 7.87 0.0 0.524 6.009 82.9 6.2267 5.0 311.0 \n", "12 0.09378 12.5 7.87 0.0 0.524 5.889 39.0 5.4509 5.0 311.0 \n", "13 0.62976 0.0 8.14 0.0 0.538 5.949 61.8 4.7075 4.0 307.0 \n", "14 0.63796 0.0 8.14 0.0 0.538 6.096 84.5 4.4619 4.0 307.0 \n", "15 0.62739 0.0 8.14 0.0 0.538 5.834 56.5 4.4986 4.0 307.0 \n", "16 1.05393 0.0 8.14 0.0 0.538 5.935 29.3 4.4986 4.0 307.0 \n", "17 0.78420 0.0 8.14 0.0 0.538 5.990 81.7 4.2579 4.0 307.0 \n", "18 0.80271 0.0 8.14 0.0 0.538 5.456 36.6 3.7965 4.0 307.0 \n", "19 0.72580 0.0 8.14 0.0 0.538 5.727 69.5 3.7965 4.0 307.0 \n", "20 1.25179 0.0 8.14 0.0 0.538 5.570 98.1 3.7979 4.0 307.0 \n", "21 0.85204 0.0 8.14 0.0 0.538 5.965 89.2 4.0123 4.0 307.0 \n", "22 1.23247 0.0 8.14 0.0 0.538 6.142 91.7 3.9769 4.0 307.0 \n", "23 0.98843 0.0 8.14 0.0 0.538 5.813 100.0 4.0952 4.0 307.0 \n", "24 0.75026 0.0 8.14 0.0 0.538 5.924 94.1 4.3996 4.0 307.0 \n", "25 0.84054 0.0 8.14 0.0 0.538 5.599 85.7 4.4546 4.0 307.0 \n", "26 0.67191 0.0 8.14 0.0 0.538 5.813 90.3 4.6820 4.0 307.0 \n", "27 0.95577 0.0 8.14 0.0 0.538 6.047 88.8 4.4534 4.0 307.0 \n", "28 0.77299 0.0 8.14 0.0 0.538 6.495 94.4 4.4547 4.0 307.0 \n", "29 1.00245 0.0 8.14 0.0 0.538 6.674 87.3 4.2390 4.0 307.0 \n", ".. ... ... ... ... ... ... ... ... ... ... \n", "476 4.87141 0.0 18.10 0.0 0.614 6.484 93.6 2.3053 24.0 666.0 \n", "477 15.02340 0.0 18.10 0.0 0.614 5.304 97.3 2.1007 24.0 666.0 \n", "478 10.23300 0.0 18.10 0.0 0.614 6.185 96.7 2.1705 24.0 666.0 \n", "479 14.33370 0.0 18.10 0.0 0.614 6.229 88.0 1.9512 24.0 666.0 \n", "480 5.82401 0.0 18.10 0.0 0.532 6.242 64.7 3.4242 24.0 666.0 \n", "481 5.70818 0.0 18.10 0.0 0.532 6.750 74.9 3.3317 24.0 666.0 \n", "482 5.73116 0.0 18.10 0.0 0.532 7.061 77.0 3.4106 24.0 666.0 \n", "483 2.81838 0.0 18.10 0.0 0.532 5.762 40.3 4.0983 24.0 666.0 \n", "484 2.37857 0.0 18.10 0.0 0.583 5.871 41.9 3.7240 24.0 666.0 \n", "485 3.67367 0.0 18.10 0.0 0.583 6.312 51.9 3.9917 24.0 666.0 \n", "486 5.69175 0.0 18.10 0.0 0.583 6.114 79.8 3.5459 24.0 666.0 \n", "487 4.83567 0.0 18.10 0.0 0.583 5.905 53.2 3.1523 24.0 666.0 \n", "488 0.15086 0.0 27.74 0.0 0.609 5.454 92.7 1.8209 4.0 711.0 \n", "489 0.18337 0.0 27.74 0.0 0.609 5.414 98.3 1.7554 4.0 711.0 \n", "490 0.20746 0.0 27.74 0.0 0.609 5.093 98.0 1.8226 4.0 711.0 \n", "491 0.10574 0.0 27.74 0.0 0.609 5.983 98.8 1.8681 4.0 711.0 \n", "492 0.11132 0.0 27.74 0.0 0.609 5.983 83.5 2.1099 4.0 711.0 \n", "493 0.17331 0.0 9.69 0.0 0.585 5.707 54.0 2.3817 6.0 391.0 \n", "494 0.27957 0.0 9.69 0.0 0.585 5.926 42.6 2.3817 6.0 391.0 \n", "495 0.17899 0.0 9.69 0.0 0.585 5.670 28.8 2.7986 6.0 391.0 \n", "496 0.28960 0.0 9.69 0.0 0.585 5.390 72.9 2.7986 6.0 391.0 \n", "497 0.26838 0.0 9.69 0.0 0.585 5.794 70.6 2.8927 6.0 391.0 \n", "498 0.23912 0.0 9.69 0.0 0.585 6.019 65.3 2.4091 6.0 391.0 \n", "499 0.17783 0.0 9.69 0.0 0.585 5.569 73.5 2.3999 6.0 391.0 \n", "500 0.22438 0.0 9.69 0.0 0.585 6.027 79.7 2.4982 6.0 391.0 \n", "501 0.06263 0.0 11.93 0.0 0.573 6.593 69.1 2.4786 1.0 273.0 \n", "502 0.04527 0.0 11.93 0.0 0.573 6.120 76.7 2.2875 1.0 273.0 \n", "503 0.06076 0.0 11.93 0.0 0.573 6.976 91.0 2.1675 1.0 273.0 \n", "504 0.10959 0.0 11.93 0.0 0.573 6.794 89.3 2.3889 1.0 273.0 \n", "505 0.04741 0.0 11.93 0.0 0.573 6.030 80.8 2.5050 1.0 273.0 \n", "\n", " PTRATIO B LSTAT \n", "0 15.3 396.90 4.98 \n", "1 17.8 396.90 9.14 \n", "2 17.8 392.83 4.03 \n", "3 18.7 394.63 2.94 \n", "4 18.7 396.90 5.33 \n", "5 18.7 394.12 5.21 \n", "6 15.2 395.60 12.43 \n", "7 15.2 396.90 19.15 \n", "8 15.2 386.63 29.93 \n", "9 15.2 386.71 17.10 \n", "10 15.2 392.52 20.45 \n", "11 15.2 396.90 13.27 \n", "12 15.2 390.50 15.71 \n", "13 21.0 396.90 8.26 \n", "14 21.0 380.02 10.26 \n", "15 21.0 395.62 8.47 \n", "16 21.0 386.85 6.58 \n", "17 21.0 386.75 14.67 \n", "18 21.0 288.99 11.69 \n", "19 21.0 390.95 11.28 \n", "20 21.0 376.57 21.02 \n", "21 21.0 392.53 13.83 \n", "22 21.0 396.90 18.72 \n", "23 21.0 394.54 19.88 \n", "24 21.0 394.33 16.30 \n", "25 21.0 303.42 16.51 \n", "26 21.0 376.88 14.81 \n", "27 21.0 306.38 17.28 \n", "28 21.0 387.94 12.80 \n", "29 21.0 380.23 11.98 \n", ".. ... ... ... \n", "476 20.2 396.21 18.68 \n", "477 20.2 349.48 24.91 \n", "478 20.2 379.70 18.03 \n", "479 20.2 383.32 13.11 \n", "480 20.2 396.90 10.74 \n", "481 20.2 393.07 7.74 \n", "482 20.2 395.28 7.01 \n", "483 20.2 392.92 10.42 \n", "484 20.2 370.73 13.34 \n", "485 20.2 388.62 10.58 \n", "486 20.2 392.68 14.98 \n", "487 20.2 388.22 11.45 \n", "488 20.1 395.09 18.06 \n", "489 20.1 344.05 23.97 \n", "490 20.1 318.43 29.68 \n", "491 20.1 390.11 18.07 \n", "492 20.1 396.90 13.35 \n", "493 19.2 396.90 12.01 \n", "494 19.2 396.90 13.59 \n", "495 19.2 393.29 17.60 \n", "496 19.2 396.90 21.14 \n", "497 19.2 396.90 14.10 \n", "498 19.2 396.90 12.92 \n", "499 19.2 395.77 15.10 \n", "500 19.2 396.90 14.33 \n", "501 21.0 391.99 9.67 \n", "502 21.0 396.90 9.08 \n", "503 21.0 396.90 5.64 \n", "504 21.0 393.45 6.48 \n", "505 21.0 396.90 7.88 \n", "\n", "[506 rows x 13 columns]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each column in an independent variable. (The columns were described when we did `print(boston_dict.DESCR)`). The dependent variable that we want to predict is linked to the key called `target`, so we will add it to our dataframe as a column." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "boston[\"price\"] = boston_dict.target " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the column was added correctly." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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CRIMZNINDUSCHASNOXRMAGEDISRADTAXPTRATIOBLSTATprice
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" ], "text/plain": [ " CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX \\\n", "0 0.00632 18.0 2.31 0.0 0.538 6.575 65.2 4.0900 1.0 296.0 \n", "1 0.02731 0.0 7.07 0.0 0.469 6.421 78.9 4.9671 2.0 242.0 \n", "2 0.02729 0.0 7.07 0.0 0.469 7.185 61.1 4.9671 2.0 242.0 \n", "3 0.03237 0.0 2.18 0.0 0.458 6.998 45.8 6.0622 3.0 222.0 \n", "4 0.06905 0.0 2.18 0.0 0.458 7.147 54.2 6.0622 3.0 222.0 \n", "\n", " PTRATIO B LSTAT price \n", "0 15.3 396.90 4.98 24.0 \n", "1 17.8 396.90 9.14 21.6 \n", "2 17.8 392.83 4.03 34.7 \n", "3 18.7 394.63 2.94 33.4 \n", "4 18.7 396.90 5.33 36.2 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boston.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at how a few of the variables relate to the median housing price.\n", "\n", "Let's see how the per capita crime rate per town (column `CRIM`) relates to median housing price (column `price` which is in $1000s) by plotting a scatter plot of the two variables. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "boston.plot.scatter(x = \"CRIM\", y = \"price\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
Hint:\n", " df.plot.scatter(x = \"x_column_name\", y = \"y_column_name\")\n", "
\n", "\n", "Make a scatter plot of the relationship between the average number of rooms per dwelling (column `RM`) and the price." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "boston.plot.scatter(x = \"RM\", y = \"price\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally plot the relationship between the pupil-teacher ratio per town (column `PTRATIO`) and the price." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "boston.plot.scatter(x = \"PTRATIO\", y = \"price\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of the three variable, `CRIM`, `RM`, and `PTRATIO`, which seems to have the most linear relationship with `price`? Which of the relationships were positive (had a positive slope) and which were negative?\n", "\n", "Let's perform linear regression using `RM` (average number of rooms) as the independent variable. We want to predict `price` our dependent variable." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: price R-squared: 0.484
Model: OLS Adj. R-squared: 0.483
Method: Least Squares F-statistic: 471.8
Date: Tue, 17 Sep 2019 Prob (F-statistic): 2.49e-74
Time: 17:41:10 Log-Likelihood: -1673.1
No. Observations: 506 AIC: 3350.
Df Residuals: 504 BIC: 3359.
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept -34.6706 2.650 -13.084 0.000 -39.877 -29.465
RM 9.1021 0.419 21.722 0.000 8.279 9.925
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 102.585 Durbin-Watson: 0.684
Prob(Omnibus): 0.000 Jarque-Bera (JB): 612.449
Skew: 0.726 Prob(JB): 1.02e-133
Kurtosis: 8.190 Cond. No. 58.4


Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: price R-squared: 0.484\n", "Model: OLS Adj. R-squared: 0.483\n", "Method: Least Squares F-statistic: 471.8\n", "Date: Tue, 17 Sep 2019 Prob (F-statistic): 2.49e-74\n", "Time: 17:41:10 Log-Likelihood: -1673.1\n", "No. Observations: 506 AIC: 3350.\n", "Df Residuals: 504 BIC: 3359.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "Intercept -34.6706 2.650 -13.084 0.000 -39.877 -29.465\n", "RM 9.1021 0.419 21.722 0.000 8.279 9.925\n", "==============================================================================\n", "Omnibus: 102.585 Durbin-Watson: 0.684\n", "Prob(Omnibus): 0.000 Jarque-Bera (JB): 612.449\n", "Skew: 0.726 Prob(JB): 1.02e-133\n", "Kurtosis: 8.190 Cond. No. 58.4\n", "==============================================================================\n", "\n", "Warnings:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "\"\"\"" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lm = smf.ols('price ~ RM',boston).fit()\n", "lm.summary()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's the equation of our linear model?\n", "\n", "We can visualize the line using Seaborn:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.regplot(y=\"price\", x=\"RM\", data=boston, fit_reg = True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *residuals* are the difference between the actual value of price and the value predicted by the regression line, for each row of the data." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 -1.175746\n", "1 -2.174021\n", "2 3.971968\n", "3 4.374062\n", "4 5.817848\n", "5 4.844060\n", "6 2.848742\n", "7 5.592404\n", "8 -0.083355\n", "9 -1.078442\n", "10 -8.373528\n", "11 -1.123952\n", "12 2.768301\n", "13 0.922174\n", "14 -2.615836\n", "15 1.468917\n", "16 3.749604\n", "17 -2.351012\n", "18 5.209514\n", "19 0.742843\n", "20 -2.428126\n", "21 -0.023459\n", "22 -6.034533\n", "23 -3.739939\n", "24 -3.650273\n", "25 -2.392087\n", "26 -1.639939\n", "27 -5.569832\n", "28 -6.047577\n", "29 -5.076855\n", " ... \n", "476 -7.647454\n", "477 -1.606965\n", "478 -7.025923\n", "479 -0.626416\n", "480 0.855257\n", "481 -3.068615\n", "482 -4.599371\n", "483 4.024269\n", "484 1.832139\n", "485 -1.581891\n", "486 -1.879674\n", "487 1.522667\n", "488 0.227718\n", "489 -7.608197\n", "490 -3.586420\n", "491 -6.187297\n", "492 0.312703\n", "493 4.524885\n", "494 5.231523\n", "495 6.161663\n", "496 5.310253\n", "497 0.233001\n", "498 1.085027\n", "499 1.480976\n", "500 -3.387790\n", "501 -2.939584\n", "502 -0.434286\n", "503 -4.925691\n", "504 -5.169108\n", "505 -8.315096\n", "Length: 506, dtype: float64" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lm.resid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot a histogram of the residuals. If the linear model is a good fit, the histogram should look like a normal distribution. Does it?" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lm.resid.hist(bins = 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To better understand the relationship between the actual prices and the predicted or *fitted* values, we can plot a scatterplot of the two. To get the fitted values, type `lm.fittedvalues`. Try it below." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0 25.175746\n", "1 23.774021\n", "2 30.728032\n", "3 29.025938\n", "4 30.382152\n", "5 23.855940\n", "6 20.051258\n", "7 21.507596\n", "8 16.583355\n", "9 19.978442\n", "10 23.373528\n", "11 20.023952\n", "12 18.931699\n", "13 19.477826\n", "14 20.815836\n", "15 18.431083\n", "16 19.350396\n", "17 19.851012\n", "18 14.990486\n", "19 17.457157\n", "20 16.028126\n", "21 19.623459\n", "22 21.234533\n", "23 18.239939\n", "24 19.250273\n", "25 16.292087\n", "26 18.239939\n", "27 20.369832\n", "28 24.447577\n", "29 26.076855\n", " ... \n", "476 24.347454\n", "477 13.606965\n", "478 21.625923\n", "479 22.026416\n", "480 22.144743\n", "481 26.768615\n", "482 29.599371\n", "483 17.775731\n", "484 18.767861\n", "485 22.781891\n", "486 20.979674\n", "487 19.077333\n", "488 14.972282\n", "489 14.608197\n", "490 11.686420\n", "491 19.787297\n", "492 19.787297\n", "493 17.275115\n", "494 19.268477\n", "495 16.938337\n", "496 14.389747\n", "497 18.066999\n", "498 20.114973\n", "499 16.019024\n", "500 20.187790\n", "501 25.339584\n", "502 21.034286\n", "503 28.825691\n", "504 27.169108\n", "505 20.215096\n", "Length: 506, dtype: float64" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lm.fittedvalues" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot a scatter plot of with the price as the x variable and the fitted values as the y variable. The code is slightly different since the fitted values aren't part of the `boston` " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5,1,'Prices vs Predicted Prices')" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(boston['price'], lm.fittedvalues)\n", "plt.xlabel(\"Prices ($1000s)\")\n", "plt.ylabel(\"Predicted prices ($1000s)\")\n", "plt.title(\"Prices vs Predicted Prices\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If all the prices were predicted correctly, what would this plot have looked like? By noticing where this plot is least like a plot with perfectly predicted prices, we can see where our linear model fails (makes bad predictions). Where do you notice errors in the prediction?\n", "\n", "The most expensive houses are predicted incorrectly. This is known as a *ceiling effect*, where the independent variable no longer has an effect on the dependent variable.\n", "\n", "Find the linear model showing how price depends on `PTRATIO`, the pupil-teacher ratio by town:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the fit of your model by looking at the histogram of the residuals and the scatter plot of the predicted prices vs. the actual prices." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do you think this linear model is a good predictor of prices?\n", "\n", "Let's try making a linear regression model with three independent variables:\n", "\n", "- `CRIM` (per capita crime rate by town)\n", "- `RM` (average number of rooms per dwelling)\n", "- `PTRATIO` (pupil-teacher ratio by town)\n", "\n", "The code will be similar to above, but the formula is `price ~ CRIM + RM + PTRATIO`" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the fit of your model by plotting the histogram of the residuals and the scatter plot of the predicted prices vs. the actual prices." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How did this linear model perform?" ] } ], "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": "3.4.8" } }, "nbformat": 4, "nbformat_minor": 2 }