{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [], "authorship_tag": "ABX9TyNZ7N0RTFe31w78tPkFR21T", "include_colab_link": true }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "source": [ "# Regression" ], "metadata": { "id": "FY-rJNIGJc8a" } }, { "cell_type": "markdown", "source": [ "## Introduction\n", "Regression is a huge topic but we'll try to cover the basics here with the idea that you will use regression often in business settings and that all the details will not be needed.\n", "\n", "We will mostly focus on the Method of Least Squares here. The idea is to make a prediction and to minimize the error in that prediction by minimizing the sum of the squares of that error:\n", "\n", "$$\n", "SSE = \\sum_{i=1}^n\\left(y_i-\\hat {y_i}\\right)^2\n", "$$\n", "\n" ], "metadata": { "id": "HsaTJ4tEJfSD" } }, { "cell_type": "markdown", "source": [ "## Derivation\n", "\n", "To derive the linear regression formula, we assume that $\\hat y$ is linear,\n", "$$\n", "\\hat y = \\beta_0 +\\beta_1 x\n", "$$\n", "\n", "Then we plug this into the sum of squares error and take the partial derivatives with respect to $\\beta_0$ and $\\beta_1$. To minimize we then set those derivatives to zero and solve the system.\n", "\n", "$$\n", "\\nabla SSE(\\beta_0,\\beta_1) =\n", "\\left(\n", "\\sum -2(y_i-\\beta_0 - \\beta_1 x_i)\n", ",\n", "\\sum -2(y_i-\\beta_0 - \\beta_1 x_i)x_i\n", "\\right)\n", "$$\n", "\n", "Setting each of these to zero and simplifying the summations, we arrive at\n", "$$\n", "\\sum y_i = n\\beta_0 +\\beta_1\\sum x_i\n", "$$\n", "$$\n", "\\sum x_iy_i = \\beta_0\\sum x_i +\\beta_1\\sum x^2_i\n", "$$\n", "\n", "Eliminating and solving, we see that\n", "$$\n", "\\beta_1 = \\frac{n\\sum x_iy_i - \\sum x_i \\sum y_i}{n\\sum x_i^2 - (\\sum x_i)^2}\n", "$$\n", "\n", "and\n", "$$\n", "\\beta_0 = \\frac{\\sum y_i - \\beta_1\\sum x_i}n\n", "$$\n", "\n", "Some times these are written using the bar notation, $\\bar x = \\frac{\\sum x_i}n$\n", "\n", "$$\n", "\\beta_0 = \\bar y - \\beta_1\\bar x\n", "$$\n", "\n", "$$\n", "\\beta_1 = \\frac{\\bar{xy}-\\bar x\\bar y}{\\bar{x^2} - \\left(\\bar x\\right)^2}\n", "$$" ], "metadata": { "id": "5mAexp8MKjiA" } }, { "cell_type": "markdown", "source": [ "### Example\n", "\n", "Given the points $(0,4),(3,6),(7,8),(2,5)$, find the linear regression." ], "metadata": { "id": "O90_WEdGE92e" } }, { "cell_type": "code", "source": [ "x = [0,3,7,2]\n", "y = [4,6,8,5]\n", "n = len(x)\n", "\n", "meanx = sum(x)/n\n", "meany = sum(y)/n\n", "sumsquarex = 0\n", "for i in range(n):\n", " sumsquarex += x[i]**2\n", "sumsquarex /= n\n", "\n", "xy = 0\n", "for i in range(n):\n", " xy +=x[i]*y[i]\n", "xy/=n\n" ], "metadata": { "id": "YCa57uBTFPP2" }, "execution_count": 22, "outputs": [] }, { "cell_type": "code", "source": [ "b1 = (xy - meanx*meany)/(sumsquarex-meanx**2)\n", "b1" ], "metadata": { "id": "l7Q091EVGDnk", "outputId": "8580b3a5-ca5f-4172-f560-1463ffd352e2", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 23, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "0.5769230769230769" ] }, "metadata": {}, "execution_count": 23 } ] }, { "cell_type": "code", "source": [ "b0 = meany - b1*meanx\n", "b0" ], "metadata": { "id": "1c55oAKwGl9j", "outputId": "660f56cb-292d-4ce7-8c5a-3adee77f073e", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 24, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "4.019230769230769" ] }, "metadata": {}, "execution_count": 24 } ] }, { "cell_type": "code", "source": [ "def line(x):\n", " return b1*x+b0\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "xs = np.linspace(0,8,100)\n", "ys = line(xs)\n", "\n", "plt.plot(xs,ys)\n", "plt.scatter(x,y)" ], "metadata": { "id": "xMPH5zhPGub8", "outputId": "c53018db-21a5-4080-b7a3-96aee0ffc622", "colab": { "base_uri": "https://localhost:8080/", "height": 448 } }, "execution_count": 25, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 25 }, { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "Fits the line very well! You should be asking yourself why I didn't use a built-in for this. Well I should. I picked `scipy` for my package as the code is easier to explain than `scikit-learn`." ], "metadata": { "id": "Jc5N_00b-S4p" } }, { "cell_type": "code", "source": [ "from scipy import stats\n", "\n", "stats.linregress(x,y)" ], "metadata": { "id": "YXTBbRuW_s3_", "outputId": "9bc74fd3-d4b7-4554-f679-943a00f941c7", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 26, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "LinregressResult(slope=0.5769230769230769, intercept=4.019230769230769, rvalue=0.9944903161976938, pvalue=0.005509683802306207, stderr=0.04300130725961148, intercept_stderr=0.16929631597749104)" ] }, "metadata": {}, "execution_count": 26 } ] }, { "cell_type": "markdown", "source": [ "We see that the slope $\\beta_1$ and intercept $\\beta_0$ agree with our above calculation." ], "metadata": { "id": "CfwoLn3S_8WV" } }, { "cell_type": "markdown", "source": [ "## $r$ Value\n", "\n", "The $r$ value is an evaluation of the strength of the fit. $r$ is called the correlation coefficient and is calculated as\n", "$$\n", "r_{xy} = \\frac{n\\left(\\bar{xy}-\\bar x\\bar y\\right)}{(n-1)s_xs_y}\n", "$$\n", "\n", "Where $s_x$ is the sample standard deviation $s_x = \\sqrt{\\frac1{n-1}\\sum (x_i-\\bar x)^2}$" ], "metadata": { "id": "4oRoST3vFdH1" } }, { "cell_type": "markdown", "source": [ "Let's repeat our example and compute this. The only new thing required is the sample standard deviations." ], "metadata": { "id": "QOCG58PXFial" } }, { "cell_type": "code", "source": [ "sx = 0\n", "\n", "for i in x:\n", " sx+= (i-meanx)**2\n", "\n", "sx/=len(x)-1\n", "sx = (sx)**(1/2)\n", "\n", "\n", "sy = 0\n", "\n", "for i in y:\n", " sy+= (i-meany)**2\n", "\n", "sy/=len(y)-1\n", "sy = (sy)**(1/2)" ], "metadata": { "id": "NR0HMQieIPVB" }, "execution_count": 27, "outputs": [] }, { "cell_type": "code", "source": [ "r = len(x)*(xy - meanx*meany)/((len(x)-1)*sx*sy)\n", "\n", "r" ], "metadata": { "id": "hRZGeRI6Jzee", "outputId": "fe0cb623-6548-4535-936e-01a24ece6b3a", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 28, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "0.9944903161976939" ] }, "metadata": {}, "execution_count": 28 } ] }, { "cell_type": "markdown", "source": [ "Perhaps a better way to consider the correlation coefficient in the terms of the linear fit is to see it under the regression. The correlation coffiecient can be shown to be\n", "\n", "$$\n", "r^2 = \\frac{SSR}{SST} = \\frac{\\sum(\\hat y_i-\\bar y)^2}{\\sum(y_i-\\bar y)^2}\n", "$$\n", "\n", "So it is giving us a measure of how much the regression varies from the mean compared to the data varying from the mean. Let's compute this with our data just to see that these are equivalent." ], "metadata": { "id": "9RtkWnnYKmDP" } }, { "cell_type": "code", "source": [ "SSR = 0\n", "SST = 0\n", "\n", "for i in x:\n", " SSR += (line(i)-meany)**2\n", "for i in y:\n", " SST += (i-meany)**2\n", "\n", "r = (SSR/SST)**(1/2)\n", "r" ], "metadata": { "id": "wbypaSOvMOhH", "outputId": "97cc527c-a58e-4783-c003-f9df708308ab", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 52, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([1.28388148, 1.28388148, 1.28388148])" ] }, "metadata": {}, "execution_count": 52 } ] }, { "cell_type": "markdown", "source": [ "## Multiple Regression\n", "\n", "For multiple regression, we will ask that there is some linear transformation from $\\vec x$ to $y$. So we want\n", "$$\n", "y = \\beta_1x_1 +\\beta_2x_2 +\\cdots +\\beta_n x_n\n", "$$\n", "\n", "We can accomplish this by considering all the $y$ in a column matrix and all the $x$ in a matrix then\n", "$$\n", "Y = X\\mathbf{\\beta}\n", "$$\n", "\n", "But we want to find the $\\mathbf{\\beta}$ that solve this equation. We assume that $X$ is rank $n$, then $X^TX$ is invertible so\n", "$$\n", "X^TY = X^TX\\beta\n", "$$\n", "so\n", "$$\n", "\\beta = \\left(X^TX\\right)^{-1}X^TY\n", "$$" ], "metadata": { "id": "XCRujLZ6BneJ" } }, { "cell_type": "markdown", "source": [ "### Example\n", "\n", "Let's use the same example from above and compute the linear regression in a multiple regression system. To do this, you add the intercept by creating a column of 1's in the $X$ matrix, `np.ones` is perfect for this. Matrix multiplication is in the `numpy` package with `@` and matrix inverse can be done with `np.linalg.inv`" ], "metadata": { "id": "eVSCP4rBYcAn" } }, { "cell_type": "code", "execution_count": 30, "metadata": { "id": "-HH5pppHJcbJ", "outputId": "07ab2471-e7d0-4a57-eb85-3704ab775318", "colab": { "base_uri": "https://localhost:8080/" } }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[0. 1.]\n", " [3. 1.]\n", " [7. 1.]\n", " [2. 1.]]\n" ] } ], "source": [ "x = np.array([[0,3,7,2],np.ones(4)]).T\n", "y = np.array([4,6,8,5])\n", "\n", "print(x)" ] }, { "cell_type": "code", "source": [ "a,b = np.linalg.inv(x.T@x)@(x.T@y)\n", "print(a,b)" ], "metadata": { "id": "a2Nwmi0KZTpO", "outputId": "291b815c-25f4-4fac-ca6e-e4d4788c2cf8", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 31, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "0.5769230769230764 4.019230769230767\n" ] } ] }, { "cell_type": "markdown", "source": [ "### Example with Categorical Variables\n", "\n", "I am going to add a categorical variable to my baby example and show how we would include that. $(0,4,yes),(3,6,no),(7,8,yes),(2,5,no)$,\n", "\n", "Since my dataset is tiny, I could do it by hand but what fun would that be?" ], "metadata": { "id": "AMb3Q5NDbU8b" } }, { "cell_type": "code", "source": [ "x = np.array([[0,3,7,2],['yes','no','yes','no']]).T\n", "y = np.array([4,6,7,5])\n", "\n", "x" ], "metadata": { "id": "5xgENpLPar2c", "outputId": "bc640820-ac4c-40ec-9c87-603929f9c4c1", "colab": { "base_uri": "https://localhost:8080/" } }, "execution_count": 45, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "array([['0', 'yes'],\n", " ['3', 'no'],\n", " ['7', 'yes'],\n", " ['2', 'no']], dtype='#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: 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LogisticRegression()
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\n" }, "metadata": {} } ] }, { "cell_type": "markdown", "source": [ "There is clearly some weirdness here. Partially this is the lack of data. But you should get the idea on how to fit. The reshaping of the `np.arrays` was annoying but nesseccary to get the fit done.\n", "\n", "I want to repeat the regression with some data I got from wikipedia." ], "metadata": { "id": "FfuNk9ZDIVsg" } }, { "cell_type": "code", "source": [ "x = [ \t0.50, \t0.75, \t1.00, \t1.25, \t1.50, \t1.75, \t1.75, \t2.00, \t2.25, \t2.50, \t2.75, \t3.00, \t3.25, \t3.50, \t4.00, \t4.25, \t4.50, \t4.75, \t5.00, \t5.50]\n", "y = [\t0 ,\t0 ,\t0 ,\t0 ,\t0 ,\t0 ,\t1 ,\t0 ,\t1 ,\t0 ,\t1 ,\t0 ,\t1 ,\t0 ,\t1 ,\t1 ,\t1 ,\t1, \t1, \t1 ]" ], "metadata": { "id": "_uqfOl6iEXtm" }, "execution_count": 42, "outputs": [] }, { "cell_type": "code", "source": [ "x = np.array(x).reshape(20,1)\n", "\n", "logreg = LogisticRegression()\n", "logreg.fit(x, y)\n", "\n", "xs = np.linspace(0,6,100)\n", "xs = xs.reshape(100,1)\n", "ys = logreg.predict_proba(xs)\n", "\n", "plt.plot(xs,ys)\n", "plt.scatter(x,y)" ], "metadata": { "id": "KnsY-vazFJeN", "outputId": "518d152f-e168-456e-bf4e-45591626a026", "colab": { "base_uri": "https://localhost:8080/", "height": 448 } }, "execution_count": 43, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": {}, "execution_count": 43 }, { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": {} } ] }, { "cell_type": "code", "source": [], "metadata": { "id": "-CHPG6BnKI8m" }, "execution_count": 43, "outputs": [] } ] }