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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"from IPython.display import HTML\n",
"from toggle import *\n",
"HTML(add_toggle())\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Introduction\n",
"\n",
"Let's start by looking at a data set to make things concrete.\n",
"\n",
"See\n",
"\n",
"http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2790284/\n",
"\n",
"and the data set\n",
"\n",
"http://lib.stat.cmu.edu/DASL/Datafiles/cigcancerdat.html\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 173,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"from numpy import sqrt\n",
"%matplotlib inline\n",
"df=pd.read_csv(\"/Users/jteitelbaum/Dropbox/CancerData.csv\")\n"
]
},
{
"cell_type": "code",
"execution_count": 174,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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njqnCRsen50l/JvbYAuBNYFHsfi02n3z25DONWAv6Y8AGWEPugzxilQJTgS4vb2GTYqQN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\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1168c6090>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"fig,axes=plt.subplots(nrows=2,ncols=2,figsize=(8,8))\n",
"axes[0,0].scatter(df['Cigarettes'],df['Lung'])\n",
"axes[0,0].set_title('Lung')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes[0,0].set_xticks([0,1500,3000,4500])\n",
"axes[0,0].axis([0,4500,0,30])\n",
"axes[0,0].set_yticks(range(0,40,10))\n",
"\n",
"\n",
"axes[1,0].scatter(df['Cigarettes'],df['Bladder'],color='black')\n",
"axes[1,0].set_title('Bladder')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes[1,0].set_xticks([0,1500,3000,4500])\n",
"axes[1,0].set_yticks(range(0,40,10))\n",
"\n",
"axes[0,1].scatter(df['Cigarettes'],df['Leukemia'],color='green')\n",
"axes[0,1].set_title('Leukemia')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes[0,1].set_xticks([0,1500,3000,4500])\n",
"axes[0,1].set_yticks(range(0,40,10))\n",
"\n",
"axes[1,1].scatter(df['Cigarettes'],df['Kidney'],color='red')\n",
"axes[1,1].set_title('Kidney')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes[1,1].set_xticks([0,1500,3000,4500])\n",
"axes[1,1].set_yticks(range(0,40,10))\n",
"\n",
"fig.suptitle(\"Deaths from Cancer per 100K Population\\n vs \\n Cigarette sales per capita\")\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 175,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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BCV+Aus8CM4suZvRMPjHC5ORuaD2LmOtLUu0Z9dzSCvwDeFt6/XEMV5LUVztM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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116c8cb90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axes=plt.subplots(nrows=1,ncols=1,figsize=(10,6))\n",
"axes.scatter(df['Cigarettes'],df['Lung'])\n",
"axes.set_title('Lung Cancer per 100K Population\\n vs \\n Cigarette Sales per Capita')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes.set_xticks([0,1500,3000,4500])\n",
"axes.axis([0,4500,0,30])\n",
"axes.set_yticks(range(0,40,10))\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"There are 44 data points in the set (each corresponds to a state.)"
]
},
{
"cell_type": "code",
"execution_count": 176,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Cigarettes</th>\n",
" <th>Lung</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 1820</td>\n",
" <td> 17.05</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 3034</td>\n",
" <td> 25.88</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 2582</td>\n",
" <td> 19.80</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 1824</td>\n",
" <td> 15.98</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 2860</td>\n",
" <td> 22.07</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td> 3110</td>\n",
" <td> 22.83</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td> 3360</td>\n",
" <td> 24.55</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td> 4046</td>\n",
" <td> 27.27</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td> 2827</td>\n",
" <td> 23.57</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td> 2010</td>\n",
" <td> 13.58</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Cigarettes Lung\n",
"0 1820 17.05\n",
"1 3034 25.88\n",
"2 2582 19.80\n",
"3 1824 15.98\n",
"4 2860 22.07\n",
"5 3110 22.83\n",
"6 3360 24.55\n",
"7 4046 27.27\n",
"8 2827 23.57\n",
"9 2010 13.58"
]
},
"execution_count": 176,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df[['Cigarettes','Lung']][0:10]\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"The basic problem of simple linear regression is to find the slope $m$ and intercept $b$ so that the equation\n",
"of the line\n",
"$$\n",
"y=mx+b\n",
"$$\n",
"is the *best fit* to the data above. \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"To be specific, we look at the function\n",
"$$\n",
"E(m,b)=\\sum_{i=1}^{N} (y_i-mx_i-b)^2\n",
"$$\n",
"and we want to find $m$ and $b$ so that this is as small as possible. (For our example, $N=44$.)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Calculus"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Although the equation for $E$ looks complicated, it is really a function of two variables and so we can use calculus to find\n",
"the minimum value. We compute:\n",
"$$\n",
"\\frac{\\partial E}{\\partial m}=\\sum_{i=1}^{N} 2(y_i-mx_i-b)x_i\n",
"$$\n",
"and\n",
"$$\n",
"\\frac{\\partial E}{\\partial b}=\\sum_{i=1}^{N} 2(y_i-mx_i-b).\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Remembering that the variables are $m$ and $b$, set these two equations to zero and find the following two equations:\n",
"\n",
"$$\n",
"S_{xy}=S_{xx}m+S_{x}b\n",
"$$\n",
"\n",
"and\n",
"\n",
"$$\n",
"S_{y}=S_{x}m+Nb\n",
"$$\n",
"\n",
"where I've written $S_{x}=\\sum_{i=1}^{N} x_i$, $S_{xy}=\\sum_{i=1}^{N} x_iy_i$, and so on."
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"N= 44 Sx= 109622 Sy= 874.74 Sxx= 286469700 Sxy= 2248867.14\n"
]
}
],
"source": [
"Sxcig=sum(df['Cigarettes'])\n",
"Sycig=sum(df['Lung'])\n",
"Sxycig=sum([df['Cigarettes'][i]*df['Lung'][i] for i in range(len(df['Cigarettes']))])\n",
"Sxxcig=sum([df['Cigarettes'][i]*df['Cigarettes'][i] for i in range(len(df['Cigarettes']))])\n",
"Ncig=len(df['Cigarettes'])\n",
"print 'N=',Ncig,'Sx=',Sxcig,'Sy=',Sycig,'Sxx=',Sxxcig,'Sxy=',Sxycig"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"These are two equations in two unknowns that you can solve \"by hand\" or, for the general solution, you can use\n",
"Cramer's rule. Let\n",
"\n",
"$$\n",
"M=(NS_{yx}-S_{x}S_{y})\n",
"$$\n",
"\n",
"$$\n",
"B=(S_{xx}S_y-S_{yx}S_x)\n",
"$$\n",
"\n",
"$$\n",
"D=(S_{xx}N-S_{x}^2)\n",
"$$\n",
"\n",
"Then \n",
"\n",
"$$\n",
"m=M/D\n",
"$$\n",
"\n",
"and \n",
"\n",
"$$\n",
"b=B/D.\n",
"$$\n"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"m= 0.00520586968046 b= 6.91050349746\n"
]
}
],
"source": [
"Mcig=Ncig*Sxycig-Sxcig*Sycig\n",
"Bcig=Sxxcig*Sycig-Sxycig*Sxcig\n",
"Dcig=Ncig*Sxxcig-Sxcig*Sxcig\n",
"mcig=Mcig/Dcig\n",
"bcig=Bcig/Dcig\n",
"print 'm=',mcig,'b=',bcig"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"We can apply these formula to the lung cancer data and we end up with the values\n",
"\n",
"$$\n",
"m=.0052\n",
"$$\n",
"\n",
"and \n",
"\n",
"$$\n",
"b=6.910\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 166,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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jhylJ4MEk9h2K2s/DHj17robYGyaNeqXILaUoUtKYsSFMuRam3QtN5zKyvVYb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\nSZIkSZLGtv8PSJMeTIaMFlIAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1110701d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axes=plt.subplots(nrows=1,ncols=1,figsize=(10,6))\n",
"axes.scatter(df['Cigarettes'],df['Lung'])\n",
"axes.plot(np.arange(0,4500,1),m*np.arange(0,4500,1)+b*np.ones(len(np.arange(0,4500,1))),color=\"red\",label='Regression Line')\n",
"axes.set_title('Lung Cancer per 100K Population\\n vs \\n Cigarette Sales per Capita')\n",
"#plt.xlabel('Cigarettes Sold per Capita')\n",
"axes.set_xticks([0,1500,3000,4500])\n",
"axes.axis([0,4500,0,30])\n",
"axes.set_yticks(range(0,40,10))\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Often, these calculations are done by software packages. Here is an example."
]
},
{
"cell_type": "code",
"execution_count": 171,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"-------------------------Summary of Regression Analysis-------------------------\n",
"\n",
"Formula: Y ~ <Cigarettes> + <intercept>\n",
"\n",
"Number of Observations: 44\n",
"Number of Degrees of Freedom: 2\n",
"\n",
"R-squared: 0.5059\n",
"Adj R-squared: 0.4941\n",
"\n",
"Rmse: 2.9016\n",
"\n",
"F-stat (1, 42): 42.9946, p-value: 0.0000\n",
"\n",
"Degrees of Freedom: model 1, resid 42\n",
"\n",
"-----------------------Summary of Estimated Coefficients------------------------\n",
" Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n",
"--------------------------------------------------------------------------------\n",
" Cigarettes 0.0052 0.0008 6.56 0.0000 0.0036 0.0068\n",
" intercept 6.9105 2.0258 3.41 0.0014 2.9399 10.8811\n",
"---------------------------------End of Summary---------------------------------\n",
"\n"
]
}
],
"source": [
"model = pd.ols(y=df['Lung'], x=df.ix[:, ['Cigarettes']])\n",
"print model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I'd like to try to explain (most of) the second to the last line of this output."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Linear Algebra\n",
"\n",
"Let's look at the problem from a different point of view. Let's consider three column vectors:\n",
"\n",
"$$\n",
"Y=\\left[\\begin{matrix} y_1 \\cr y_2 \\cr \\vdots \\cr y_N\\end{matrix}\\right],\n",
"X=\\left[\\begin{matrix} x_1 \\cr x_2 \\cr \\vdots \\cr x_N\\end{matrix}\\right],\n",
"E=\\left[\\begin{matrix} 1 \\cr 1 \\cr \\vdots \\cr 1 \\end{matrix}\\right]$$\n",
"\n",
"If things were \"perfect\", meaning that the points all belonged to the line $y=mx+b$, we would have\n",
"\n",
"$$\n",
"Y=mX+bE.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"But, of course, things aren't perfect. There isn't such a pair $(m,b)$. In linear algebra terms, the vector $Y$ **does not lie in the plane spanned by $X$ and $E$ in $\\mathbb{R}^{44}$**\n",
"\n",
"So let's try to find the point in the plane spanned by $E$ and $X$ which is closest to $Y$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"data": {
"image/png": 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XxavA28i1PQGJ/zgGGI+k3wcCKEPtD9aeaIcoaBUDzcLTGy4ibJcBTyACaGdE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MAAAg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H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Boi5SeEQ+RzJ4ovjy8vUUP6IIPi7KUNdsX8G5Mb14F2xXoJgvqly5t9+4QTSTJ5saX7tG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\ngiAIgiAIgiAIgiAIgqhu/D/ykEZMBQCx1QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ca8d210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"#plt.subplots(nrows=1,ncols=1,figsize=(6,10))\n",
"fig=plt.figure(figsize=(10,10))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"X = np.arange(-2, 2, 0.25)\n",
"Y = np.arange(-2, 2, 0.25)\n",
"X, Y = np.meshgrid(X, Y)\n",
"Z=2*Y-X\n",
"t=np.arange(-1,0,.1)\n",
"ax.plot_wireframe(X,Y,Z)\n",
"ax.plot(t,-2*t,6+t,color=\"red\")\n",
"ax.scatter([0,-1],[0,2],[6,5],color=\"red\")\n",
"ax.set_title(\"Closest point lying in a given plane from a point outside the plane\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can use linear algebra to solve the problem of finding the point in the plane $P$ spanned by $X$ and $E$ that is closest to $Y$. \n",
"\n",
"Take the perpendicular projection of the vector $Y$ into the plane spanned by $X$ and $E$. \n",
"\n",
"For that, we can construct an orthonormal basis for the plane $P$ by using the Gram-Schmidt process on the two vectors $E$ and $X$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"First, we normalize $E$ to obtain our first unit vector $\\mathbf{e}=E/\\sqrt{N}$, since $E\\cdot E=N$. \n",
"\n",
"Next, we subtract the projection of $X$ onto the $E$ direction and normalize. \n",
"\n",
"Let $x=X-(X\\cdot \\mathbf{e})\\mathbf{e}$\n",
"and\n",
"\n",
"$$\n",
"\\mathbf{x}=\\frac{x}{\\sqrt{x\\cdot x}}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Then the point we are interested in is\n",
"$$\n",
"\\mathbf{y}=(Y\\cdot\\mathbf{x})\\mathbf{x}+(Y\\cdot\\mathbf{e})\\mathbf{e}\n",
"$$\n",
"\n",
"This point lies in the plane $P$, and $Y-\\mathbf{y}$ is perpendicular to both $E$ and $X$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Let's make a few observations about this. \n",
"\n",
"First of all, $(Y\\cdot\\mathbf{e})\\mathbf{e}=\\overline{y}E$ and $(X\\cdot \\mathbf{e})\\mathbf{e}=\\overline{x}E$ where $\\overline{x}$ and $\\overline{y}$ are the averages (means) of the $x$ and $y$ values respectively.\n",
"\n",
"We can arrange for our data to have $\\overline{x}=0$ and $\\overline{y}=0$ by subtracting $\\overline{x}$ and $\\overline{y}$ each of the points. This amounts to a coordinate change that moves the origin of our coordinate system to $(\\overline{x},\\overline{y})$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"In these coordinates, we get a huge simplification. If both means are zero, we get\n",
"\n",
"$$\n",
"\\mathbf{x}=\\frac{X}{\\sqrt{X\\cdot X}}\n",
"$$\n",
"\n",
"and \n",
"\n",
"$$\n",
"\\mathbf{y}=\\frac{Y\\cdot X}{X\\cdot X}X\n",
"$$\n",
"\n",
"In other words, in these coordinates, $b=0$ and $m=\\frac{Y\\cdot X}{X\\cdot X}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Moving the point $(\\overline{x},\\overline{y})$ to $(0,0)$ we get a line through the origin."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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F7fQiCanqYOhcC6UBaO8HjnYdUHVV2/nPhn8IjfHzuIGO/i0s6L1wztD4PAMGmjaiJ3lJ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\nREREREREREREJAn/H6PuJtO59JasAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ca2f310>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Xnorm=df['Cigarettes']-df['Cigarettes'].mean()\n",
"Ynorm=df['Lung']-df['Lung'].mean()\n",
"plt.scatter(Xnorm,Ynorm)\n",
"m=Xnorm.dot(Ynorm)/Xnorm.dot(Xnorm)\n",
"plt.plot(Xnorm, m*Xnorm)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Statistics\n",
"\n",
"What accounts for the variation of the points around the \"true value\"? Statisticians approach this through the idea of a **statistical model**. \n",
"\n",
"Let's leave the lung cancer data behind for the moment, and imagine an abstract problem. \n",
"\n",
"Suppose\n",
"that we make measurements of a dependent variable $Y$ that is related to an independent variable $X$ by a linear equation.\n",
"\n",
"Suppose, however, that the $Y$ values include a certain amount of random error $\\epsilon$, so that\n",
"\n",
"$$\n",
"Y=mX+b+\\epsilon.\n",
"$$\n",
"\n",
"We will assume that the error term $\\epsilon$ is a *normally distributed* error, with *mean* zero, variance $\\sigma^2$, and that the errors we obtain from separate measurements of $Y$ are independent of one another."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The mean of a normal distribution gives the location of the peak. The area under the curve between two values $a$ and $b$ is the probability that a number chosen at random will lie between $a$ and $b$.\n",
"\n",
"The variance $\\sigma^2$ measures how spread out the curve is. \n",
"\n",
"The probability of landing within $\\sigma$ (the standard deviation) of the mean is about $68$ percent; of landing within $2\\sigma$ is about $95$ percent; and of landing within $3\\sigma$ is about $99.7$ percent"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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NcmIocAqpQ49HxL0e6zajapE2W7RZfMitp1y+J3CuF2OWwEkQXK3NqOFpvpW5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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10ca44590>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import norm\n",
"X=np.arange(-5,5,.1)\n",
"plt.plot(X,norm.pdf(X,scale=.7,loc=0),color='red',label='$\\sigma^2$=.5')\n",
"plt.plot(X,norm.pdf(X,scale=1),color='blue',label='$\\sigma^2$=1')\n",
"plt.plot(X,norm.pdf(X,scale=1.5),color='orange',label='$\\sigma^2$=2.25')\n",
"\n",
"plt.title('Normal Distributions')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Suppose for the sake of concreteness that the $X$ values are 0.0,0.1,...,9.9 and that $Y=X+1+\\epsilon$ where $\\epsilon$ has variance $4$. Different measurements create different scatter plots.\n"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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3V+Cv2Yio+a8297ZhMaCzoBhhCcbj0Gd9Dbi4IFtz/NjHo+iLcGTGdGCVrA5T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\nP4J3WO5jOGqEVqL1tM+k/Jr2aFR2eD+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aX1sA6xHd2IuHvj8DOLscEzt6LxY8C7/wzSQv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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c9c5c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def MB(X,Y):\n",
" Sxx=sum([X[i]*X[i] for i in range(len(X))])\n",
" Sxy=sum([X[i]*Y[i] for i in range(len(X))])\n",
" Sx=sum([X[i] for i in range(len(X))])\n",
" Sy=sum([Y[i] for i in range(len(Y))])\n",
" N=len(X)\n",
" M=N*Sxy-Sx*Sy\n",
" B=Sxx*Sy-Sxy*Sx\n",
" D=N*Sxx-Sx*Sx\n",
" m=M/D\n",
" b=B/D\n",
" return m,b\n",
"\n",
"X=np.arange(0,10,.1)\n",
"fig,ax=plt.subplots(nrows=2,ncols=2,figsize=(6,6))\n",
"epsilon=norm.rvs(size=100,scale=2,loc=0)\n",
"Y0=X+np.ones(len(X))+epsilon\n",
"epsilon=norm.rvs(size=100,scale=2,loc=0)\n",
"Y1=X+np.ones(len(X))+epsilon\n",
"epsilon=norm.rvs(size=100,scale=2,loc=0)\n",
"Y2=X+np.ones(len(X))+epsilon\n",
"epsilon=norm.rvs(size=100,scale=2,loc=0)\n",
"Y3=X+np.ones(len(X))+epsilon\n",
"for i in [0,1]:\n",
" for j in [0,1]:\n",
" ax[i,j].set_xticks(range(0,11,2))\n",
" ax[i,j].set_yticks(range(-5,17,2))\n",
"ax[0,0].scatter(X,Y0,color='blue')\n",
"ax[1,0].scatter(X,Y1,color='red')\n",
"ax[0,1].scatter(X,Y2,color='green')\n",
"ax[1,1].scatter(X,Y3,color='black')\n",
"m0,b0=MB(X,Y0)\n",
"\n",
"m1,b1=MB(X,Y1)\n",
"\n",
"m2,b2=MB(X,Y2)\n",
"m3,b3=MB(X,Y3)\n",
"ax[0,0].plot(X,m0*X+b0,color=\"blue\")\n",
"ax[1,0].plot(X,m1*X+b1,color=\"red\")\n",
"ax[0,1].plot(X,m2*X+b2,color=\"green\")\n",
"ax[1,1].plot(X,m3*X+b3,color=\"black\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"We can superimpose these different lines and you can see that they are slightly different -- with varying slope and intercept -- which come from different snapshots of the underlying random data.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
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47xjcEfwp2CWqh6834Xy8iINli3yrNSY7G1NISnO3WJA41XwTX7L7u65ztCmK7ylWYmp4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\nSimllFJKKaWUUkrd9P8BkdAi2lgQjCoAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f630050>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(X,m0*X+b0,color=\"blue\")\n",
"plt.plot(X,m1*X+b1,color=\"red\")\n",
"plt.plot(X,m2*X+b2,color=\"green\")\n",
"plt.plot(X,m3*X+b3,color=\"black\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Suppose we draw 5000 samples of 100 Y-values each, where each of the 100 $Y$ values from a given sample\n",
"satisfy $Y=X+1+\\epsilon$. For each of the 5000 samples, we calculate the slope and intercept for those $100$ $Y$-values.\n",
"The picture below shows that these slope/intercept pairs lie in an ellipse centered at $(1,1)$."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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cZSj2UQVcZ4X8TiOL6A/supuybnqBtb3D2smafxD6I1fYal+3wekpuGJw2kgY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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f05d350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"Y=X+np.ones(len(X))\n",
"M,B=[],[]\n",
"for i in range(5000):\n",
" Yn=Y+norm.rvs(size=100,loc=0,scale=2)\n",
" m,b=MB(X,Yn)\n",
" M.append(m)\n",
" B.append(b)\n",
"plt.title(\"Slope/Intercept Pairs for Different Samples\") \n",
"plt.xlabel(\"Slope\")\n",
"plt.ylabel(\"Intercept\")\n",
"plt.scatter(B,M,s=.3,alpha=.3,color='blue')\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"We get a very nice elliptical region from these points. Where does this ellipse come from?"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"To see where this ellipse comes from, let's recall the orthonormal vectors $\\mathbf{e}$ and $\\mathbf{x}$ introduced earlier. \n",
"\n",
"$$\n",
"\\mathbf{e}=\\frac{E}{\\sqrt{N}}, \\mathbf{x}=\\frac{X-(X\\cdot\\mathbf{e})\\mathbf{e}}{||X-(X\\cdot\\mathbf{e})\\mathbf{e}||}\n",
"$$\n",
"\n",
"We saw that the predicted $Y$ values corresponds to the orthogonal projection $\\hat{Y}=(Y\\cdot \\mathbf{e})\\mathbf{e}+(Y\\cdot \\mathbf{x})\\mathbf{x}$. \n",
"\n",
"The points $((Y\\cdot \\mathbf{e}),(Y\\cdot \\mathbf{x}))$ are distributed around $((X+1)\\cdot e),((X+1)\\cdot x))$, and their displacement is the orthogonal projection of the\n",
"vector whose coordinates are the errors $\\epsilon_{i}$.\n",
"\n",
"In other words, we are looking at the random vectors $\\epsilon$\n",
"projected orthogonally onto the $\\mathbf{e},\\mathbf{x}$ plane. Since the $\\epsilon$ fall in a sphere around zero, the projection is a circle."
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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wr9Otul4/HhgCbknaPrcBf83wgE3Yornbu9jxeiz4WkyJmt9Gln36YmSv6+eA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\nMzMzMzMzMzMzMzMzMzMzMzMrF/8BNh6qOia5cLgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116e01f10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def P(X,Y):\n",
" N=len(X)\n",
" Xbar=sum(X)/N\n",
" Sx=sum((X-Xbar*np.ones(N))**2)\n",
" A=sum(Y)/sqrt(N)\n",
" Z=(X-Xbar*np.ones(N))/sqrt(Sx)\n",
" B=sum([Z[i]*Y[i] for i in range(N)])\n",
" return A,B\n",
"\n",
"A=[]\n",
"B=[]\n",
"sigmas=[]\n",
"a0,b0=P(X,X+1)\n",
"for i in range(5000):\n",
" Yn=Y+norm.rvs(size=100,loc=0,scale=2)\n",
" a,b=P(X,Yn)\n",
" A.append(a)\n",
" B.append(b)\n",
" s=sum((Yn-Y)**2)/(N-2)\n",
" sigmas.append(s)\n",
" \n",
"\n",
"fig,axes=plt.subplots(nrows=1,ncols=2,figsize=(15,6))\n",
"axes[0].set_title(\"Orthogonal\\n Projection of Residuals\") \n",
"axes[0].axis([-10+a0,10+a0,-10+b0,10+b0])\n",
"axes[0].set_aspect('equal')\n",
"#plt.gca().set_aspect('equal')\n",
"axes[0].scatter(A,B,s=.3,alpha=.3,color='blue')\n",
"u=np.arange(-10+a0,10+a0,.05)\n",
"v=np.arange(-10+b0,10+b0,.05)\n",
"U,V=np.meshgrid(u,v)\n",
"axes[0].contour(U,V,(U-a0)**2+(V-b0)**2,[4,16,36])\n",
"axes[1].hist(A,normed='True')\n",
"axes[1].hist(B,normed='True')\n",
"axes[1].plot(np.arange(-10+a0,10+a0,.1),norm.pdf(np.arange(-10+a0,10+a0,.1),scale=2,loc=a0),color='black')\n",
"axes[1].plot(np.arange(-10+b0,10+b0,.1),norm.pdf(np.arange(-10+b0,10+b0,.1),scale=2,loc=b0),color='black')\n",
"\n",
"axes[1].set_title(\"Distribution of Residuals\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Here the circles show the regions within one and two standard deviations from the origin."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"We can make a change of variables from the $x$,$e$ coordinate system to the $X$, $E$ coordinates; the coefficients of the $\\hat{Y}$ vector in these coordinates are $m$ and $b$. Let\n",
"\n",
"$$\n",
"S=\\sum_{i=1}^{N} (x_i-\\overline{x})^2.\n",
"$$\n",
"\n",
"The coordinates are\n",
"$$\n",
"b=\\frac{1}{\\sqrt{N}}(Y\\cdot\\mathbf{e})-\\frac{\\overline{x}}{\\sqrt(S)}(Y\\cdot\\mathbf{x})\n",
"$$\n",
"\n",
"and\n",
"\n",
"$$\n",
"m=\\frac{1}{\\sqrt{S}}(Y\\cdot\\mathbf{x})\n",
"$$\n",
"\n",
"In these coordinates the circular cloud above becomes an elliptical cloud. The ellipses correspond to the circles where about 68% of the points lie, 95%; and 99.7%.\n"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
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AbgnSfryXaC5p3gaIhmgb3dI2CxmCpHkbMMRZH3iY+ncKpvVcFAItKU6mr5T0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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116c95ed0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#plt.xlabel(\"Slope\")\n",
"#plt.ylabel(\"Intercept\")\n",
"#axes[0].set_xticks(np.arange(-.5,.5,.1))\n",
"fig=plt.figure(num=1,figsize=(10,10))\n",
"\n",
"axes=fig.gca()\n",
"\n",
"A=np.array(A)\n",
"B=np.array(B)\n",
"axes.set_title('Samples of Slope, Intercept pairs')\n",
"axes.axis([1-2,1+2,1-.3,1+.3])\n",
"axes.set_xticks(np.arange(-2,4,1))\n",
"N=len(X)\n",
"Xbar=sum(X)/N\n",
"Sx=sum((X-Xbar*np.ones(N))**2)\n",
"R=Sx+N*Xbar**2\n",
"S=2*N*Xbar\n",
"T=N\n",
"u=np.arange(1-3,1+4,.01)\n",
"v=np.arange(1-3,1+4,.01)\n",
"U,V=np.meshgrid(u,v)\n",
"axes.contour(U,V,T*(U-1)**2+S*(U-1)*(V-1)+R*(V-1)**2,levels=[4,16,36],colors=['black','black','black'])\n",
"#axes.set_aspect('equal',adjustable='box')\n",
"axes.scatter(1/sqrt(N)*A-Xbar/sqrt(Sx)*B,1/sqrt(Sx)*B,s=.5,alpha=.3,color='red') \n",
"axes.set_ylabel('Slope')\n",
"axes.set_xlabel('Intercept')\n",
"axes.grid('on')\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"It is a theorem from probability that the sum of independent normally distributed random variables with variances $\\sigma_1^2$ and $\\sigma_2^2$ is again normally distributed with variance $\\sigma_1^2+\\sigma_2^2$. If we we look at the distributions of $b$ and $m$, we see this, with \n",
"\n",
"- the variance of $m$ being $\\sigma^2/S$\n",
"\n",
"- the variance of $b$ being $(\\frac{1}{N}+\\frac{\\overline{x}^2}{S})$."
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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hBMgltWoVZwCOHaO1HM8nRfZF4Nppt32o4PJJDFyqKMPtYbsm4nyvVLri4fNd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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116e0f3d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axes=plt.subplots(ncols=2,nrows=1,figsize=(15,6))\n",
"axes[0].hist(1.0/sqrt(Sx)*B,normed='True',bins=np.arange(0.5,1.5,.025),color='yellow',alpha=0.5)\n",
"axes[0].plot(np.arange(0,1.5,.025),norm.pdf(np.arange(0,1.5,.025),scale=2/sqrt(Sx),loc=1),color='black',linewidth=2)\n",
"axes[0].set_title('Distribution of slope')\n",
"axes[1].set_title('Distribution of intercept')\n",
"axes[1].plot(np.arange(-2,4,0.05),norm.pdf(np.arange(-2,4,0.05),loc=1,scale=sqrt((4.0/N+4.0*Xbar**2/Sx))),color='black',linewidth=2)\n",
"axes[1].hist(1/sqrt(N)*A-Xbar/sqrt(Sx)*B,bins=np.arange(-2,4,0.1),normed='True',alpha=0.5)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Estimation of parameters\n",
"\n",
"Let's look back at our lung cancer example from the statistical viewpoint. Suppose that the numbers that we have are just one sample from a statistical model of the form $Y=m^{*}X+b^{*}+\\epsilon$ of the type we have just studied. This model is determined by three parameters -- the (true) slope $m^{*}$ and intercept $b^{*}$, and the variance $\\sigma_{*}^2$ of the error term.\n",
"\n",
"We don't know the true slope $m^{*}$, true intercept $b^{*}$, or true variance $\\sigma_{*}^2$ that gave rise to our data. All we have our the slope $m$ and intercept $b$ that we computed from the sample data. How should we interpret these?\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"One can show that the values of $m$ and $b$ that we computed by minimizing the sum of the squared errors are the \n",
"** most likely ** values of $m$ and $b$ that could give rise to this particular set of data. This isn't hard to prove, but it requires more statistical terminology than I am willing to introduce at this point.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## What about the variance?\n",
"\n",
"The shape of the model $y=mx+b+\\epsilon$ means that the values $y-mx-b$ are chosen at random from a normal distribution $\\epsilon$ with mean zero and variance $\\sigma_{*}^2$. \n",
"\n",
"One can show that if one makes $N$ draws $\\epsilon_{i}$ from such a normal distribution, then the\n",
"\"sample variance\"\n",
"\n",
"$$\n",
"\\frac{1}{N}\\sum_{i=1}^{N} \\epsilon_{i}^2\n",
"$$\n",
"\n",
"is the most likely estimate for the true variance, and as $N\\to\\infty$ the values of this cluster more and more closely around the true variance."
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.41906931227\n",
"833.25\n"
]
}
],
"source": [
"Cigpredictions=mcig*df['Cigarettes']+bcig*np.ones(len(df['Cigarettes']))\n",
"\n",
"sigmacig=sum(1.0/(len(Cigpredictions)-2)*(df['Lung']-Cigpredictions)**2)\n",
"print sigmacig\n",
"print Sx"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"So our estimate for the variance in general will be \n",
"\n",
"$\\sigma^2=\\frac{1}{N}\\sum_{i=1}^{N} (y_{i}-mx_{i}-b)^2.$\n",
"\n",
"(Note to the experts: this is the maximum likelihood estimate of the variance, which is biased; the unbiased\n",
"estimate of the sample variance has $\\frac{1}{N-2}$. For $N$ large this is not important.)\n",
"\n",
"In our cigarette example this gives a variance for the $\\epsilon$ is about $8.4$.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"So here's what we assume, and observe from the data:\n",
"\n",
"- the cigarette data comes from a linear model of the form $y=mx+b+\\epsilon$ where the errors $\\epsilon$ are independent, normally distributed with the same variance $\\sigma^2$.\n",
" \n",
"- We've drawn a sample from this model with $44$ data points, and from that we have the *estimated* values $m=.0052$, $b=6.91$, and $\\sigma^{2}=8.4$.\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Let's look for the moment at $m$. Under our assumptions, we've drawn $m$ from a normal distribution as above. Since our estimate for the total variance is $\\sigma^2=8.4$, our estimate for the standard deviation of the $m$-distribution is\n",
"$\\sqrt{\\sigma^2/Sx}=.0008$. (This is called the \"standard error\" of the $m$-value.)\n",
"\n",
"Roughly speaking, this means that 95% of the time, the value of $m$ we would get from this model is within $.0016$\n",
"of the estimated value $.0052$. In particular, it's very unlikely that we would have gotten these values if the **true** value $m^{*}$ of $m$ were in fact zero."
]
},
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"slide_type": "skip"
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"cell_type": "code",
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{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"-------------------------Summary of Regression Analysis-------------------------\n",
"\n",
"Formula: Y ~ <Cigarettes> + <intercept>\n",
"\n",
"Number of Observations: 44\n",
"Number of Degrees of Freedom: 2\n",
"\n",
"R-squared: 0.5059\n",
"Adj R-squared: 0.4941\n",
"\n",
"Rmse: 2.9016\n",
"\n",
"F-stat (1, 42): 42.9946, p-value: 0.0000\n",
"\n",
"Degrees of Freedom: model 1, resid 42\n",
"\n",
"-----------------------Summary of Estimated Coefficients------------------------\n",
" Variable Coef Std Err t-stat p-value CI 2.5% CI 97.5%\n",
"--------------------------------------------------------------------------------\n",
" Cigarettes 0.0052 0.0008 6.56 0.0000 0.0036 0.0068\n",
" intercept 6.9105 2.0258 3.41 0.0014 2.9399 10.8811\n",
"---------------------------------End of Summary---------------------------------\n",
"\n"
]
}
],
"source": [
"model = pd.ols(y=df['Lung'], x=df.ix[:, ['Cigarettes']])\n",
"print model"
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6.5\n"
]
}
],
"source": [
"sqrt(8.4/sum((df['Cigarettes']-df['Cigarettes'].mean())**2))\n",
"print .0052/.0008"
]
},
{
"cell_type": "code",
"execution_count": null,
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"collapsed": true
},
"outputs": [],
"source": []
}
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