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Created December 30, 2019 14:51
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Quiz 1.ipynb
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**1. Load the \"Matching\" library.**"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:03.698041Z",
"start_time": "2019-12-30T14:49:02.701Z"
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"name": "stderr",
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"text": [
"Loading required package: MASS\n",
"## \n",
"## Matching (Version 4.9-3, Build Date: 2018-05-03)\n",
"## See http://sekhon.berkeley.edu/matching for additional documentation.\n",
"## Please cite software as:\n",
"## Jasjeet S. Sekhon. 2011. ``Multivariate and Propensity Score Matching\n",
"## Software with Automated Balance Optimization: The Matching package for R.''\n",
"## Journal of Statistical Software, 42(7): 1-52. \n",
"##\n",
"\n"
]
}
],
"source": [
"library(Matching)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**2. Load the lalonde data set into working memory.**"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:05.378258Z",
"start_time": "2019-12-30T14:49:05.338Z"
}
},
"outputs": [],
"source": [
"data(lalonde)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**3. What are the dimensions of the data set?**"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:05.741347Z",
"start_time": "2019-12-30T14:49:05.713Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>445</li>\n",
"\t<li>12</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 445\n",
"\\item 12\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 445\n",
"2. 12\n",
"\n",
"\n"
],
"text/plain": [
"[1] 445 12"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dim(lalonde)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**4. What are the names of the columns?**"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:06.127030Z",
"start_time": "2019-12-30T14:49:06.100Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"<ol class=list-inline>\n",
"\t<li>'age'</li>\n",
"\t<li>'educ'</li>\n",
"\t<li>'black'</li>\n",
"\t<li>'hisp'</li>\n",
"\t<li>'married'</li>\n",
"\t<li>'nodegr'</li>\n",
"\t<li>'re74'</li>\n",
"\t<li>'re75'</li>\n",
"\t<li>'re78'</li>\n",
"\t<li>'u74'</li>\n",
"\t<li>'u75'</li>\n",
"\t<li>'treat'</li>\n",
"</ol>\n"
],
"text/latex": [
"\\begin{enumerate*}\n",
"\\item 'age'\n",
"\\item 'educ'\n",
"\\item 'black'\n",
"\\item 'hisp'\n",
"\\item 'married'\n",
"\\item 'nodegr'\n",
"\\item 're74'\n",
"\\item 're75'\n",
"\\item 're78'\n",
"\\item 'u74'\n",
"\\item 'u75'\n",
"\\item 'treat'\n",
"\\end{enumerate*}\n"
],
"text/markdown": [
"1. 'age'\n",
"2. 'educ'\n",
"3. 'black'\n",
"4. 'hisp'\n",
"5. 'married'\n",
"6. 'nodegr'\n",
"7. 're74'\n",
"8. 're75'\n",
"9. 're78'\n",
"10. 'u74'\n",
"11. 'u75'\n",
"12. 'treat'\n",
"\n",
"\n"
],
"text/plain": [
" [1] \"age\" \"educ\" \"black\" \"hisp\" \"married\" \"nodegr\" \"re74\" \n",
" [8] \"re75\" \"re78\" \"u74\" \"u75\" \"treat\" "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"names(lalonde)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**5. How many different variable types are represented in this data set?**"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:06.869218Z",
"start_time": "2019-12-30T14:49:06.488Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"integer \n",
"integer \n",
"integer \n",
"integer \n",
"integer \n",
"integer \n",
"numeric \n",
"numeric \n",
"numeric \n",
"integer \n",
"integer \n",
"integer \n"
]
},
{
"data": {
"text/html": [
"2"
],
"text/latex": [
"2"
],
"text/markdown": [
"2"
],
"text/plain": [
"[1] 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"### To see the different variable types:\n",
"for(i in 1:length(names(lalonde))) {cat( class(lalonde[,i]), \"\\n\")}\n",
"\n",
"### To count the unique types:\n",
"length(unique(sapply(lalonde, class)))\n",
"\n",
"### The answer is \"2\" -- there are two variable types.\n",
"\n",
"### To see the help file for the \"sapply\" function, type:\n",
"?sapply"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**6. What's the maximum value of the re74 column? (re74 indicates the person's real earnings in 1974)**"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:07.230251Z",
"start_time": "2019-12-30T14:49:06.864Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"39570.7"
],
"text/latex": [
"39570.7"
],
"text/markdown": [
"39570.7"
],
"text/plain": [
"[1] 39570.7"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"max(lalonde['re74'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**7. What's the minimum value of this column?**"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:07.610234Z",
"start_time": "2019-12-30T14:49:07.312Z"
},
"code_folding": []
},
"outputs": [
{
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"text/html": [
"0"
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"text/latex": [
"0"
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"text/markdown": [
"0"
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"text/plain": [
"[1] 0"
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"output_type": "display_data"
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],
"source": [
"min(lalonde['re74'])\n",
"\n",
"### or\n",
"\n",
"min(lalonde$re74)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**8. How many of the elements of this column are equal to zero?**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:08.037698Z",
"start_time": "2019-12-30T14:49:08.001Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"326"
],
"text/latex": [
"326"
],
"text/markdown": [
"326"
],
"text/plain": [
"[1] 326"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"326"
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"text/latex": [
"326"
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"text/markdown": [
"326"
],
"text/plain": [
"[1] 326"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sum(lalonde['re74'] == 0)\n",
"\n",
"### or\n",
"\n",
"length(which(lalonde$re74 == 0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**9. How many elements of this column are less than \\$15000 OR greater than 20000?**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:08.917789Z",
"start_time": "2019-12-30T14:49:08.889Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"440"
],
"text/latex": [
"440"
],
"text/markdown": [
"440"
],
"text/plain": [
"[1] 440"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sum((lalonde['re74'] < 15000) | (lalonde['re74'] > 20000))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**10. How many people in this data set are married and have more than 8 years of education (\"educ\")?**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:12.528204Z",
"start_time": "2019-12-30T14:49:12.501Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"68"
],
"text/latex": [
"68"
],
"text/markdown": [
"68"
],
"text/plain": [
"[1] 68"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sum((lalonde$married == 1) & (lalonde$educ > 8))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**11. What is the interquartile range of \"re78\" (real earnings in 1978)? Use the \"quantile\" function.**"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:13.050673Z",
"start_time": "2019-12-30T14:49:13.014Z"
}
},
"outputs": [
{
"data": {
"text/html": [
"<strong>75%:</strong> 8124.72"
],
"text/latex": [
"\\textbf{75\\textbackslash{}\\%:} 8124.72"
],
"text/markdown": [
"**75%:** 8124.72"
],
"text/plain": [
" 75% \n",
"8124.72 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<strong>25%:</strong> 0"
],
"text/latex": [
"\\textbf{25\\textbackslash{}\\%:} 0"
],
"text/markdown": [
"**25%:** 0"
],
"text/plain": [
"25% \n",
" 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"### upper-bound of the interquartile range:\n",
"quantile(lalonde$re78, 0.75)\n",
"\n",
"### lower-bound of the interquartile range:\n",
"quantile(lalonde$re78, 0.25)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**12. Create a scatterplot, with re74 on the x-axis, and re78 on the y-axis. Label the axes. Draw a regression line if you wish (and choose a fun color).**"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:13.661064Z",
"start_time": "2019-12-30T14:49:13.552Z"
}
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"options(repr.plot.width = 4, repr.plot.height = 4)\n",
"plot(lalonde$re74, lalonde$re78, xlab = 'Earnings in 1974', ylab = 'Earnings in 1978')\n",
"abline(lm(lalonde$re78 ~ lalonde$re74), lwd=3, col = \"magenta\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**13. Make a function with a single argument (column number) that outputs the median of that column. Advanced: if the user specifies a non-numeric column, then the function returns an error message.**"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:14.667317Z",
"start_time": "2019-12-30T14:49:14.602Z"
}
},
"outputs": [
{
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"source": [
"median_lalonde_column <-\n",
" function(column)\n",
" {\n",
" if (is.numeric(lalonde[, column])) \n",
" {return(median(lalonde[, column]))} \n",
" else return('Error')\n",
" }\n",
"\n",
"### How you would use the function...\n",
"median_lalonde_column(column = 7)\n",
"\n",
"median_lalonde_column(column = 8)\n",
"\n",
"median_lalonde_column(column = 9)\n",
"\n",
"median_lalonde_column(column = 10)\n",
"\n",
"median_lalonde_column(10)\n",
"\n",
"median_lalonde_column(9)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**14. Run a univariate regression, with \"age\" as a predictor (x variable), re75 as outcome (the \"y\"). Interpret the 2 coefficients (of the intercept, and the x variable).**"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:49:15.492351Z",
"start_time": "2019-12-30T14:49:15.464Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = lalonde$re75 ~ lalonde$age)\n",
"\n",
"Coefficients:\n",
"(Intercept) lalonde$age \n",
" 784.62 23.35 \n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lm(formula = lalonde$re75 ~ lalonde$age)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The regression coefficients identify the following linear model:\n",
"\n",
"$$\\text{re75} = 784.62 + 23.35 \\times \\text{age}$$\n",
"\n",
"In other words, the intercept means that if we interpret our model literally, our model predicts real earnings in 1975 is \n",
"\\\\$784.62 for someone with an age of zero. And, the coefficient on \"age\" means that our model predicts that every additional year of age is associated with \\\\$23.35 more real earnings in 1975, e.g., our model predicts that someone 50 years old would earn \\\\$784.62 + \\\\$1167.50 = \\\\$1952.12 in 1975."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**15. Run a regression with 2 predictors, \"age\" and \"educ\", with re75 as the outcome (the \"y\").**"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"ExecuteTime": {
"end_time": "2019-12-30T14:51:00.097356Z",
"start_time": "2019-12-30T14:51:00.057Z"
}
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = lalonde$re75 ~ lalonde$age + lalonde$educ)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-2073.4 -1403.5 -1209.8 -67.1 23553.9 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|)\n",
"(Intercept) 348.95 1006.16 0.347 0.729\n",
"lalonde$age 23.10 21.08 1.096 0.274\n",
"lalonde$educ 43.36 83.51 0.519 0.604\n",
"\n",
"Residual standard error: 3153 on 442 degrees of freedom\n",
"Multiple R-squared: 0.003377,\tAdjusted R-squared: -0.001132 \n",
"F-statistic: 0.7489 on 2 and 442 DF, p-value: 0.4735\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"lm2 <- lm(lalonde$re75 ~ lalonde$age + lalonde$educ)\n",
"summary(lm2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The regression coefficients identify the following linear model:\n",
"\n",
"$$ \\text{re75} = 348.95 + 23.10 \\times \\text{age} + 43.36 \\times \\text{educ}$$\n",
"\n",
"In other words, the intercept means that if we interpret the model literally, our model predicts real earnings in 1975 is \\\\$348.95 for someone with an age of zero. And, the coefficient on \"age\" means that our model predicts that every additional year of age is associated with $23.10 more real earnings in 1975. Every additional year of education is associated with \\\\$43.36 more real earnings in 1975. For example, our model predicts that someone 50 years old with 12 years of education would earn \\\\$348.95 + \\\\$1155 + \\\\$520.32 = \\\\$2024.27 in 1975.\n",
"\n",
"If you'd like to see the predicted values for every person in the data set (given this regression model), just type:\n",
"```predict(lm2)```"
]
},
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"<table>\n",
"<thead><tr><th scope=col>age</th><th scope=col>educ</th><th scope=col>black</th><th scope=col>hisp</th><th scope=col>married</th><th scope=col>nodegr</th><th scope=col>re74</th><th scope=col>re75</th><th scope=col>re78</th><th scope=col>u74</th><th scope=col>u75</th><th scope=col>treat</th><th scope=col>predict(lm2)</th></tr></thead>\n",
"<tbody>\n",
"\t<tr><td>37 </td><td>11 </td><td>1 </td><td>0 </td><td>1 </td><td>1 </td><td>0 </td><td>0 </td><td> 9930.05</td><td>1 </td><td>1 </td><td>1 </td><td>1680.688</td></tr>\n",
"\t<tr><td>22 </td><td> 9 </td><td>0 </td><td>1 </td><td>0 </td><td>1 </td><td>0 </td><td>0 </td><td> 3595.89</td><td>1 </td><td>1 </td><td>1 </td><td>1247.429</td></tr>\n",
"\t<tr><td>30 </td><td>12 </td><td>1 </td><td>0 </td><td>0 </td><td>0 </td><td>0 </td><td>0 </td><td>24909.50</td><td>1 </td><td>1 </td><td>1 </td><td>1562.325</td></tr>\n",
"\t<tr><td>27 </td><td>11 </td><td>1 </td><td>0 </td><td>0 </td><td>1 </td><td>0 </td><td>0 </td><td> 7506.15</td><td>1 </td><td>1 </td><td>1 </td><td>1449.659</td></tr>\n",
"\t<tr><td>33 </td><td> 8 </td><td>1 </td><td>0 </td><td>0 </td><td>1 </td><td>0 </td><td>0 </td><td> 289.79</td><td>1 </td><td>1 </td><td>1 </td><td>1458.204</td></tr>\n",
"\t<tr><td>22 </td><td> 9 </td><td>1 </td><td>0 </td><td>0 </td><td>1 </td><td>0 </td><td>0 </td><td> 4056.49</td><td>1 </td><td>1 </td><td>1 </td><td>1247.429</td></tr>\n",
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"text/latex": [
"\\begin{tabular}{r|lllllllllllll}\n",
" age & educ & black & hisp & married & nodegr & re74 & re75 & re78 & u74 & u75 & treat & predict(lm2)\\\\\n",
"\\hline\n",
"\t 37 & 11 & 1 & 0 & 1 & 1 & 0 & 0 & 9930.05 & 1 & 1 & 1 & 1680.688\\\\\n",
"\t 22 & 9 & 0 & 1 & 0 & 1 & 0 & 0 & 3595.89 & 1 & 1 & 1 & 1247.429\\\\\n",
"\t 30 & 12 & 1 & 0 & 0 & 0 & 0 & 0 & 24909.50 & 1 & 1 & 1 & 1562.325\\\\\n",
"\t 27 & 11 & 1 & 0 & 0 & 1 & 0 & 0 & 7506.15 & 1 & 1 & 1 & 1449.659\\\\\n",
"\t 33 & 8 & 1 & 0 & 0 & 1 & 0 & 0 & 289.79 & 1 & 1 & 1 & 1458.204\\\\\n",
"\t 22 & 9 & 1 & 0 & 0 & 1 & 0 & 0 & 4056.49 & 1 & 1 & 1 & 1247.429\\\\\n",
"\\end{tabular}\n"
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"\n",
"age | educ | black | hisp | married | nodegr | re74 | re75 | re78 | u74 | u75 | treat | predict(lm2) | \n",
"|---|---|---|---|---|---|\n",
"| 37 | 11 | 1 | 0 | 1 | 1 | 0 | 0 | 9930.05 | 1 | 1 | 1 | 1680.688 | \n",
"| 22 | 9 | 0 | 1 | 0 | 1 | 0 | 0 | 3595.89 | 1 | 1 | 1 | 1247.429 | \n",
"| 30 | 12 | 1 | 0 | 0 | 0 | 0 | 0 | 24909.50 | 1 | 1 | 1 | 1562.325 | \n",
"| 27 | 11 | 1 | 0 | 0 | 1 | 0 | 0 | 7506.15 | 1 | 1 | 1 | 1449.659 | \n",
"| 33 | 8 | 1 | 0 | 0 | 1 | 0 | 0 | 289.79 | 1 | 1 | 1 | 1458.204 | \n",
"| 22 | 9 | 1 | 0 | 0 | 1 | 0 | 0 | 4056.49 | 1 | 1 | 1 | 1247.429 | \n",
"\n",
"\n"
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"text/plain": [
" age educ black hisp married nodegr re74 re75 re78 u74 u75 treat\n",
"1 37 11 1 0 1 1 0 0 9930.05 1 1 1 \n",
"2 22 9 0 1 0 1 0 0 3595.89 1 1 1 \n",
"3 30 12 1 0 0 0 0 0 24909.50 1 1 1 \n",
"4 27 11 1 0 0 1 0 0 7506.15 1 1 1 \n",
"5 33 8 1 0 0 1 0 0 289.79 1 1 1 \n",
"6 22 9 1 0 0 1 0 0 4056.49 1 1 1 \n",
" predict(lm2)\n",
"1 1680.688 \n",
"2 1247.429 \n",
"3 1562.325 \n",
"4 1449.659 \n",
"5 1458.204 \n",
"6 1247.429 "
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"source": [
"# Or, to see both the data and the predictions, we \"column bind\" the dataset to the output of predict().\n",
"head(cbind(lalonde, predict(lm2)))"
]
}
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