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vincenttzc/ECON207 Assignment 1 (Part2)

Created September 15, 2017 00:58
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ECON207 Assignment 1 (Part2)
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ECON207 Assignment 1 (Part2)
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# ECON207 Assignment 1 (Part 2)\n",
"\n",
"## Tan Zhi Chong"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# 1b."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"# Step 1 : Prepare library and set working directory\n",
"\n",
"## Prepare library for data preparation and data visualisation\n",
"\n",
"library(ggplot2)\n",
"library(dplyr)\n",
"\n",
"## Set the working directory to obtain the data\n",
"\n",
"setwd(\"C:\\\\Users\\\\vince\\\\Documents\\\\R Scripts\\\\R data\")\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" year lprice \n",
" Min. :1978 Min. :10.17 \n",
" 1st Qu.:1978 1st Qu.:10.94 \n",
" Median :1978 Median :11.23 \n",
" Mean :1978 Mean :11.18 \n",
" 3rd Qu.:1978 3rd Qu.:11.41 \n",
" Max. :1978 Max. :12.61 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Step 2 : Data Preparation\n",
"\n",
"## Load data using read.csv function\n",
"data_all <- read.csv(\"hprice3.csv\",header = FALSE, fileEncoding=\"UTF-8-BOM\")\n",
"## Add names of the columns since csv files does not contain the name\n",
"colnames(data_all) <- c(\"year\", \"age\" , \"agesq\" , \"nbh\" , \"cbd\" , \"inst\" , \"linst\" , \"price\" , \n",
" \"rooms\" , \"area\" , \"land\" , \"baths\" , \"dist\" , \"ldist\" , \"lprice\" , \"y81\" , \n",
" \"larea\" , \"lland\" , \"linstsq\" )\n",
"\n",
"## Use filter function from dplyr library to form a subset of the data, data with year 1978\n",
"## Let's call this data1978\n",
"data1978 <- filter(data_all, year == 1978)\n",
"\n",
"## Quick summary statistic of the data to understand \n",
"summary(data1978[c(\"year\",\"lprice\")])"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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H6AXi9x85QtpCPfP+0AnA3p9P3tH+v7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\nAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Step 3: Create scatterplot to better understand the data \n",
"\n",
"## Create scatterplot using ggplot2 library\n",
"\n",
"viz <- ggplot(data = data1978, aes(x = area, y = lprice))\n",
"viz + geom_point()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"lm(formula = lprice ~ area, data = data1978)\n",
"\n",
"Residuals:\n",
" Min 1Q Median 3Q Max \n",
"-1.02434 -0.12669 0.07708 0.17790 0.78470 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 1.045e+01 7.052e-02 148.14 <2e-16 ***\n",
"area 3.659e-04 3.362e-05 10.88 <2e-16 ***\n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"Residual standard error: 0.2849 on 177 degrees of freedom\n",
"Multiple R-squared: 0.4009,\tAdjusted R-squared: 0.3975 \n",
"F-statistic: 118.4 on 1 and 177 DF, p-value: < 2.2e-16\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Step 4: Run OLS Regression\n",
"\n",
"## lm function in R uses OLS method\n",
"## Regress log price on area (lprice ~ area)\n",
"\n",
"fit <- lm(data = data1978, lprice ~ area)\n",
"\n",
"## View regression results\n",
"\n",
"summary(fit)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<dl class=dl-horizontal>\n",
"\t<dt>(Intercept)</dt>\n",
"\t\t<dd>10.447432287893</dd>\n",
"\t<dt>area</dt>\n",
"\t\t<dd>0.000365890065143563</dd>\n",
"</dl>\n"
],
"text/latex": [
"\\begin{description*}\n",
"\\item[(Intercept)] 10.447432287893\n",
"\\item[area] 0.000365890065143563\n",
"\\end{description*}\n"
],
"text/markdown": [
"(Intercept)\n",
": 10.447432287893area\n",
": 0.000365890065143563\n",
"\n"
],
"text/plain": [
" (Intercept) area \n",
"1.044743e+01 3.658901e-04 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Step 5: Obtain predicted log price\n",
"\n",
"## Obtain coefficients of our model\n",
"coeff <- coefficients(fit)\n",
"\n",
"coeff"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"11.9109925484672"
],
"text/latex": [
"11.9109925484672"
],
"text/markdown": [
"11.9109925484672"
],
"text/plain": [
"[1] 11.91099"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Find predicted price using our obtained coefficients\n",
"\n",
"logprice <- coeff[1] + coeff[2]*4000\n",
"logprice <- unname(logprice)\n",
"logprice"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<span style=white-space:pre-wrap>'Predicted Price: 155059.426093949'</span>"
],
"text/latex": [
"'Predicted Price: 155059.426093949'"
],
"text/markdown": [
"<span style=white-space:pre-wrap>'Predicted Price: 155059.426093949'</span>"
],
"text/plain": [
"[1] \"Predicted Price: 155059.426093949\""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"<span style=white-space:pre-wrap>'Predicted Standard Error: 45080.7789308043'</span>"
],
"text/latex": [
"'Predicted Standard Error: 45080.7789308043'"
],
"text/markdown": [
"<span style=white-space:pre-wrap>'Predicted Standard Error: 45080.7789308043'</span>"
],
"text/plain": [
"[1] \"Predicted Standard Error: 45080.7789308043\""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Step 6: Transformation to obtain price\n",
"\n",
"## Obtain variance of the residual\n",
"var_residual <- (summary(fit)$sigma)^2\n",
"\n",
"## Trasnformation\n",
"price <- exp(logprice + 0.5 * var_residual)\n",
"paste(\"Predicted Price: \", price)\n",
"\n",
"price_se <- (exp(2*(logprice + var_residual))- exp(2*logprice + var_residual))^0.5\n",
"paste(\"Predicted Standard Error: \", price_se)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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IcLp40pWMlrRGLXrgswpUiLS2ZfkYbR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\nrkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"## Residual plot\n",
"df <- fortify(fit)\n",
"ggplot(data = df, aes(x = area, y = .resid)) + geom_point() + geom_hline(yintercept = 0)\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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