From cd812562803277ff62cfb95c9596de95a3176f3c Mon Sep 17 00:00:00 2001 From: Delores Tang Date: Wed, 24 Oct 2018 01:55:33 -0500 Subject: [PATCH] Updating A3 submission --- Assignments/A2/Assign_2_DeloresTang.Rmd | 170 +++++++++++ Assignments/A3/A3-1.pdf | Bin 0 -> 117838 bytes Assignments/A3/A3-2.pdf | Bin 0 -> 71344 bytes Assignments/A3/Assign#3.ipynb | 377 ++++++++++++++++++++++++ 4 files changed, 547 insertions(+) create mode 100644 Assignments/A2/Assign_2_DeloresTang.Rmd create mode 100644 Assignments/A3/A3-1.pdf create mode 100644 Assignments/A3/A3-2.pdf create mode 100644 Assignments/A3/Assign#3.ipynb diff --git a/Assignments/A2/Assign_2_DeloresTang.Rmd b/Assignments/A2/Assign_2_DeloresTang.Rmd new file mode 100644 index 0000000..dda609b --- /dev/null +++ b/Assignments/A2/Assign_2_DeloresTang.Rmd @@ -0,0 +1,170 @@ +--- +title: "Homework#2" +author: "Delores Tang" +date: "10/14/2018" +output: + pdf_document: default + html_document: + df_print: paged +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) +library(lattice) +library(MASS) +library(dplyr) +``` + + +1. Imputing age and gender +```{r, include = F} +#Import datasets +BestInc <- read.csv("C:/Users/delor/persp-analysis_A18/Assignments/A2/BestIncome.txt", header=FALSE) +SurvInc <- read.csv("C:/Users/delor/persp-analysis_A18/Assignments/A2/SurvIncome.txt", header=FALSE) +IncIntel <- read.csv("C:/Users/delor/persp-analysis_A18/Assignments/A2/IncomeIntel.txt", header=FALSE) + +# Rename variables +names(BestInc) <- c("L_inc","C_inc","Height","Weight") +names(SurvInc) <- c("T_inc","Weight", "Age", "Gender") +names(IncIntel) <- c("year","gre","salary") +``` + +(a) In order to impute age and gender from SurvIncome to BestIncome, I would like to fit a generalized linear model to variables in SurvIncome. +```{r, tidy = TRUE} +#Linear Regression in SurvIncome +Agelm <- lm(Age ~ Weight + T_inc, data = SurvInc) +summary(Agelm) +Genderlm <- lm(Gender ~ Weight + T_inc, data = SurvInc) +summary(Genderlm) +``` + + +Therefore, the equations that could be used to impute Age and Gender to BestIncome will be: $$\text{Age} = 44.21 - 6.722\times 10^{-3} \times \text{Weight} + 2.52 \times 10^{-5} \times\text{Total Income}$$ and $$\text{Gender} = 3.761 - 1.953\times 10^{-2} \times \text{Weight} -5.25 \times 10^{-6} \times\text{Total Income.}$$ + + +(b) Using the equations obtained from question (a), I imputed Age and Gender to BestIncome based on the SurveyIncome dataset. Since gender has to be binay, I set all imputed gende that is greater than 0.5 as 1, and others as 0. Also, I assumed that the sum of labor and capital income in BestIncome data is equivalent to the variable Total Income in SurveyIncome data. + +```{r, tidy = TRUE} +BestInc$Age <- 4.421e+01 -6.722e-03 * BestInc$Weight + 2.520e-05 * (BestInc$L_inc + BestInc$C_inc) +BestInc$Gender <- 3.761e+00 -1.953e-02 * BestInc$Weight -5.250e-06 * (BestInc$L_inc + BestInc$C_inc) + +# Since Gender has to be binary +for (i in 1:length(BestInc$Gender)){ + if (BestInc$Gender[i] < 0.5){ + BestInc$Gender[i] <- 0 + }else{ + BestInc$Gender[i] <- 1 + } +} +``` + +(c) For age, +mean: 44.89, sd = 0.219, min = 43.98, max = 45.70, no. of observation = 10000; +For Gender, +mean: 0.4614 sd = 0.499, min = 0, max = 1, no. of observation = 10000. +```{r, tidy = TRUE} +summary(BestInc$Age) +summary(BestInc$Gender) +sd(BestInc$Age) +sd(BestInc$Gender) +length(BestInc$Age) +length(BestInc$Gender) +``` + +(d) Correlation matrix: +```{r, tidy = TRUE} +res <- cor(BestInc) +round(res, 2) +``` + + +2.(a) Coefficients for intercept: 89541.293, Std.Error: 878.764 + Coefficients for GRE score: -25.763, Std.Error: 1.36 +```{r, tidy = TRUE} +salmod1 <- lm(salary ~ gre, data = IncIntel) +summary(salmod1) +``` + +(b) Due to the change in GRE's scoring system, a system drift on the data occurred at the year 2010-2011. Therefore, as indicated by the scatterplot, people's GRE scores dropped significantly due to this change. + +```{r, tidy = TRUE} +#Scatter plot of Gre scores vs. Graduation year +xyplot(gre ~ year, xlab = "Graduation year", ylab = "Gre Quantitative Scores", data = IncIntel) +``` + +To accurately test our hypothesis, we would have to rescale GRE scores to eliminate the effect of the data drift by using the percentile a person gets in the year he takes GRE test, instead of the general GRE quantitative score, to indicate his or her academic performance on a GRE test. +```{r, tidy = TRUE} +#Define a function that extract a list for each year's gre scores +grefunc <- function(yr) { + grelist <- list() + for (i in (1:nrow(IncIntel))) { + if (IncIntel$year[i] == yr) { + grelist <- append(grelist, IncIntel$gre[i]) + } + } + return(grelist) +} + +#Make a dictionary that sort each year's participants' gre scores +gredic <- list() +for (yr in (2001:2013)){ + grelist <- grefunc(yr) + gredic <- append(gredic, list(grelist)) + +} +``` + + +```{r, tidy=TRUE} +#Create a new variable gre_perc that indicates the participant's percentile GRE in that year +for (yr in (2001:2013)) { + + for (i in (1:nrow(IncIntel))) { + if (IncIntel$year[i] == yr) { + dicyr <- IncIntel$year[i] - 2000 + gredic_yr <- unlist(gredic[dicyr]) + gredic_yr_rank <- ecdf(gredic_yr) + IncIntel$gre_perc[i] <- gredic_yr_rank(IncIntel$gre[i]) + } + } +} + +xyplot(IncIntel$gre_perc ~ IncIntel$year, xlab = "Graduation year", + ylab = "Percentile GRE Quantitative Scores") +``` + + +(c) +```{r, tidy = TRUE} +#Scatterplot of the original salary vs. year +xyplot(salary ~ year, xlab = "Graduation year", ylab = "Salary after 4 years of graduation", data = IncIntel) +``` + + As indicated by the scatter plot, salary inflates gradually over the years. In that case, years is a stationarity that could confound our hypothesis testing. Therefore, we could calculate the average annual growth rate of income, and balance out this annual rate of salary growth by dividing a person's salary by the growth rate to the power of time (in years). + +```{r, tidy = TRUE} +#Control for stationarity +##Average income per year +avg_inc <- aggregate(select(IncIntel,salary), list(IncIntel$year), mean) +avg_inc + +##Average growth rate +avg_growth <- mean((avg_inc$salary[13:2] - avg_inc$salary[12:1]) / avg_inc$salary[12:1]) +IncIntel$ctrSalary <- IncIntel$salary/((1 + avg_growth)**(IncIntel$year - 2001)) +xyplot(IncIntel$ctrSalary ~ IncIntel$year) +``` + +(d) Estimated coefficients: +Intercept: 61643.2, Std.Error: 455.9; +GRE percentiles: -411, Std.Error: 782.0. + +Now the coefficient for GRE percentile, unlike that in (a), turned to be insignificant (p > 0.05). + +Due to the change we made in (b), the estimated values of both coefficients varied signifiantly as we adjusted GRE variable to a new GRE percentile variable that ranges from 0 to 1. + +Similarly, after controlling for system drift in GRE scores and the stationarity of time, the results of linear regression model suggests that GRE quantitative score is not a significant predicting factor of one's salary after 4 years of graduation. It suggests that the alternative hypothesis is likely to be rejected. + +```{r, tidy = TRUE} +adjustLm <- lm(ctrSalary ~ gre_perc, data = IncIntel) +summary(adjustLm) +``` \ No newline at end of file diff --git a/Assignments/A3/A3-1.pdf b/Assignments/A3/A3-1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f71640e19172292aa0d1276e572ce3fe918d411f GIT binary patch literal 117838 zcmce+WpE_TvZg6!YB8(C%*@QptQIpftHsRBEpD}#nVFfHnVCo5Id^8x?p(9oUsIN4 zS)S$@mHztU=3x;@svsgp%SguxL)!I}{|UnZU;x+|TEg(~0O(~bY)uRtEj&$(0gT@k zfRT}%gP8+BF9Fa7uro3M7+IJBx&V5403#ECUKGI0%E0#hLk_?UpjY|FnU#qJz{dw; zVr%@*h=BjA9~jR62t>uh-UL9ep=4tE9fpamnX@^7^*bUl3u|W+$M3VXfwPH-iIJW0 zx7WYV3I>igPJn+z5Vo^+v9WamumI>498HWZjGXNp{|T6n4?wT}Ed(Qg>HGUFgQTso ziTn2j4ge#^zim@H03-YNV<-XWmF(=C0pF7S%TWH76u`vxuK`{EEfnkjTO4{x5r8(2 z0W&9qDYG#HJDUNE5rYYbAtSr72?IL=qcNL_0V_Kr-~YFV?msDTa&|N^uz_*UGBPyY zHq$rM=YS?ja}CrO6bPsx5U~bBK9>~8zhw&J&h`(lSw$!e@{flC0rF~t;QuFk|8@8O 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individual])\n", + "minorLocator = MultipleLocator(1)\n", + "ax.xaxis.set_minor_locator(minorLocator)\n", + "plt.grid(b=True, which='major', color='0.65', linestyle='-')\n", + "plt.title('Individual Simulated Income', fontsize=10)\n", + "plt.xlabel(r'Year ($t$)')\n", + "plt.ylabel(r'Annual wealth (\\$s)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(b) 4% of the class will earn more than 100,000, and 15% of the class will earn less than 70,000." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5,1,'Histogram of Initial Income for 50-bin Simulations')" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Plot histograms for bins = 50\n", + "plt.hist(income_mat[0,:], bins = 50)\n", + "plt.xlabel(\"Income\")\n", + "plt.ylabel(\"Number of Respondents in Income Bins\")\n", + "plt.title(\"Histogram of Initial Income for 50-bin Simulations\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0417\n", + "0.1512\n" + ] + } + ], + "source": [ + "#calculate the percentages\n", + "income0 = np.ndarray.tolist(income_mat[0,:])\n", + "print(len([i for i in income0 if i > 100000]) / len(income0))\n", + "print(len([i for i in income0 if i < 70000]) / len(income0))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "290.481782626689 8.369169350300544e-64\n", + "80653.27431763953\n", + "79865.11458578068\n" + ] + } + ], + "source": [ + "#testing normality\n", + "stat,p = normaltest(income_mat[0,:])\n", + "print(stat,p)\n", + "print(np.mean(income_mat[0,:]))\n", + "print(np.median(income_mat[0,:]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "According to observation and the test performed, the distribution is normally distributed. But because the median of this distribution is less than the mean, I would say that the distribution is slightly right skewed. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(c) Only in about 16.78% of the simulations that I will be able to pay off the loan in 10 years. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.1678\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def years_to_pay_off(mat):\n", + " '''\n", + " Define a function that will return a histogram and a percentage for both question (c) and (d)\n", + " '''\n", + "\n", + " #create a payment matrix\n", + " pay_mat = mat * 0.1\n", + " pay_yr = []\n", + " \n", + " for i in range(len(pay_mat[0,:])):\n", + " yr = 1\n", + " while sum(pay_mat[:,i][:yr]) < 95000:\n", + " yr += 1\n", + " if sum(pay_mat[:,i][:yr]) >= 95000:\n", + " pay_yr.append(int(yr)) \n", + " #pay_yr returns a list with 10,000 entries of the years needed to clear the debts\n", + " break\n", + " \n", + " # plot the histogram\n", + " plt.hist(pay_yr)\n", + " plt.xlabel(\"Years to clear the debts ($t$)\")\n", + " plt.ylabel(\"No. of simulations\")\n", + " plt.title(\"Histogram for years to clear the debts\")\n", + " \n", + " #calculating percentage\n", + " print(len([i for i in pay_yr if i <= 10])/len(pay_yr))\n", + "\n", + "years_to_pay_off(income_mat)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(d) In this case, the parameters that I would use for my simulations would change to:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7602\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#new dictionary with new parameters\n", + "para_new = {\n", + " 'inc0' : 90000, #starting income\n", + " 'sigma' : 0.17, #sd of normal distributed error term\n", + " 'rho' : 0.4, #persistence\n", + " 'g' : 0.025, #growth rate\n", + " 'n_years' : 40, #years to work\n", + " 'base_year' : int(2020), #starting year\n", + " 'no_sim' : 10000 #number of simulations\n", + "}\n", + "\n", + "#calling functions defined in previous questions\n", + "income_mat_new = income_gr(para_new)\n", + "years_to_pay_off(income_mat_new)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case, 76% of the simulations would be able to pay off the loan in 10 years. " + ] + } + ], + "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": "3.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}