Econometrics Lab 2
Homework 2
Janithe Siriwardana
Setup
Set working directory and activate necessary packages:
setwd("~/Desktop/R WD")
library(ggplot2)
library(stargazer)
##
## Please cite as:
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
library(data.table)
Data Analysis
Start by loading the data set and converting it to the data.table format:
load("datasets/ceosal2.RData")
dt.ceo.salaries <- data.table(data)
rm(data)
Descriptive Statistics
How many CEOs are in the sample?
nrow(dt.ceo.salaries)
## [1] 177
How many CEOs have a graduate degree?
dt.ceo.salaries[, sum(grad)]
## [1] 94
Alternatively, count the number of rows in which grad = 1
nrow(dt.ceo.salaries[grad==1,])
## [1] 94
What is the percentage of CEOs with graduate degrees?
dt.ceo.salaries[, sum(grad)]/nrow(dt.ceo.salaries)
## [1] 0.5310734
Or the mean of grad:
dt.ceo.salaries[, mean(grad)]
## [1] 0.5310734
What is the average CEO salary?
dt.ceo.salaries[, mean(salary)]
## [1] 865.8644
Alternatively:
mean(dt.ceo.salaries[, salary])
## [1] 865.8644
What is the mean CEO salary for those with a graduate degree?
dt.ceo.salaries[grad==1, mean(salary)]
## [1] 864.2128
What is the mean CEO salary for those without a graduate degree?
dt.ceo.salaries[grad==0, mean(salary)]
## [1] 867.7349
How many CEOs have/don’t have a college degree?
dt.ceo.salaries[, list(n_ceo=.N), by = college]
## college n_ceo
## 1: 1 172
## 2: 0 5
Can we say that the mean salary is statistically different from 800?
t.test(dt.ceo.salaries[, salary], mu = 800)
##
## One Sample t-test
##
## data: dt.ceo.salaries[, salary]
## t = 1.4913, df = 176, p-value = 0.1377
## alternative hypothesis: true mean is not equal to 800
## 95 percent confidence interval:
## 778.7015 953.0274
## sample estimates:
## mean of x
## 865.8644
P-value = 0.1377 > 0.05 so we cannot reject the null hypothesis that the population mean is 800. Additionally, 800 is within the 95% confidence interval.
Is the average salary different for CEOs with a graduate degree and those without?
t.test(dt.ceo.salaries[, salary] ~ dt.ceo.salaries[, grad])
##
## Welch Two Sample t-test
##
## data: dt.ceo.salaries[, salary] by dt.ceo.salaries[, grad]
## t = 0.038973, df = 149.94, p-value = 0.969
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -175.0489 182.0932
## sample estimates:
## mean in group 0 mean in group 1
## 867.7349 864.2128
Alternatively:
dt.ceo.salaries[ , t.test (salary ~ grad)]
##
## Welch Two Sample t-test
##
## data: salary by grad
## t = 0.038973, df = 149.94, p-value = 0.969
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -175.0489 182.0932
## sample estimates:
## mean in group 0 mean in group 1
## 867.7349 864.2128
Alternatively:
t.test(dt.ceo.salaries[grad==0, salary] , dt.ceo.salaries[grad==1, salary])
##
## Welch Two Sample t-test
##
## data: dt.ceo.salaries[grad == 0, salary] and dt.ceo.salaries[grad == 1, salary]
## t = 0.038973, df = 149.94, p-value = 0.969
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -175.0489 182.0932
## sample estimates:
## mean of x mean of y
## 867.7349 864.2128
P-value = 0.969 > 0.05 so we cannot reject the null hypothesis that the population means are the same. Additionally, 0 is within the 95% confidence interval.
Create a table with descriptive statistics
dt.ceo.salaries[, list( mean_salary = mean(salary)
, sd_salary = sd(salary)
, min_salary = min(salary)
, max_salary = max(salary)
, median_salary = median(salary))]
## mean_salary sd_salary min_salary max_salary median_salary
## 1: 865.8644 587.5893 100 5299 707
You can also compute the summary statistics for different groups:
dt.ceo.salaries[, list( mean_salary = mean(salary)
, sd_salary = sd(salary)
, min_salary = min(salary)
, max_salary = max(salary)), by = list(grad, college)]
## grad college mean_salary sd_salary min_salary max_salary
## 1: 1 1 864.2128 501.3924 100 2265
## 2: 0 1 853.0897 679.0268 174 5299
## 3: 0 0 1096.2000 633.4569 300 1738
Alternatively, you can use the stargazer function to get summary statistics for all variables in the data set:
stargazer(dt.ceo.salaries, type = "text")
##
## ===================================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## -------------------------------------------------------------------
## salary 177 865.864 587.589 100 471 1,119 5,299
## age 177 56.429 8.422 33 52 62 86
## college 177 0.972 0.166 0 1 1 1
## grad 177 0.531 0.500 0 0 1 1
## comten 177 22.503 12.295 2 12 33 58
## ceoten 177 7.955 7.151 0 3 11 37
## sales 177 3,529.463 6,088.654 29 561 3,500 51,300
## profits 177 207.831 404.454 -463 34 208 2,700
## mktval 177 3,600.316 6,442.276 387 644 3,500 45,400
## lsalary 177 6.583 0.606 4.605 6.155 7.020 8.575
## lsales 177 7.231 1.432 3.367 6.330 8.161 10.845
## lmktval 177 7.399 1.133 5.958 6.468 8.161 10.723
## comtensq 177 656.684 577.123 4 144 1,089 3,364
## ceotensq 177 114.124 212.566 0 9 121 1,369
## profmarg 177 6.420 17.861 -203.077 4.231 10.947 47.458
## -------------------------------------------------------------------
You can also get summary statistics for a subset of observations and for a specific list of variables:
stargazer(dt.ceo.salaries[grad==1, list(age, salary)], type="text")
##
## =========================================================
## Statistic N Mean St. Dev. Min Pctl(25) Pctl(75) Max
## ---------------------------------------------------------
## age 94 55.457 8.155 38 50 61 86
## salary 94 864.213 501.392 100 481.5 1,167.8 2,265
## ---------------------------------------------------------
Quick plots
Histogram
Salary
qplot( data = dt.ceo.salaries
, x = salary
, geom = "histogram")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Age
qplot( data = dt.ceo.salaries
, x = age
, geom = "histogram")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scatterplot
qplot( data = dt.ceo.salaries
, x = sales
, y = profits
, geom = "point")
Barplot
qplot( data = dt.ceo.salaries
, x = factor(grad)
, geom = "bar")
Line
qplot( data = dt.ceo.salaries
, x = sales
, y = profits
, geom = "line")
Facet Wrap
qplot( data = dt.ceo.salaries
, x = salary
, geom = "histogram") + facet_wrap(~ grad)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Customising plots:
Salary
qplot( data = dt.ceo.salaries
, x = salary
, geom = "histogram"
, fill = factor(grad, levels = c(0,1), labels = c("Yes", "No"))) +
theme_bw() +
ylim(0,50) +
xlim(0, 4000) +
labs( title = "MY PLOT", x = "CEO Salary", y = "Number of CEOs", fill = "Grad. Degree")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 1 rows containing non-finite values (stat_bin).
## Warning: Removed 4 rows containing missing values (geom_bar).
