Applied Econometrics

HW 3: RStudio

> library(readxl)

> caschool_4_1_ <- read_excel("C:/Users/Owner/Downloads/caschool (4) (1).xlsx")

> View(caschool_4_1_)

#Question 1: There are are 18 Variables in data set

#Question 2: Str= Student Teacher Ratio, and Testscr=Average Test Score

#Question 3: Before finding mean, first, seperate the data using the below commands:

> str<-caschool_4_1_$str

> testscr<-caschool_4_1_$testscr

#Then, find mean and variance using codes

> mean(str)

[1] 19.64043

> mean(testscr)

[1] 654.1565

> var(str)

[1] 3.578952

> var(testscr)

[1] 363.0301

#Question 4: Find correlation and covariance with codes cor,cov

> cor(str,testscr)

[1] -0.2263628

> cov(str,testscr)

[1] -8.159324

#Question 5: Please see scatter plot

#Question 6: Standard deviation and standard error are found using sd, and std.error

> sd(str)

[1] 1.891812

> sd(testscr)

[1] 19.05335

#to find standard error first install plotrix

> library("plotrix", lib.loc="~/R/win-library/3.5")

> std.error(str)

[1] 0.09231096

> std.error(testscr)

[1] 0.9297082

#Question 7: Regression of Testscr~str

Call:

lm(formula = testscr ~ str)

Residuals:

Min 1Q Median 3Q Max

-47.727 -14.251 0.483 12.822 48.540

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 698.9330 9.4675 73.825 < 2e-16 ***

str -2.2798 0.4798 -4.751 2.78e-06 ***

---

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 18.58 on 418 degrees of freedom

Multiple R-squared: 0.05124, Adjusted R-squared: 0.04897

F-statistic: 22.58 on 1 and 418 DF, p-value: 2.783e-06

#Population Model Equation= beta0+beta1(str)+U

#Population Model Equation for this example: testscr= 698.9330+(-2.2798)+U

#Regression Model Equation= beta0 -beta1(str)

#For this example Regression Equation= testscr= 698.9330-2.2798(str)

#Question 8: Str=20, predicted test scr = 698.9330-2.2798(20) = 652.937