Lab Assignment 7

# Import data
setwd("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 7")
PISA <- read.csv("C:/Users/Qiu J/Desktop/MSSP+DA 2021FALL/MSSP 897-002 Applied Linear Modeling/Assignment/Lab Assignment 7/PISA.csv")
Sys.setenv(language="en")

1. Estimate a regression model where Reading performance on the PISA (PISARead) is regressed on gross national income (GNI) and gross domestic product (GDP).

# Regression model
lm <- lm(PISARead ~ GNI + GDP, data=PISA)
summary(lm)

Call:
lm(formula = PISARead ~ GNI + GDP, data = PISA)

Residuals:
    Min      1Q  Median      3Q     Max 
-64.781 -12.074   5.929  16.787  44.816 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.950e+02  6.083e+00  81.381   <2e-16 ***
GNI          2.014e-04  9.587e-05   2.100   0.0430 *  
GDP         -2.063e-04  9.833e-05  -2.098   0.0431 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 28.27 on 35 degrees of freedom
Multiple R-squared:  0.1122,    Adjusted R-squared:  0.06147 
F-statistic: 2.212 on 2 and 35 DF,  p-value: 0.1246

2. Is there multicollinearity between the independent variables?

# Test for multicollinearity using Variance Inflation Factor (VIF)
library(car)
vif(lm)

     GNI      GDP 
4159.901 4159.901 

The VIF is extremely high at 4159.9, indicating a severe multicollinearity problem.

# Test for multicollinearity using correlation matrix
cor(PISA[,c("GNI","GDP")],use="complete.obs")

          GNI       GDP
GNI 1.0000000 0.9998798
GDP 0.9998798 1.0000000

The correlation matrix indicates a high correlation between independent variables. So that there is multicollinearity between the independent variables.