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# Earnings Regression with Multicollinearity Tests #
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# clean all variables
rm(list=ls())

# options and libraries
library(readxl)
library(car) 

# read data
setwd("c:/Documents/Classes/Econ4230/R_and_Stata/")
data = read_excel("Data/wage.xlsx")

# check for missing values
colSums(is.na(data))

# scatterplot matrix
pairs(data)

#correlation matrix
cor(data)

# correlation matrix on rhs variables only
agesq = data$age^2
rhs = data.frame(agesq, age = data$age, exp = data$exp, grade = data$grade, union = data$union)
cor(rhs)

# original regression
regOrig = lm(wage ~ age + agesq + grade + union, data)
     
# calculate VIFs using CAR package
vif(regOrig)

# calculate VIFs by hand

    # auxillary regressions
    regAge = lm(age ~ agesq + grade + union, data)
    regGrade = lm(grade ~ age + agesq + union, data)
    regUnion = lm(union ~ grade + age + agesq, data)
    
    # calculate VIFs
    VIFage = 1/(1-summary(regAge)$r.squared)
    VIFgrade = 1/(1-summary(regGrade)$r.squared)
    VIFunion = 1/(1-summary(regUnion)$r.squared)