/***************************************************************
ECO375 Example
Topic 4: Multiple Regression Model
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* a simple random variable called mars generated and compare the R square between with/without it 
clear all
set seed 12345678
use http://bigblue.depaul.edu/jlee141/econdata/eco375/wage1

* Multiple Regression Model
regr wage educ exper

* Generate a random variable
gen mars = rnormal(0,1)

* Multiple Regression with Mars
regr wage educ exper mars

* Multiple Regression with tenure
regr wage educ exper tenure

* Retricted F test Ho: b2=b3 =0
test exper tenure

* Manual Calculation of Restricted F Statistic
display [(5980.68 - 4966.30)/2]/[4966.30/522]

* Residuals Comparison for three models 
quietly regr wage educ 
predict ei1, resid

quietly regr wage educ exper
predict ei2, resid

quietly regr wage educ exper tenure
predict ei3, resid

* Summary Stat for the residuals 
sum ei* 

hist ei1, normal bin(16) saving(ei1, replace)
hist ei2, normal bin(16) saving(ei2, replace)
hist ei3, normal bin(16) saving(ei3, replace)
graph combine ei1.gph ei2.gph ei3.gph, xcommon col(1) ycommon