ASSIGNMENT: Homework $($Ch $03)$

$5.$ Comparison of simple and multiple regression estimates

Suppose you are interested in studying the factors that influence wages. You plan on using a multiple regression model with $k=3$ explanatory variables. In particular, you plan on estimating:

widehat$($ wage $)=$widehat$({}_0)+$widehat$({}_1)$ educ $+$widehat$({}_2)exper+$widehat$({}_3)$ age

where

wage $=$ hourly wage in dollars

educ $=$ years of education

exper $=$ years of work experience

age $=$ age, in years

An alternative way of estimating widehat$({}_2)$ would be to regress wage on widehat$(r_{i2}),($wage wa $($:${?}_i={}_0+{}_1(widehat(r_{i2}))\},$ where widehat$(r_{i2})$ are the residuals from a regression of

Suppose the following represents a simple regression model of wage on educ.