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:
wage = β0 + β1 educ + β2 exper + β3 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 β3 would be to regress wage on ri3, (wagei = β0 + β1 ri3), where ri3 are the residuals from a regression of age on educ and exper.
Suppose the following represents a simple regression model of wage on educ.
wage = β0 + β1 educ
where
wage = hourly wage in dollars
educ = years of education
True or False: If educ is uncorrelated with both age and exper, then β1 from the multiple regression will be the same as β1 from the simple regression.
True
False