Question

Consider the Binary Dummy Variable Gender which takes the values “M” and “F”. In a Linear Regression with the dependent variable the amount contributed to political campaigns in the last election, Gender is interacted with Years of Education. Suppose the excluded category for Gender is “F”. If the coefficient on Gender is −$44.55, the coefficient on Years of Education is $21.78, and the coefficient on the Interaction Term, Years of Education*Gender is $10.23, what is the relationship between Years of Education and variable the amount contributed to political campaigns in the last election for a person whose Gender is category “M”?

Group of answer choices

One more Year of Education reduces campaign contributions by −$44.55

One more Year of Education increases campaign contributions by $10.23

One more Year of Education increases campaign contributions by $21.78

One more Year of Education increases campaign contributions by $32.01

Answer 1

The Binary Dummy Variable Gender takes the values “M” and “F”.

Also given that:

Suppose the excluded category for Gender is “F”. Then Gender=0 means female and Gender=1 means male.

And, we are further given that Gender is interacted with Years of Education. They also are used individually in the regression.

Hence, we can write the structural equation as something like:

where

camp is the amount contributed to political campaigns in the last election

u is the residual error term

The estimated equation is something like:

We have to find he relationship between Years of Education and the amount contributed to political campaigns in the last election for a person whose Gender is category “M”

Since, Female is the reference group, gender=1 means male M.

So, let us put gender=1 in the above estimated equation.

or,

or,

Hence, the coefficient of education gives us:

One more Year of Education increases campaign contributions by $32.01 for a person who is a male.

This is gotten as: