Multiple Regression Forecast This is straightforward enough just reading off the coefficients table.

Parker Pitts 2022-09-27 Answered
Multiple Regression Forecast
"Part C: asks what salary would you forecast for a man with 12 years of education, 10 months of experience, and 15 months with the company."
This is straight forward enough just reading off the coefficients table. y = 3526.4 + ( 722.5 ) ( 1 ) + ( 90.02 ) ( 12 ) + ( 1.269 ) ( 10 ) + ( 23.406 ) ( 15 ) = 5692.92
"Part D: asks what salary would you forecast for men with 12 years of education, 10 months of experience, and 15 months with the company."
I know that the answer to this must be different from C, but I have no idea why, I would of just done exactly the same as in part C,
What is wrong with my train of thought or intuition and how might I go about calculating the salary for men, rather than a man?
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Answered 2022-09-28 Author has 9 answers
To the best of my knowledge, the point estimator will not differ. However, I guess there should be further questions regarding the CI or the variance of the forecasted value. That will be different of each other. This difference stems from the fact that the second forecast is for the mean value, i.e., E [ y ] = β 0 + j = 1 p β j x, (assuming E ϵ = 0) while the first one is for an individual, i.e., y = β 0 + j = 1 p β j x + ϵ. As such, the individual case should account implicitly for the variance of ϵ, while the mean/expectation case (men) won't.
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