Applied Regression Modeling

3rd edition

Iain Pardoe

A concise, comprehensive treatment of the application of statistical regression analysis suitable for undergraduate and graduate students. Covers simple linear regression, multiple linear regression, model building, and advanced regression topics.

by Iain P
on July 30, 2021

Answer the following questions based on Section 5.4: Model selection.

Consider the estimated regression equation:

Y-hat = 1.4 + 0.3 D1 + 0.7 D2 + 0.6 X1 + 0.2 D1X1 + 0.2 X12 + 0.1 D2 X12 + 0.5 X2 – 0.3 D1X2.

D1 and D2 are indicator variables where D1 = D2 = 0 represents “low,” D1 = 1 and D2 = 0 represents “medium,” and D1 = 0 and D2 = 1 represents “high.”

X1 is a quantitative predictor variable with sample mean 2 and X2 is a quantitative predictor variable with sample mean 4.

1. 

Consider how predicted Y changes as X1 changes according to the estimated regression equation. First, consider an individual in the “low” category with X2 = 4 (the sample mean). Derive the “X1 effect” for this individual.

2. 

Next, consider an individual in the “medium” category with X2 = 4 (the sample mean). Derive the “X1 effect” for this individual.

3. 

Next, consider an individual in the “high” category with X2 = 4 (the sample mean). Derive the “X1 effect” for this individual.

4. 

What would a predictor effect plot for X1 look like?

5. 

Consider how predicted Y changes as X2 changes according to the estimated regression equation. First, consider an individual in the “low” category with X1 = 2 (the sample mean). Derive the “X2 effect” for this individual.

6. 

Next, consider an individual in the “medium” category with X1 = 2 (the sample mean). Derive the “X2 effect” for this individual.

7. 

Next, consider an individual in the “high” category with X1 = 2 (the sample mean). Derive the “X2 effect” for this individual.

8. 

What would a predictor effect plot for X2 look like?

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