Applied Regression Modeling

Consider the following data:

X	0.8	0.6	0.8	0.2	0.5	1.0	0.3	0.1	0.2	0.5
D1	0	0	1	1	1	0	0	0	0	0
D2	0	0	0	0	0	1	0	0	1	1
Y	1.0	0.8	2.2	1.4	1.7	3.4	0.3	0.4	1.5	1.9

D₁ and D₂ are indicator variables representing a qualitative predictor with three levels (e.g., D₁ = D₂ = 0 represents “low,” D₁ = 1 and D₂ = 0 represents “medium,” and D₁ = 0 and D₂ = 1 represents “high”). Use statistical software to fit a multiple linear regression model with response variable, Y, and predictor variables, D₁, D₂, X, D₁X, and D₂X (the last two are interaction variables). Use the fitted model to answer the following questions.

Which predictor variables have p-values for their regression parameters that are less than a significance level of 0.05 (select all that apply)?

Fit a second multiple linear regression model omitting the predictor variable with the largest p-value. For this second model, which predictor variables have p-values for their regression parameters that are less than a significance level of 0.05 (select all that apply)?

This fitted model represents three regression lines for low (D₁ = D₂ = 0), medium (D₁ = 1 and D₂ = 0), and high (D₁ = 0 and D₂ = 1). Which of the following best describes these three fitted lines?

Which expression represents the predicted (or fitted) values of Y with respect to X for low (D₁ = D₂ = 0)?

Which expression represents the predicted (or fitted) values of Y with respect to X for medium (D₁ = 1 and D₂ = 0)?

Which expression represents the predicted (or fitted) values of Y with respect to X for high (D₁ = 0 and D₂ = 1)?

Compare s, R², and adjusted R² for the second model to the first model.