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
D	0	0	1	0	0	1	1	0	1	1
Y	1.1	0.7	2.9	0.1	0.9	4.0	1.8	0.3	1.4	2.8

D is an indicator variable representing a qualitative predictor with two levels (e.g., D = 0 represents “low” and D = 1 represents “high”). Use statistical software to fit a multiple linear regression model with response variable, Y, and predictor variables, D, X, and DX (interaction variable). Use the fitted model to answer the following questions.

Which p-value indicates that the linear association between Y and X differs between D = 0 and D = 1?

Which of the following best describes the fitted model?

Which expression represents the predicted (or fitted) values of Y with respect to X when D = 0?

Which expression represents the predicted (or fitted) values of Y with respect to X when D = 1?

Define D^* = 1 – D (i.e., D^* = 0 represents “high” and D^* = 1 represents “low”). Which expression represents the estimated regression equation for a simple linear regression model with response variable, Y, and predictor variables, D^*, X, and D^*X?