Question: Question 2: Consider the data from Question 1. The following model is used:

\[y={{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}{{x}_{2}}+{{\beta }_{3}}{{x}_{1}}{{x}_{2}}+u\]

This model is known as the interaction model and the term (x1 × x2) is known as the interaction term.

a. Obtain the best fitted model and interpret the estimated coefficients.

b. Based on the result in part (a), obtain the best fitted equation for each type of client. (i.e. you will have 3 equations, one for the manufacturing client, one for the service client, and one for the government client). Plot the three best fitted equations on the same group.

c. Based on the result in part (b), explain how the interaction term affect those lines.

d. If the interaction term is not in the model, how would the plot in part (c) looks like (no calculation)?

e. At 1% level of significance, is x2 a useful variable in explaining y? (Note: think carefully what should be dropped from the model if x2 is not useful.)