Question

Do movies of different types have different rates of return on their budgets?

The response variable: US Gross( $M)

Explanatory variable:   Budget ( $M)

Categorical variable :  Type of movie : Comedy =1 ; Action Picture =0.

Using the regression output with an indicator variable:

MODEL 1:

Summary of Fit

RSquare	0.318
RSquare Adj	0.338
Root Mean Square Error	46.50
Mean of Response
Number of observations	58

Parameter Estimates

Term	Estimate	Std Error	t Ratio	Prob>|t|
Intercept	-7.03913	16.20	-0.435	0.6655*
Budget( $M)	1.0048	0.1895	5.30	<.0001*
Comedy	25.4175	10.62	2.397	<.00204*

Model 2:

Summary of Fit

RSquare	0.41
RSquare Adj	0.374
Root Mean Square Error	58.45
Mean of Response
Number of observations	58

Parameter Estimates

Term	Estimate	Std Error	t Ratio	Prob>|t|
Intercept	-13.28	29.20	-0.455	0.6512*
Budget( $M)	1.589	0.3457	4.60	<.0001*
Budget*Comedy	-0.652	0.4863	-1.34	<.1857
Comedy	34.479	33.85	1.02	0.3134

1. (Model 1) Write out the sample regression  equation and write separate equations for each type of movies.
2. (Model 1) In this regression, the variable Comedy is an indicator variable that is 1 for movies that are comedies. How would you interpret the coefficients  of Comedy  and Budget($M)?
3. (Model 1) What null Hypothesis can we test with the t-test  for Comedy? State conclusion.
4. (Model 2) Write out the sample regression equation and write separate equations for each type of movies.:
5. (Model 2) In this regression, the variable Budget*Comedy is an interaction term. How would you interpret the coefficient of Budget*Comedy?
6. (Model2) What Null Hypothesis can we test with the t-test for Budget*Comedy? State conclusion
7. Which model will you choose (Model1 or  Model2)?  Make decision either based on R²adj, or an F-partial test , or the t-test from part f)

Answer 1