Chapter 15.5, Problem 23E

Testing Significance in Theater Revenue. Refer to exercise 5.

1. a. Use α = .01 to test the hypotheses

$\begin{array}{l}{H}_0:{\beta }_1={\beta }_2=0\\ H_a:{\beta }_1\text{and/or}{\beta }_2\text{is}\text{not}\text{equal}\text{to}\text{zero}\end{array}$

for the model y = β₀ + β₁x₁ + β₂x₂ + ϵ, where

$\begin{array}{l}{x}_1=\text{television}\text{advertising}(\$1000s)\\ x_2=\text{newspaper}\text{advertising}(\$1000s)\end{array}$

1. b. Use α = .05 to test the significance of β₁. Should x₁ be dropped from the model?
2. c. Use α = .05 to test the significance of β_2. Should x₂ be dropped from the model?

5. Theater Revenue. The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

1. a. Develop an estimated regression equation with the amount of television advertising as the independent variable.
2. b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.
3. c. Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)? Interpret the coefficient in each case.
4. d. Predict weekly gross revenue for a week when $3500 is spent on television advertising and $2300 is spent on newspaper advertising.