Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

  Market Weekly Gross Revenue
($100s) Television Advertising
($100s) Newspaper Advertising
($100s)

  Mobile 102.5 5.1 1.6

  Shreveport 52.7 3.2 3.0

  Jackson 75.8 4.0 1.5

  Birmingham 127.8 4.3 4.0

  Little Rock 137.8 3.5 4.3

  Biloxi 101.4 3.6 2.3

  New Orleans 237.8 5.0 8.4

  Baton Rouge 219.6 6.9 5.8

(a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable.

Let x represent the amount of television advertising.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

=  +  x

Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?

There  a significant relationship between the amount spent on television advertising and weekly gross revenue. The estimated regression equation is the best estimate of the  given the  .

(b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?

If required, round your answer to two decimal places.

%

(c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.

Let x₁ represent the amount of television advertising.

Let x₂ represent the amount of newspaper advertising.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

=  +  x₁ +  x₂

Test whether each of the regression parameters β₀, β₁, and β₂ is equal to zero at a 0.05 level of significance.

We  conclude that β₀ = 0.

We  conclude that β₁ = 0.

We  conclude that β₂ = 0.

What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?

(i) β₀ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β₁ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β₂ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. The interpretation of β₀ is not reasonable but the interpretations of β₁ and β₂ are reasonable.

(ii) β₀ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β₁ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β₂ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. The interpretation of β₀, β₁, and β₂ are all reasonable.

(iii) β₀ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β₁ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β₂ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. The interpretation of β₀ is not reasonable but the interpretations of β₁ and β₂ are reasonable.

(d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?

If required, round your answer to two decimal places.

%

(e) Given the results in part (a) and part (c), what should your next step be? Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(f) What are the managerial implications of these results?

Management can feel confident that increased spending on  advertising results in increased weekly gross revenue. The results also suggest that  advertising may be slightly more effective than  advertising in generating revenue.

Question

Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow.

Market	Weekly Gross Revenue ($100s)	Television Advertising ($100s)	Newspaper Advertising ($100s)
Mobile	102.5		5.1	1.6
Shreveport	52.7		3.2	3.0
Jackson	75.8		4.0	1.5
Birmingham	127.8		4.3	4.0
Little Rock	137.8		3.5	4.3
Biloxi	101.4		3.6	2.3
New Orleans	237.8		5.0	8.4
Baton Rouge	219.6		6.9	5.8

(a)

Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable.

Let x represent the amount of television advertising.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x

Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?

There a significant relationship between the amount spent on television advertising and weekly gross revenue. The estimated regression equation is the best estimate of the given the .

(b)

How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain?

If required, round your answer to two decimal places.

%

(c)

Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables.

Let x₁ represent the amount of television advertising.

Let x₂ represent the amount of newspaper advertising.

If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

= + x₁ + x₂

Test whether each of the regression parameters β₀, β₁, and β₂ is equal to zero at a 0.05 level of significance.

We conclude that β₀ = 0.

We conclude that β₁ = 0.

We conclude that β₂ = 0.

What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?

(i)	β₀ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β₁ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β₂ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. The interpretation of β₀ is not reasonable but the interpretations of β₁ and β₂ are reasonable.
(ii)	β₀ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β₁ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. β₂ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. The interpretation of β₀, β₁, and β₂ are all reasonable.
(iii)	β₀ is the estimate of the weekly gross revenue when television and newspaper advertising are both zero. β₁ is the estimate of change in the weekly gross revenue if newspaper advertising is held constant and there is a $100 increase in television advertising. β₂ is the estimate of change in the weekly gross revenue if television advertising is held constant and there is a $100 increase in newspaper advertising. The interpretation of β₀ is not reasonable but the interpretations of β₁ and β₂ are reasonable.

(d)

How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain?

If required, round your answer to two decimal places.

%

(e)

Given the results in part (a) and part (c), what should your next step be? Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(f)

What are the managerial implications of these results?

Management can feel confident that increased spending on advertising results in increased weekly gross revenue. The results also suggest that advertising may be slightly more effective than advertising in generating revenue.

Accepted Answer

Given data indicates weekly gross revenue as a function of advertising expenditures for a sample of…

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