A statistical program is recommended. 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. Weekly Television Newspaper Gross Advertising Advertising Revenue ($1,000s) ($1,000s) ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s and y represent the weekly gros revenue in $1,000s.) 988.64 +1.60x1 X (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) ŷ= 83.23 +2.29x + 1.30x2 (e) Is the estimated regression equation coefficient for television advertising expenditures the same in nart (a) and in part (h)?
A statistical program is recommended. 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. Weekly Television Newspaper Gross Advertising Advertising Revenue ($1,000s) ($1,000s) ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 (a) Develop an estimated regression equation with the amount of television advertising as the independent variable. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s and y represent the weekly gros revenue in $1,000s.) 988.64 +1.60x1 X (b) Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. (Round your numerical values to two decimal places. Let x, represent the amount of television advertising in $1,000s, x₂ represent the amount of newspaper advertising in $1,000s, and y represent the weekly gross revenue in $1,000s.) ŷ= 83.23 +2.29x + 1.30x2 (e) Is the estimated regression equation coefficient for television advertising expenditures the same in nart (a) and in part (h)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Regression Analysis for Showtime Movie Theaters, Inc.
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 are provided below.
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($1,000s) |
|--------------------------------|----------------------------------|----------------------------------|
| 85 | 5.0 | 1.5 |
| 90 | 2.0 | 2.0 |
| 92 | 4.0 | 1.5 |
| 95 | 2.5 | 2.5 |
| 95 | 3.0 | 3.3 |
| 90 | 5.5 | 2.0 |
| 102 | 3.0 | 4.0 |
| 94 | 2.5 | 4.2 |
#### (a) Estimated Regression Equation (Television Advertising Only)
Develop an estimated regression equation with the amount of television advertising as the independent variable. Using the data provided, the regression equation is calculated as:
\[ \hat{y} = 88.64 + 1.60x_1 \]
where \( x_1 \) represents the amount of television advertising in $1,000s and \( \hat{y} \) represents the weekly gross revenue in $1,000s.
#### (b) Estimated Regression Equation (Television and Newspaper Advertising)
Next, an estimated regression equation is developed with both television advertising and newspaper advertising as independent variables. The regression equation is:
\[ \hat{y} = 83.23 + 2.29x_1 + 1.30x_2 \]
where \( x_1 \) represents the amount of television advertising in $1,000s, \( x_2 \) represents the amount of newspaper advertising in $1,000s, and \( \hat{y} \) represents the weekly gross revenue in $1,000s.
#### (c) Comparison of Coefficients
Finally, we compare the estimated regression equation coefficient for television advertising expenditures in part (a) and part (b). In part (a), the coefficient for television advertising (\( x_1 \))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac470ff6-15fd-4fdc-a5f2-c97f7b5a1d30%2Fe00d8b66-9e3d-4b8a-8268-7394893e3389%2Fwtlijt9_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis for Showtime Movie Theaters, Inc.
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 are provided below.
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($1,000s) |
|--------------------------------|----------------------------------|----------------------------------|
| 85 | 5.0 | 1.5 |
| 90 | 2.0 | 2.0 |
| 92 | 4.0 | 1.5 |
| 95 | 2.5 | 2.5 |
| 95 | 3.0 | 3.3 |
| 90 | 5.5 | 2.0 |
| 102 | 3.0 | 4.0 |
| 94 | 2.5 | 4.2 |
#### (a) Estimated Regression Equation (Television Advertising Only)
Develop an estimated regression equation with the amount of television advertising as the independent variable. Using the data provided, the regression equation is calculated as:
\[ \hat{y} = 88.64 + 1.60x_1 \]
where \( x_1 \) represents the amount of television advertising in $1,000s and \( \hat{y} \) represents the weekly gross revenue in $1,000s.
#### (b) Estimated Regression Equation (Television and Newspaper Advertising)
Next, an estimated regression equation is developed with both television advertising and newspaper advertising as independent variables. The regression equation is:
\[ \hat{y} = 83.23 + 2.29x_1 + 1.30x_2 \]
where \( x_1 \) represents the amount of television advertising in $1,000s, \( x_2 \) represents the amount of newspaper advertising in $1,000s, and \( \hat{y} \) represents the weekly gross revenue in $1,000s.
#### (c) Comparison of Coefficients
Finally, we compare the estimated regression equation coefficient for television advertising expenditures in part (a) and part (b). In part (a), the coefficient for television advertising (\( x_1 \))
Transcribed Image Text:**Understanding Regression Coefficients in Advertising Expenditure Models**
---
**(c) Estimating Regression Equation Coefficients for Television Advertising**
- **Question:** Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and in part (b)?
- **Options:**
- No: *Correct Answer Checked*
- Coefficient in part (a): `it is 1.60` (correct answer checked)
- Coefficient in part (b): `it is 2.29` (correct answer checked)
**Interpretation of Coefficients:**
- **Options:**
1. In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant.
2. In part (a) it represents the change in revenue due to a one-unit increase in television advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant.
3. In part (a) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant.
4. In part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising with television advertising held constant. In part (b) it represents the change in revenue due to a one-unit increase in television advertising expenditure.
5. In part (a) it represents the change in revenue due to a one-unit increase in newspaper advertising expenditure. In part (b) it represents the change in revenue due to a one-unit increase in television advertising with newspaper advertising held constant.
**(d) Prediction of Weekly Gross Revenue:**
- **Question:** Predict weekly gross revenue (in dollars) for a week when $3,300 is spent on television advertising and $1,500 is spent on newspaper advertising. (Round your answer to the nearest cent.)
- **Response:** $94
**Detailed Explanation:**
- **Part (c):** This part examines whether the coefficient for television advertising expenditure is consistent between part (a) and part (b) of an analysis.
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