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 Revenue Gross Advertising Advertising ($1,000s) ($1,000s) ($1,000s) 96 90 95 92 95 94 94 94 5.0 X 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 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 x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) (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 x₁ 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=
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 Revenue Gross Advertising Advertising ($1,000s) ($1,000s) ($1,000s) 96 90 95 92 95 94 94 94 5.0 X 2.0 4.0 2.5 3.0 3.5 2.5 3.0 1.5 2.0 1.5 2.5 3.3 2.3 4.2 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 x₁ represent the amount of television advertising in $1,000s and y represent the weekly gross revenue in $1,000s.) (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 x₁ 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=
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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Question
![### Regression Analysis for Advertising Expenditures
#### Part (b)
**Task:** Develop an estimated regression equation with both television advertising and newspaper advertising as independent variables.
- **Variables:**
- \( x_1 \): Amount of television advertising in \$1,000s
- \( x_2 \): Amount of newspaper advertising in \$1,000s
- \( y \): Weekly gross revenue in \$1,000s
- **Equation Form:**
- \( \hat{y} = \) [Blank for input]
#### Part (c)
**Question:** Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and part (b)?
- **Answer Options:**
- No [Selected]
- **Interpretation of the Coefficient:**
- [Correct Answer Selected]
- 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.
#### Part (d)
**Prediction Task:**
- **Objective:** Predict the weekly gross revenue (in dollars) for a week when \$3,100 is spent on television advertising and \$1,800 is spent on newspaper advertising.
- **Output:** \$ [Blank for input] (round your answer to the nearest cent; incorrect attempt indicated)
This regression analysis assists in understanding the impact of different advertising mediums on revenue, allowing for informed decision-making in allocating advertising budgets.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2F5c2577c0-0dc5-4db3-8c55-254758803600%2Fnnpwxx_processed.png&w=3840&q=75)
Transcribed Image Text:### Regression Analysis for Advertising Expenditures
#### Part (b)
**Task:** Develop an estimated regression equation with both television advertising and newspaper advertising as independent variables.
- **Variables:**
- \( x_1 \): Amount of television advertising in \$1,000s
- \( x_2 \): Amount of newspaper advertising in \$1,000s
- \( y \): Weekly gross revenue in \$1,000s
- **Equation Form:**
- \( \hat{y} = \) [Blank for input]
#### Part (c)
**Question:** Is the estimated regression equation coefficient for television advertising expenditures the same in part (a) and part (b)?
- **Answer Options:**
- No [Selected]
- **Interpretation of the Coefficient:**
- [Correct Answer Selected]
- 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.
#### Part (d)
**Prediction Task:**
- **Objective:** Predict the weekly gross revenue (in dollars) for a week when \$3,100 is spent on television advertising and \$1,800 is spent on newspaper advertising.
- **Output:** \$ [Blank for input] (round your answer to the nearest cent; incorrect attempt indicated)
This regression analysis assists in understanding the impact of different advertising mediums on revenue, allowing for informed decision-making in allocating advertising budgets.
![**Explanation of Weekly Gross Revenue and Advertising Expenditures**
The owner of Showtime Movie Theaters, Inc., is aiming to predict weekly gross revenue based on advertising expenditures. Below is the historical data from a sample of eight weeks:
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($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 |
**Tasks:**
(a) **Regression Equation with Television Advertising:**
Develop an estimated regression equation where the amount of television advertising is the independent variable. Round the numerical values to two decimal places. Let \( x_1 \) denote the amount of television advertising in $1,000s, and \( y \) denote the weekly gross revenue in $1,000s.
\[ \hat{y} = \]
(b) **Regression Equation with Both Advertising Types:**
Develop an estimated regression equation considering both television and newspaper advertising as independent variables. Round the numerical values to two decimal places. Let \( x_1 \) represent the amount of television advertising in $1,000s, \( x_2 \) represent the amount of newspaper advertising in $1,000s, and \( y \) represent the weekly gross revenue in $1,000s.
\[ \hat{y} = \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2F5c2577c0-0dc5-4db3-8c55-254758803600%2Fh4ysut_processed.png&w=3840&q=75)
Transcribed Image Text:**Explanation of Weekly Gross Revenue and Advertising Expenditures**
The owner of Showtime Movie Theaters, Inc., is aiming to predict weekly gross revenue based on advertising expenditures. Below is the historical data from a sample of eight weeks:
| Weekly Gross Revenue ($1,000s) | Television Advertising ($1,000s) | Newspaper Advertising ($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 |
**Tasks:**
(a) **Regression Equation with Television Advertising:**
Develop an estimated regression equation where the amount of television advertising is the independent variable. Round the numerical values to two decimal places. Let \( x_1 \) denote the amount of television advertising in $1,000s, and \( y \) denote the weekly gross revenue in $1,000s.
\[ \hat{y} = \]
(b) **Regression Equation with Both Advertising Types:**
Develop an estimated regression equation considering both television and newspaper advertising as independent variables. Round the numerical values to two decimal places. Let \( x_1 \) represent the amount of television advertising in $1,000s, \( x_2 \) represent the amount of newspaper advertising in $1,000s, and \( y \) represent the weekly gross revenue in $1,000s.
\[ \hat{y} = \]
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