Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. SSE SST ŷ= 30.21 + 1.59 b. Test whether revenue and advertising expenditures are related at a 0.05 level of significance. Compute the following (to 2 decimals). SSR a. Let equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables (t decimals). MSR X X X x MSE Compute the F test statistic (to 2 decimals). Advertising Expenditures What is the p-value? Use Table 4 from Appendix B. between 0.01 and 0.025 1 2 4 6 10 14 20 Revenue 20 32 45 40 53 54 55
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. SSE SST ŷ= 30.21 + 1.59 b. Test whether revenue and advertising expenditures are related at a 0.05 level of significance. Compute the following (to 2 decimals). SSR a. Let equal advertising expenditures and y equal revenue. Use the method of least squares to develop a straight line approximation of the relationship between the two variables (t decimals). MSR X X X x MSE Compute the F test statistic (to 2 decimals). Advertising Expenditures What is the p-value? Use Table 4 from Appendix B. between 0.01 and 0.025 1 2 4 6 10 14 20 Revenue 20 32 45 40 53 54 55
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Analysis of Advertising Expenditures and Revenue for the Four Seasons Restaurant
Below is the data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant:
| Advertising Expenditures (x) | Revenue (y) |
|-------------------------------|-------------|
| 1 | 20 |
| 2 | 32 |
| 4 | 45 |
| 6 | 40 |
| 10 | 53 |
| 14 | 54 |
| 20 | 55 |
---
#### Task a:
**Objective:** Develop a straight line approximation of the relationship between advertising expenditures (x) and revenue (y) using the method of least squares.
The resulting linear equation is:
\[ \hat{y} = 30.21 + 1.59x \]
---
#### Task b:
**Objective:** Test whether revenue and advertising expenditures are related at a 0.05 level of significance.
**Steps to compute (to 2 decimal places):**
1. **Sum of Squared Errors (SSE):**
\[ \text{(Input box unavailable for direct value input)} \]
2. **Total Sum of Squares (SST):**
\[ \text{(Input box unavailable for direct value input)} \]
3. **Regression Sum of Squares (SSR):**
\[ \text{(Input box unavailable for direct value input)} \]
4. **Mean Square Regression (MSR):**
\[ \text{(Input box unavailable for direct value input)} \]
5. **Mean Square Error (MSE):**
\[ \text{(Input box unavailable for direct value input)} \]
6. **Compute the F test statistic:**
\[ \text{(Input box unavailable for direct value input)} \]
**Determine the p-value:**
Use Table 4 from [Appendix B](#).
Given the F-test result, the p-value is:
\[ \text{between 0.01 and 0.025} \]
---
This structured approach enables learners to understand the process of determining the relation between two quantitative variables through statistical analysis and hypothesis testing. By following these steps, students can grasp the methodology for establishing and verifying linear relationships in business and economic data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc3ad949-79b2-4a66-83f9-922936cf2321%2Fed28efa3-fc02-45fc-9408-aa65693dfe3e%2Fjcuuf9f_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Advertising Expenditures and Revenue for the Four Seasons Restaurant
Below is the data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant:
| Advertising Expenditures (x) | Revenue (y) |
|-------------------------------|-------------|
| 1 | 20 |
| 2 | 32 |
| 4 | 45 |
| 6 | 40 |
| 10 | 53 |
| 14 | 54 |
| 20 | 55 |
---
#### Task a:
**Objective:** Develop a straight line approximation of the relationship between advertising expenditures (x) and revenue (y) using the method of least squares.
The resulting linear equation is:
\[ \hat{y} = 30.21 + 1.59x \]
---
#### Task b:
**Objective:** Test whether revenue and advertising expenditures are related at a 0.05 level of significance.
**Steps to compute (to 2 decimal places):**
1. **Sum of Squared Errors (SSE):**
\[ \text{(Input box unavailable for direct value input)} \]
2. **Total Sum of Squares (SST):**
\[ \text{(Input box unavailable for direct value input)} \]
3. **Regression Sum of Squares (SSR):**
\[ \text{(Input box unavailable for direct value input)} \]
4. **Mean Square Regression (MSR):**
\[ \text{(Input box unavailable for direct value input)} \]
5. **Mean Square Error (MSE):**
\[ \text{(Input box unavailable for direct value input)} \]
6. **Compute the F test statistic:**
\[ \text{(Input box unavailable for direct value input)} \]
**Determine the p-value:**
Use Table 4 from [Appendix B](#).
Given the F-test result, the p-value is:
\[ \text{between 0.01 and 0.025} \]
---
This structured approach enables learners to understand the process of determining the relation between two quantitative variables through statistical analysis and hypothesis testing. By following these steps, students can grasp the methodology for establishing and verifying linear relationships in business and economic data.
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