Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (cu. ft.) and list price can be found below. Model ŷ= Model 1 Model 2 Model 3 with Thru-the-Door Ice and Water Model 4 Model 5 Model 6 with Thru-the-Door Ice and Water Model 7 Model 8 Model 9 with Thru-the-Door Ice and Water Model 10 with Thru-the-Door Ice and Water Model 11. with Thru-the-Door Ice and Water Model 12 Model 13 with Thru-the-Door Ice and Water Model 14 Model 14 Model 15 Model 16 with Thru-the-Door Ice and Water Model 17 Model 18 with Thru-the-Door Ice and Water Model 19 with Thru-the-Door Ice and Water Model 20 with Thru-the-Door Ice and Water Model 21 Ho: P₁ 20 H₂: P₂ <0 Cu.Ft. List Price Ho: P₁50 H₂: P₂ > 0 18.3 Ho: ₁0 H₂: P₁0 24.8 25.4 19.3 17.3 19.6 25.0 25.4 26.0 18.0 25.0 24.5 $1,299.99 20.2 20.2 15.5 28.2 27.8 25.6 $1,099.99 23.6 22.6 $899.99 21.8 $1,799.99 20.9 $1,799.99 $749.99 $599.99 $1,619.99 $999.99 $1,299.99 $1,299.99 $679.99 $2,199.99 $849.99 $849.99 $549.99 $2,599.99 $2,999.99 $2,399.99 (a) Develop the estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. (Round your numerical values to four decimal places. Let x₁ represent the cubic feet and y represent the list price.) $1,099.99 $1,499.99 (b) At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between list price and cubic feet. State the null and alternative hypotheses. $1,669.99
Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (cu. ft.) and list price can be found below. Model ŷ= Model 1 Model 2 Model 3 with Thru-the-Door Ice and Water Model 4 Model 5 Model 6 with Thru-the-Door Ice and Water Model 7 Model 8 Model 9 with Thru-the-Door Ice and Water Model 10 with Thru-the-Door Ice and Water Model 11. with Thru-the-Door Ice and Water Model 12 Model 13 with Thru-the-Door Ice and Water Model 14 Model 14 Model 15 Model 16 with Thru-the-Door Ice and Water Model 17 Model 18 with Thru-the-Door Ice and Water Model 19 with Thru-the-Door Ice and Water Model 20 with Thru-the-Door Ice and Water Model 21 Ho: P₁ 20 H₂: P₂ <0 Cu.Ft. List Price Ho: P₁50 H₂: P₂ > 0 18.3 Ho: ₁0 H₂: P₁0 24.8 25.4 19.3 17.3 19.6 25.0 25.4 26.0 18.0 25.0 24.5 $1,299.99 20.2 20.2 15.5 28.2 27.8 25.6 $1,099.99 23.6 22.6 $899.99 21.8 $1,799.99 20.9 $1,799.99 $749.99 $599.99 $1,619.99 $999.99 $1,299.99 $1,299.99 $679.99 $2,199.99 $849.99 $849.99 $549.99 $2,599.99 $2,999.99 $2,399.99 (a) Develop the estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. (Round your numerical values to four decimal places. Let x₁ represent the cubic feet and y represent the list price.) $1,099.99 $1,499.99 (b) At the 0.05 level of significance, test whether the estimated regression equation developed in part (a) indicates a significant relationship between list price and cubic feet. State the null and alternative hypotheses. $1,669.99
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
![**(b)**
- **Find the test statistic:** (Round your answer to two decimal places.)
[Input Box]
- **Find the p-value:** (Round your answer to four decimal places.)
[Input Box]
- **State your conclusion:**
- [ ] Reject \( H_{0} \). There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [ ] Reject \( H_{0} \). There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [ ] Do not reject \( H_{0} \). There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [✔] Do not reject \( H_{0} \). There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.
**(c)**
Develop a dummy variable that will account for whether the refrigerator has the thru-the-door ice and water feature. Code the dummy variable with a value of 1 if the refrigerator has the thru-the-door ice and water feature and with 0 otherwise. Use this dummy variable to develop the estimated multiple regression equation to show how list price is related to cubic feet and the thru-the-door ice and water feature. (Round your numerical values to four decimal places. Let \( x_1 \) represent the cubic feet, \( x_2 \) represent whether the refrigerator has the thru-the-door ice and water feature, and \( y \) represent the list price.)
\( \hat{y} = \)
[Input Box]
**(d)**
At \( \alpha = 0.05 \), is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator?
- **State the null and alternative hypotheses:**
- \[ H_{0} : \beta_{2} \geq 0 \]
- \[ H_{a} : \beta_{2} < 0 \]
- \[ H_{0} : \beta_{2} \leq 0 \]
- [✔] \[ H_{a} : \beta_{2} > 0 \]
- \[ H_{0} : \beta_{2} = 0 \]
- \[ H_{a} : \beta_{2} \neq 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2Ffa6ad657-258c-4d37-a602-37926435b5ca%2Fbm15uwl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**(b)**
- **Find the test statistic:** (Round your answer to two decimal places.)
[Input Box]
- **Find the p-value:** (Round your answer to four decimal places.)
[Input Box]
- **State your conclusion:**
- [ ] Reject \( H_{0} \). There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [ ] Reject \( H_{0} \). There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [ ] Do not reject \( H_{0} \). There is sufficient evidence to conclude there is a significant relationship between list price and cubic feet.
- [✔] Do not reject \( H_{0} \). There is insufficient evidence to conclude there is a significant relationship between list price and cubic feet.
**(c)**
Develop a dummy variable that will account for whether the refrigerator has the thru-the-door ice and water feature. Code the dummy variable with a value of 1 if the refrigerator has the thru-the-door ice and water feature and with 0 otherwise. Use this dummy variable to develop the estimated multiple regression equation to show how list price is related to cubic feet and the thru-the-door ice and water feature. (Round your numerical values to four decimal places. Let \( x_1 \) represent the cubic feet, \( x_2 \) represent whether the refrigerator has the thru-the-door ice and water feature, and \( y \) represent the list price.)
\( \hat{y} = \)
[Input Box]
**(d)**
At \( \alpha = 0.05 \), is the thru-the-door ice and water feature a significant factor in the list price of a refrigerator?
- **State the null and alternative hypotheses:**
- \[ H_{0} : \beta_{2} \geq 0 \]
- \[ H_{a} : \beta_{2} < 0 \]
- \[ H_{0} : \beta_{2} \leq 0 \]
- [✔] \[ H_{a} : \beta_{2} > 0 \]
- \[ H_{0} : \beta_{2} = 0 \]
- \[ H_{a} : \beta_{2} \neq 0
Transcribed Image Text:### Analysis of Refrigerator Models from a Retailer
---
#### Data on Refrigerator Models
Below is a table showing a random sample of refrigerator models sold by a retailer, along with their corresponding cubic feet (cu. ft.) and list price.
| Model | Cu. Ft. | List Price |
|--------|---------|--------------|
| Model 1 | 18.3 | $899.99 |
| Model 2 | 24.8 | $1,799.99 |
| Model 3 | 25.4 | $1,799.99 |
| Model 4 | 19.7 | $949.99 |
| Model 5 | 17.3 | $599.99 |
| Model 6 | 19.6 | $1,619.99 |
| Model 7 | 20.6 | $999.99 |
| Model 8 | 24.5 | $1,299.99 |
| Model 9 | 25.4 | $1,699.99 |
| Model 10 | 20.5 | $1,299.99 |
| Model 11 | 25.6 | $1,099.99 |
| Model 12 | 18.0 | $679.99 |
| Model 13 | 25.0 | $2,199.99 |
| Model 14 | 20.2 | $849.99 |
| Model 15 | 15.5 | $549.99 |
| Model 16 | 28.2 | $2,599.99 |
| Model 17 | 27.8 | $2,999.99 |
| Model 18 | 23.6 | $2,399.99 |
| Model 19 | 22.6 | $1,199.99 |
| Model 20 | 21.8 | $1,499.99 |
| Model 21 | 20.9 | $1,669.99 |
#### Analysis Tasks
(a) **Linear Regression Analysis**
Develop an estimated simple linear regression equation to show how list price is related to the independent variable cubic feet. In this analysis, \( x
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