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. Cu.Ft. List Price Model 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 18.3 24.8 25.4 19.3 17.3 19.6 25.0 24.5 25.4 26.0 $899.99 18.0 $1,799.99 $1,799.99 $749.99 $599.99 $1,619.99 $999.99 $1,299.99 $1,299.99 $1,299.99 25.6 $1,099.99 $679.99 Model 16 with Thru-the-Door Ice and Water Model 17 Model 18 with Thru-the-Door Ice and Water Model 20 with Thru-the-Door Ice and Water Model 21 Model 19 with Thru-the-Door Ice and Water 22.6 28.2 Ho: B₂ 20 H₂₂ <0 27.8 x Ho: B₂ So H₂: ₂0 23.6 21.8 $2,599.99 $2,999.99 $2,399.99 20.9 (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 represent the cubic feet and y represent the list price.) 9-1604.75x+134.203x $1,099.99 $1,499.99 $1,669.99 (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.
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. Cu.Ft. List Price Model 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 18.3 24.8 25.4 19.3 17.3 19.6 25.0 24.5 25.4 26.0 $899.99 18.0 $1,799.99 $1,799.99 $749.99 $599.99 $1,619.99 $999.99 $1,299.99 $1,299.99 $1,299.99 25.6 $1,099.99 $679.99 Model 16 with Thru-the-Door Ice and Water Model 17 Model 18 with Thru-the-Door Ice and Water Model 20 with Thru-the-Door Ice and Water Model 21 Model 19 with Thru-the-Door Ice and Water 22.6 28.2 Ho: B₂ 20 H₂₂ <0 27.8 x Ho: B₂ So H₂: ₂0 23.6 21.8 $2,599.99 $2,999.99 $2,399.99 20.9 (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 represent the cubic feet and y represent the list price.) 9-1604.75x+134.203x $1,099.99 $1,499.99 $1,669.99 (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.
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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Transcribed Image Text:**Transcription for Educational Website**
---
**Retailer Refrigerators Data Analysis**
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 | Cu. Ft. | List Price |
|---------------------------------------|---------|-------------|
| Model 1 | 18.3 | $899.99 |
| Model 2 | 24.8 | **$1,799.99** |
| Model 3 with Thru-the-Door Ice and Water | 24.5 | **$1,799.99** |
| Model 4 | 19.7 | $649.99 |
| Model 5 | 17.3 | $599.99 |
| Model 6 with Thru-the-Door Ice and Water | 19.6 | $1,619.99 |
| Model 7 | 20.5 | $999.99 |
| Model 8 | 24.5 | $1,299.99 |
| Model 9 with Thru-the-Door Ice and Water | 25.4 | $1,599.99 |
| Model 10 with Thru-the-Door Ice and Water| 26.0 | $1,299.99 |
| Model 11 with Thru-the-Door Ice and Water| 25.6 | $1,099.99 |
| Model 12 | 18.0 | **$679.99** |
| Model 13 with Thru-the-Door Ice and Water| 25.0 | $1,199.99 |
| Model 14 | 20.2 | $949.99 |
| Model 15 | 15.5 | $549.99 |
| Model 16 with Thru-the-Door Ice and Water| 28.2 | $2,599.99 |
| Model 17 | 27.8 | $2,399.99 |
| Model 18 with Thru-the-Door Ice and Water| 23.6 | $2,399.99 |
| Model 19 | 21.6
![## Statistical Analysis of Refrigerator Pricing
### (b) Test for a Relationship between List Price and Cubic Feet
**Find the test statistic.**
(Round your answer to two decimal places.)
**Answer:** 4.44
**Find the p-value.**
(Round your answer to four decimal places.)
**Answer:** 0.0003
**State your conclusion.**
- **Options:**
- 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.**
**Conclusion:** Do not reject \( H_0 \).
### (c) Development of a Dummy Variable
To assess the influence of the thru-the-door ice and water feature on list price, we develop a dummy variable. Code this variable as 1 if the refrigerator has the feature; otherwise, use 0.
Using this dummy variable, apply the following regression equation to estimate how list price is related to cubic feet, along with the thru-the-door feature:
\[
\hat{y} = -1525.37 + 129.0112x_1 + 79.81081x_2
\]
- \( x_1 \): Cubic feet
- \( x_2 \): Thru-the-door ice and water feature (dummy variable)
- \( \hat{y} \): Estimated list price
### (d) Significance of the Thru-the-Door Ice and Water Feature
**Test at \(\alpha = 0.05\): Is this feature a significant factor in the list price?**
**State the null and alternative hypotheses:**
- \( H_0: \beta_2 = 0 \)
- \( H_a: \beta_2 \neq 0 \)
**Find the test statistic.**
(Round your answer to two decimal places.)
**Find the p-value.**
(Round your answer to four decimal places.)
**State your conclusion.**
- **Options:**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2fdea76-24b5-4e92-ab93-0d275ab88ec3%2Ff3204329-69c4-45bc-a5c1-6f0ae2ce9128%2Ffusl1y4_processed.png&w=3840&q=75)
Transcribed Image Text:## Statistical Analysis of Refrigerator Pricing
### (b) Test for a Relationship between List Price and Cubic Feet
**Find the test statistic.**
(Round your answer to two decimal places.)
**Answer:** 4.44
**Find the p-value.**
(Round your answer to four decimal places.)
**Answer:** 0.0003
**State your conclusion.**
- **Options:**
- 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.**
**Conclusion:** Do not reject \( H_0 \).
### (c) Development of a Dummy Variable
To assess the influence of the thru-the-door ice and water feature on list price, we develop a dummy variable. Code this variable as 1 if the refrigerator has the feature; otherwise, use 0.
Using this dummy variable, apply the following regression equation to estimate how list price is related to cubic feet, along with the thru-the-door feature:
\[
\hat{y} = -1525.37 + 129.0112x_1 + 79.81081x_2
\]
- \( x_1 \): Cubic feet
- \( x_2 \): Thru-the-door ice and water feature (dummy variable)
- \( \hat{y} \): Estimated list price
### (d) Significance of the Thru-the-Door Ice and Water Feature
**Test at \(\alpha = 0.05\): Is this feature a significant factor in the list price?**
**State the null and alternative hypotheses:**
- \( H_0: \beta_2 = 0 \)
- \( H_a: \beta_2 \neq 0 \)
**Find the test statistic.**
(Round your answer to two decimal places.)
**Find the p-value.**
(Round your answer to four decimal places.)
**State your conclusion.**
- **Options:**
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