The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Click the icon to view the Minitab display. The linear correlation coefficient is (Round to three decimal places as needed.)
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Click the icon to view the Minitab display. The linear correlation coefficient is (Round to three decimal places as needed.)
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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![### Minitab Output Analysis
#### Introduction
This page presents an analysis of regression output generated from Minitab statistical software. This is useful for educational purposes to understand how to interpret regression results.
#### Regression Equation
The regression equation provided by Minitab is:
\[ \text{Highway} = 50.4 - 0.00543 \times \text{Weight} \]
#### Coefficients and Statistics
| Predictor | Coef | SE Coef | T | P |
|------------|-----------|---------|-------|------|
| Constant | 50.442 | 2.896 | 17.45 | 0.000|
| Weight | -0.0054268| 0.0007554 | -7.05 | 0.000|
- **S = 2.14999**
- **R-Sq = 63.2%**
- **R-Sq (adj) = 60.4%**
##### Explanation:
- **Coef:** The coefficients of the regression equation.
- Constant: 50.442
- Weight: -0.0054268
- **SE Coef:** Standard Error of the coefficient.
- **T:** T-statistic for the hypothesis test.
- **P:** P-value for the hypothesis test (indicating statistical significance).
The negative coefficient for Weight suggests that as weight increases, Highway mileage decreases.
#### Predicted Values for New Observations
Details on the predicted values for new observations are as follows:
| New Obs | Fit | SE Fit | 95% CI | 95% PI |
|---------|--------|--------|-------------------|-------------------|
| 1 | 34.162 | 0.518 | (33.159, 35.165) | (29.566, 38.758) |
**Values of Predictors for New Observations**
| Obs | Weight |
|-----|--------|
| 1 | 3000 |
This section provides the predicted Highway value when Weight is 3000 along with confidence intervals (CI) and prediction intervals (PI).
- **Fit:** The predicted value.
- **SE Fit:** The standard error of the predicted value.
- **95% CI:** The 95% confidence interval for the mean response.
- **95% PI:** The 95% prediction interval](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96fb4f59-e2d0-4223-b88e-b1f942117eac%2F86c472fb-3f16-4e61-a4a5-e5d1a35e9003%2F688olio_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Minitab Output Analysis
#### Introduction
This page presents an analysis of regression output generated from Minitab statistical software. This is useful for educational purposes to understand how to interpret regression results.
#### Regression Equation
The regression equation provided by Minitab is:
\[ \text{Highway} = 50.4 - 0.00543 \times \text{Weight} \]
#### Coefficients and Statistics
| Predictor | Coef | SE Coef | T | P |
|------------|-----------|---------|-------|------|
| Constant | 50.442 | 2.896 | 17.45 | 0.000|
| Weight | -0.0054268| 0.0007554 | -7.05 | 0.000|
- **S = 2.14999**
- **R-Sq = 63.2%**
- **R-Sq (adj) = 60.4%**
##### Explanation:
- **Coef:** The coefficients of the regression equation.
- Constant: 50.442
- Weight: -0.0054268
- **SE Coef:** Standard Error of the coefficient.
- **T:** T-statistic for the hypothesis test.
- **P:** P-value for the hypothesis test (indicating statistical significance).
The negative coefficient for Weight suggests that as weight increases, Highway mileage decreases.
#### Predicted Values for New Observations
Details on the predicted values for new observations are as follows:
| New Obs | Fit | SE Fit | 95% CI | 95% PI |
|---------|--------|--------|-------------------|-------------------|
| 1 | 34.162 | 0.518 | (33.159, 35.165) | (29.566, 38.758) |
**Values of Predictors for New Observations**
| Obs | Weight |
|-----|--------|
| 1 | 3000 |
This section provides the predicted Highway value when Weight is 3000 along with confidence intervals (CI) and prediction intervals (PI).
- **Fit:** The predicted value.
- **SE Fit:** The standard error of the predicted value.
- **95% CI:** The 95% confidence interval for the mean response.
- **95% PI:** The 95% prediction interval
![**Understanding Linear Correlation Coefficient in Highway Fuel Consumption**
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts?
[Click the icon to view the Minitab display.]
**The linear correlation coefficient is [ ].**
(Round to three decimal places as needed.)
---
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**Explanation of Graphs/Diagrams:**
There are no specific graphs or diagrams provided in this particular image. However, it mentions "Click the icon to view the Minitab display," suggesting that the Minitab display, which likely contains the necessary statistical data for analysis, is available upon clicking an icon in the interface.
For educational purposes, understanding how to interpret a Minitab output is crucial. Typically, such outputs will provide values for the linear correlation coefficient, which measures the strength and direction of the linear relationship between two variables. Values close to 1 or -1 indicate a strong linear relationship, while those close to 0 suggest a weak or no linear relationship.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F96fb4f59-e2d0-4223-b88e-b1f942117eac%2F86c472fb-3f16-4e61-a4a5-e5d1a35e9003%2F6462c0l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Linear Correlation Coefficient in Highway Fuel Consumption**
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts?
[Click the icon to view the Minitab display.]
**The linear correlation coefficient is [ ].**
(Round to three decimal places as needed.)
---
*Interactive Elements:*
- Help me solve this
- View an example
- Get more help
[Clear all | Check answer]
---
**Explanation of Graphs/Diagrams:**
There are no specific graphs or diagrams provided in this particular image. However, it mentions "Click the icon to view the Minitab display," suggesting that the Minitab display, which likely contains the necessary statistical data for analysis, is available upon clicking an icon in the interface.
For educational purposes, understanding how to interpret a Minitab output is crucial. Typically, such outputs will provide values for the linear correlation coefficient, which measures the strength and direction of the linear relationship between two variables. Values close to 1 or -1 indicate a strong linear relationship, while those close to 0 suggest a weak or no linear relationship.
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