MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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please do all parts!
The estimated regression equation for this data set is y=4.4878+1.9549x.
Part A: (in image)
Part B: is the linear
Part C: do the residuals have a constant variance?
Part D: are the residuals independent?
Part E: are the error terms are
y x
22 8
21 8
18 8
46 22
41 22
54 22
76 32
58 32
68 32
![Below is a transcription of the dataset, which is useful for educational purposes, especially in statistics and data analysis:
| x | y | Residual |
|----|----|----------|
| 8 | 22 | [ ] |
| 8 | 21 | [ ] |
| 8 | 18 | [ ] |
| 22 | 46 | [ ] |
| 22 | 41 | [ ] |
| 22 | 54 | [ ] |
| 32 | 76 | [ ] |
| 32 | 58 | [ ] |
| 32 | 68 | [ ] |
### Explanation:
- **Columns:**
- **x**: Represents the independent variable.
- **y**: Represents the dependent variable.
- **Residual**: This column is left blank and is meant for calculating the residuals, which are the differences between the observed and predicted values of y in a regression analysis.
### Educational Context:
Residuals are essential in regression analysis for understanding the accuracy of the model's predictions. They help determine how well a statistical model, such as a linear regression, fits the data. A residual is calculated by subtracting the predicted value from the observed value (Residual = Observed y - Predicted y). Analyzing the pattern of residuals can indicate whether the model assumptions are valid and highlight any potential areas for model improvement.](https://content.bartleby.com/qna-images/question/de74f136-44f2-4a02-80e8-fc7d1b4c57d8/79a22865-61ec-46ba-b390-4a9612c243bb/2noyry8_processed.png)
Transcribed Image Text:Below is a transcription of the dataset, which is useful for educational purposes, especially in statistics and data analysis:
| x | y | Residual |
|----|----|----------|
| 8 | 22 | [ ] |
| 8 | 21 | [ ] |
| 8 | 18 | [ ] |
| 22 | 46 | [ ] |
| 22 | 41 | [ ] |
| 22 | 54 | [ ] |
| 32 | 76 | [ ] |
| 32 | 58 | [ ] |
| 32 | 68 | [ ] |
### Explanation:
- **Columns:**
- **x**: Represents the independent variable.
- **y**: Represents the dependent variable.
- **Residual**: This column is left blank and is meant for calculating the residuals, which are the differences between the observed and predicted values of y in a regression analysis.
### Educational Context:
Residuals are essential in regression analysis for understanding the accuracy of the model's predictions. They help determine how well a statistical model, such as a linear regression, fits the data. A residual is calculated by subtracting the predicted value from the observed value (Residual = Observed y - Predicted y). Analyzing the pattern of residuals can indicate whether the model assumptions are valid and highlight any potential areas for model improvement.
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