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 function is the appropriate regression function for this data set?Part C: do the residuals have a constant variance?Part D: are the residuals independent?Part E: are the error terms are normally distributed?y x22 821 818 846 2241 2254 2276 3258 3268 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.

A:The residual plot is obtained as:The residuals are obtained using the following…

Answered: The estimated regression equation for…

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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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 function is the appropriate regression function for this data set?

Part C: do the residuals have a constant variance?

Part D: are the residuals independent?

Part E: are the error terms are normally distributed?

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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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