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Construct a residual plot. 16- 16 16- 16- 12 12 12 12 8. 8- 8 8- 4 4 4 4 -4 -4- -4 -4 .. -8 -8 -8 -8- -12 -12 -12 -12 -16 -16 -16 -16- 6 8 4 6 8 6 8 2 4 10 12 14 2 4 6 10 12 14 10 12 14 4 10 12 14 Years of Experience Years of Experience Years of Experience Years of Experience Do the assumptions about the error terms seem reasonable in light of the residual plot? O The plot suggests a funnel pattern in the residuals indicating that the error term assumptions appear reasonable. O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions do not appear reasonable. O The plot suggests curvature in the residuals indicating that the error term assumptions appear reasonable. O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions appear reasonable. O The plot suggests a funnel pattern in the residuals indicating that the error term assumptions do not appear reasonable Residuals Residuals

Construct a residual plot. 16- 16 16- 16- 12 12 12 12 8. 8- 8 8- 4 4 4 4 -4 -4- -4 -4 .. -8 -8 -8 -8- -12 -12 -12 -12 -16 -16 -16 -16- 6 8 4 6 8 6 8 2 4 10 12 14 2 4 6 10 12 14 10 12 14 4 10 12 14 Years of Experience Years of Experience Years of Experience Years of Experience Do the assumptions about the error terms seem reasonable in light of the residual plot? O The plot suggests a funnel pattern in the residuals indicating that the error term assumptions appear reasonable. O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions do not appear reasonable. O The plot suggests curvature in the residuals indicating that the error term assumptions appear reasonable. O The plot suggests a generally horizontal band of residual points indicating that the error term assumptions appear reasonable. O The plot suggests a funnel pattern in the residuals indicating that the error term assumptions do not appear reasonable Residuals Residuals

MATLAB: An Introduction with Applications
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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**Residual Plot Analysis:** The image contains four separate residual plots, each depicting the residuals (differences between observed and predicted values) against "Years of Experience". The plots are laid out in a four-panel grid, showing varying patterns in the distribution of residuals. **Details of Each Plot:** 1. **First Residual Plot:** - **X-axis:** Years of Experience, ranging from 0 to 14. - **Y-axis:** Residuals, ranging from -16 to 16. - **Description:** The residuals are scattered around the horizontal axis with no discernible pattern. 2. **Second Residual Plot:** - **X-axis:** Years of Experience, same range as the first plot. - **Y-axis:** Residuals, same range as the first plot. - **Description:** The residuals form a somewhat funnel shape, with a wider spread at lower years of experience and narrowing as experience increases. 3. **Third Residual Plot:** - **X-axis:** Years of Experience, consistent range across all plots. - **Y-axis:** Residuals, consistent range across all plots. - **Description:** The residuals vary consistently around the horizontal axis, showing no curvature or pattern, indicating stability in variance. 4. **Fourth Residual Plot:** - **X-axis:** Years of Experience. - **Y-axis:** Residuals. - **Description:** There appears to be a slight curve in the distribution of residuals, suggesting a non-linear relationship. **Questions (b): Analyzing Error Term Assumptions:** (b) Do the assumptions about the error terms seem reasonable in light of the residual plot? - **Option 1:** The plot suggests a funnel pattern in the residuals indicating that the error term assumptions appear reasonable. - **Option 2:** The plot suggests a generally horizontal band of residual points indicating that the error term assumptions do not appear reasonable. - **Option 3:** The plot suggests curvature in the residuals indicating that the error term assumptions appear reasonable. - **Option 4:** The plot suggests a generally horizontal band of residual points indicating that the error term assumptions appear reasonable. - **Option 5:** The plot suggests a funnel pattern in the residuals indicating that the error term assumptions do not appear reasonable. The context of the analysis is vital in understanding how the residual patterns affect assumptions about
Transcribed Image Text:**Residual Plot Analysis:** The image contains four separate residual plots, each depicting the residuals (differences between observed and predicted values) against "Years of Experience". The plots are laid out in a four-panel grid, showing varying patterns in the distribution of residuals. **Details of Each Plot:** 1. **First Residual Plot:** - **X-axis:** Years of Experience, ranging from 0 to 14. - **Y-axis:** Residuals, ranging from -16 to 16. - **Description:** The residuals are scattered around the horizontal axis with no discernible pattern. 2. **Second Residual Plot:** - **X-axis:** Years of Experience, same range as the first plot. - **Y-axis:** Residuals, same range as the first plot. - **Description:** The residuals form a somewhat funnel shape, with a wider spread at lower years of experience and narrowing as experience increases. 3. **Third Residual Plot:** - **X-axis:** Years of Experience, consistent range across all plots. - **Y-axis:** Residuals, consistent range across all plots. - **Description:** The residuals vary consistently around the horizontal axis, showing no curvature or pattern, indicating stability in variance. 4. **Fourth Residual Plot:** - **X-axis:** Years of Experience. - **Y-axis:** Residuals. - **Description:** There appears to be a slight curve in the distribution of residuals, suggesting a non-linear relationship. **Questions (b): Analyzing Error Term Assumptions:** (b) Do the assumptions about the error terms seem reasonable in light of the residual plot? - **Option 1:** The plot suggests a funnel pattern in the residuals indicating that the error term assumptions appear reasonable. - **Option 2:** The plot suggests a generally horizontal band of residual points indicating that the error term assumptions do not appear reasonable. - **Option 3:** The plot suggests curvature in the residuals indicating that the error term assumptions appear reasonable. - **Option 4:** The plot suggests a generally horizontal band of residual points indicating that the error term assumptions appear reasonable. - **Option 5:** The plot suggests a funnel pattern in the residuals indicating that the error term assumptions do not appear reasonable. The context of the analysis is vital in understanding how the residual patterns affect assumptions about
## Analysis of Sales Data ### Data Collection A sales manager collected data using the variables: - **x** = years of experience - **y** = annual sales (in $1,000s) The estimated regression equation for these data is: \[ \hat{y} = 80 + 4x \] ### Table of Data | Salesperson | Years of Experience | Annual Sales ($1,000s) | |-------------|---------------------|------------------------| | 1 | 1 | 80 | | 2 | 3 | 97 | | 3 | 4 | 92 | | 4 | 4 | 102 | | 5 | 6 | 103 | | 6 | 8 | 111 | | 7 | 10 | 119 | | 8 | 10 | 123 | | 9 | 11 | 117 | | 10 | 13 | 136 | ### Task #### (a) Compute the Residuals A residual is the difference between the observed value and the predicted value from the regression equation. #### Table: Residuals Calculation | Years of Experience | Annual Sales ($1,000s) | Residuals | |---------------------|------------------------|-----------| | 1 | 80 | | | 3 | 97 | | | 4 | 92 | | | 4 | 102 | | | 6 | 103 | | | 8 | 111 | | | 10 | 119 | | | 10 | 123 | | | 11 | 117 | | | 13 | 136 | | ### Explanation To compute the residuals, use the regression equation to find the predicted sales for each given year of experience and subtract this from the actual sales. Fill in the residuals in the table above.
Transcribed Image Text:## Analysis of Sales Data ### Data Collection A sales manager collected data using the variables: - **x** = years of experience - **y** = annual sales (in $1,000s) The estimated regression equation for these data is: \[ \hat{y} = 80 + 4x \] ### Table of Data | Salesperson | Years of Experience | Annual Sales ($1,000s) | |-------------|---------------------|------------------------| | 1 | 1 | 80 | | 2 | 3 | 97 | | 3 | 4 | 92 | | 4 | 4 | 102 | | 5 | 6 | 103 | | 6 | 8 | 111 | | 7 | 10 | 119 | | 8 | 10 | 123 | | 9 | 11 | 117 | | 10 | 13 | 136 | ### Task #### (a) Compute the Residuals A residual is the difference between the observed value and the predicted value from the regression equation. #### Table: Residuals Calculation | Years of Experience | Annual Sales ($1,000s) | Residuals | |---------------------|------------------------|-----------| | 1 | 80 | | | 3 | 97 | | | 4 | 92 | | | 4 | 102 | | | 6 | 103 | | | 8 | 111 | | | 10 | 119 | | | 10 | 123 | | | 11 | 117 | | | 13 | 136 | | ### Explanation To compute the residuals, use the regression equation to find the predicted sales for each given year of experience and subtract this from the actual sales. Fill in the residuals in the table above.
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