### Residual Plot Analysis#### Residual Plots DescriptionThe image displays four residual plots, each representing residuals plotted against "Years of Experience." The y-axis is labeled "Residuals," ranging from -16 to 16, while the x-axis is labeled "Years of Experience," spanning from 0 to 14. 1. **Plot A (First Plot)** - Residuals appear scattered around the horizontal axis with no clear pattern. 2. **Plot B (Second Plot)** - Residuals exhibit a slight upward funnel shape from left to right. 3. **Plot C (Third Plot)** - Residuals seem randomly scattered, showing a slightly uniform horizontal band. 4. **Plot D (Fourth Plot)** - Residuals depict an apparent downward funnel pattern.#### Evaluation of Error Term AssumptionsThe question associated with the plots evaluates whether the assumptions about error terms seem reasonable based on the residual patterns:- **Option 1**: The plot suggests curvature in the residuals, indicating that the error term assumptions appear reasonable.- **Option 2**: The plot suggests a funnel pattern in the residuals, indicating that the error term assumptions appear reasonable.- **Option 3**: The plot suggests a generally horizontal band of residual points, indicating that the error term assumptions appear reasonable.- **Option 4**: The plot suggests a funnel pattern in the residuals, indicating that the error term assumptions do not appear reasonable.- **Option 5**: The plot suggests a generally horizontal band of residual points, indicating that the error term assumptions do not appear reasonable.These options guide the interpretation of the residual plots, focusing on the presence of patterns like curvature or funnel shapes, which affect the validity of the error term assumptions in regression analysis. A sales manager collected the following data on $ x = $ years of experience and $ y = $ annual sales (\$1,000s). The estimated regression equation for these data is $ \hat{y} = 80 + 4x $.| Salesperson | Years of Experience | Annual Sales (\$1,000s) ||-------------|---------------------|-------------------------|| 1 | 1 | 80 || 2 | 3 | 97 || 3 | 4 | 97 || 4 | 4 | 102 || 5 | 6 | 103 || 6 | 8 | 101 || 7 | 10 | 119 || 8 | 10 | 118 || 9 | 11 | 127 || 10 | 13 | 136 |**(a) Compute the residuals.**| Years of Experience | Annual Sales (\$1,000s) | Residuals ||---------------------|-------------------------|-----------|| 1 | 80 | || 3 | 97 | || 4 | 97 | || 4 | 102 | || 6 | 103 | || 8 | 101 | || 10 | 119 | || 10 | 118 | || 11 | 127 | || 13 | 136 | |**Explanation:**The table above shows data collected by a sales manager, including years of experience and corresponding annual sales. The estimated regression equation $ \hat{y} = 80 + 4x $ is used to predict annual sales based on years of experience (x). The task is to compute the residuals, which are the differences between the observed sales and the predicted sales from the regression equation. Residuals help in assessing the fit of the regression model.

The residual value is nothing but the error term. It is calculated using the observed value and the…

Answered: A sales manager collected the following…

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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A statistical program is recommended. A sales manager collected the following data on x = years of experience and y = annual sales ($1,000s). The estimated regression equation for these data is ý = 82 + 4x. Years of Annual Sales Salesperson Experience ($1,000s) 1 80 2 97 3 4 97 4 4 107 5 6 103 6 8 116 7 10 119 8 10 118 9 11 127 10 13 136 (a) Compute the residuals. Years of Experience Annual Sales ($1,000s) Residuals 1 80 3 97 4 97 4 107 6 103 8 116 10 119 10 118 11 127 13 136 Construct a residual plot.

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