As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities.Your first step in the analysis is to construct a scatterplot of the data.**Figure**: Scatterplot for U.S. Department of Transportation Problem*Scatterplot Description*The scatterplot titled "U.S. Department of Transportation: The Relationship Between Fatal Accident Frequency and Driver Age" shows data points representing various cities. The x-axis represents the percentage of drivers under age 21, ranging from 6 to 20. The y-axis represents fatal accidents per 1000 licenses, ranging from 0 to 4.5. The plot indicates a positive trend, where an increase in the percentage of drivers under 21 corresponds to an increase in fatal accidents per 1000 licenses.Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear regression analysis. The results are as follows:**Table**: Linear Regression Output for U.S. Department of Transportation Problem| | Coefficients | Standard Error | t Statistic | p-value ||----------------------|--------------|----------------|-------------|---------|| Intercept | -1.5974 | 0.3717 | -4.2979 | 0.0001 || Percent Under 21 | 0.2871 | 0.0294 | 9.7671 | 0.0000 |The table indicates a significant relationship between the percentage of drivers under 21 and the number of fatal accidents, with a positive coefficient for the percentage under 21 variable, suggesting that as the percentage of younger drivers increases, so do fatal accidents. ### Analyzing Residual Plots in Regression Analysis**Purpose of Residual Plots**In regression analysis, a crucial step is examining the residuals using a residual plot. This examination helps test the assumptions of the regression model by identifying patterns in the residuals.**Figure Overview****Title:** Residual Plot for U.S. Department of Transportation Problem- **Graph Components:** - **X-axis:** Percent Under 21 - **Y-axis:** Residuals - **Data Points:** Plotted residuals shown as "X" marks distributed across the range of the percent under 21 values.**Interpretation**The plot shows residuals scattered around a horizontal line at zero, with the residual spread appearing fairly consistent across different values of the "percent under 21." This consistency (or lack thereof) can provide insights into the suitability of the regression model.**Questions for Evaluation:**Which statement offers the best interpretation of the residual plot?- ○ It appears that the residual plot exhibits a pattern whereby a linear model may not be adequate or the best fit, indicating that an assumption of the linear model may have been violated.- ○ It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported.- ○ It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is not supported.- ○ It appears that the residual plot exhibits a pattern of non-constant variance, indicating that an assumption of the linear model may have been violated.Understanding the pattern of residuals can indicate whether the assumptions about linearity and variance in the regression model are appropriate or if they have been violated.

There is an assumption of homoscedasticity which states that the residual should have same or equal variance. If the variance is not equal, there is a problem of heteroskedasticity.From the figure, it appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported. This is because the residual values lie close to the line and they have almost equal distance from the line. Therefore, option b is correct. Explanation for incorrect options: A: No assumption has been violated because the residual has constant variance. C: Since constant variance is there, the assumption is not violated but followed. D: No assumption has been violated because the residual has constant variance.

Business

Economics

A final step in regression analysis is an examination of the residuals in a residual plot. This allows you to test the assumptions of the regression model itself by looking for patterns in the residuals. The residual plot for the problem is as follows: FIGURE. RESIDUAL PLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM Percent Under 21 Residual Plot 2 1.5 1 0.5 半 to 16 10 12 14 18 20 -0.5 -1 -1.5 Percent under 21 Which statement offers the best interpretation of the residual plot? O It appears that the residual plot exhibits a pattern whereby a linear model may not be adequate or the best fit, indicating that an assumption of the linear model may have been violated. O It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported. aEcumption of the model is not supported. Residuals -00

A final step in regression analysis is an examination of the residuals in a residual plot. This allows you to test the assumptions of the regression model itself by looking for patterns in the residuals. The residual plot for the problem is as follows: FIGURE. RESIDUAL PLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM Percent Under 21 Residual Plot 2 1.5 1 0.5 半 to 16 10 12 14 18 20 -0.5 -1 -1.5 Percent under 21 Which statement offers the best interpretation of the residual plot? O It appears that the residual plot exhibits a pattern whereby a linear model may not be adequate or the best fit, indicating that an assumption of the linear model may have been violated. O It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported. aEcumption of the model is not supported. Residuals -00

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Solve using Excel
IV. 得分 What information can be obtained from this summary output? a to enter = 0.05, a to remove = 0.05 Analysis of Variance Source DF Adi sS Adi MS F-Value P-Value www Regression 4 37260200 9315050 45. 23 0. 000 0. 000 0. 000 Poten 1 4727687 4727687 22. 95 AdvExp 4630364 4630364 22. 48 Share 1 3009401 3009401 14. 61 0.001 Accounts 1 2129972 2129972 10. 34 0.004 Error 20 4119349 205967 Total 24 41379549 R-sq R-sq (adi) R-sq (pred) 453. 836 90. 04% 88. 05% 85. 97% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant -1442 424 -3. 40 0,003 Poten 0. 03822 0. 00798 4. 79 0. 000 1. 83 AdvExp 0. 1750 0. 0369 4. 74 0. 000 1. 15 Share 190. 1 49. 7 3. 82 0.001 1.74 Accounts 9. 21 2. 87 3. 22 0. 004 1. 99 Fits and Diagnostics for Unusual Observations Std Obs Sales Fit Resid Resid www 10 4876 3942 934 2. 14 R
Help!
9
An analyst working for your firm provided an estimated log-linear demand function based on the natural logarithm of the quantity sold, price, and the average income of consumers. Results are summarized in the following table: SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept LN Price LN Income df 0.968 0.937 0.933 0.003 30 SS MS F 2 0.003637484 0.001818742 202.48598 0.000242516 8.98206E-06 27 29 0.00388 Coefficients Standard Error 0.57 0.00 0.13 0.51 -0.08 0.15 t Stat 0.90 -19.50 1.13 P-value 0.37 0.00 0.27 Significance F 5.55598E-17 Lower 95% -0.65 -0.09 -0.12 How would a 4 percent increase in income impact the demand for your product? Demand would increase by 60 percent. Demand would increase by 0.6 percent. Demand would decrease by 60 percent. Demand would decrease by 0.6 percent. Upper 95% 1.68 -0.07 0.41
q11-
Please no written by hand solution a) Suppose in a regression of weekly salaries on years of schooling for males(m) and females(f), the following results are obtained. Wm = 50Sm and Wf = 40Sf. where Wm (Wf) denotes weekly salary and Sm (Sf) denotes years of schooling for males and females respectively. 50 and 40 are the coefficients on schooling in the male and female regression respectively. On average, men have 12 years of schooling and women have 10 years of schooling. What is the average male-female wage differential? Is this a good estimate of discrimination? Explain why/why not. Using the information in the question, what would you propose as a better estimate of discrimination? State any assumptions that you use and explain your answer.
The dependent variable in the regression in our cost driver analysis is which of the following? Company sales Total overhead cost for the entire period of time Total overhead cost per month
6 9 13 Yi 7 18 9. 26 23 a. Which of the following scatter diagrams accurately represents the data? A. 24+ 24+ 20- 20- 16+ 16+ 12+ 12+ 8+ 8+ 4- -4 4 12 16 24 28 x -4 4 8. 12 16 20 24 28 x -4t -4t С. D. 24 -----24+ 20- 20- 16- 16- 20 B. 20 00 00 O.
please answer in text form and in proper format answer with must explanation , calculation for each part and steps clearly
When running a ols regression, if my control variables are insignificant via T-test should I keep them in the regression? Are they significant?
please answer in text form and in proper format answer with must explanation , calculation for each part and steps clearly