U.S. Department of Transportation As an auto insurance risk analyst, it is your
ID: 3221653 • Letter: U
Question
U.S. Department of Transportation
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 TRANSPORATION PROBLEM
1) What is the predicted value for accidents per 1000 licenses for a city that has 13% of its licensed drivers under age 21, according to the estimated regression equation?
Answer: 2.131
The p-value for "Percent under 21" in the regression output is p = 0.0000. The t test for significance in simple linear regression is
2) What does the p-value tell you about the estimated regression line?
A) p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be rejected
B) p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should not be rejected.
C) p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should be rejected.
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:
3) Which statement offers the best interpretation of the residual plot?
A) It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported.
B) 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.
C) 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.
3.5 2.5 1.5 U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 10 18 Percentage of drivers under age 21Explanation / Answer
Answer:
1) What is the predicted value for accidents per 1000 licenses for a city that has 13% of its licensed drivers under age 21, according to the estimated regression equation?
Predicted value = -1.5974+0.2871*13=2.1349
Answer: 2.135
2) What does the p-value tell you about the estimated regression line?
Answer: A) p = 0.0000 indicates that the slope of the estimated regression line is not zero, a significant relationship exists between the two variables, and H0 should be rejected
B) p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should not be rejected.
C) p = 0.0000 indicates that the slope of the estimated regression line is zero, a significant relationship does not exist between the two variables, and H0 should be rejected.
3) Which statement offers the best interpretation of the residual plot?
Answer: A) It appears that the residual plot exhibits a good pattern of constant variance, indicating that the equal variance assumption of the model is supported.
B) 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.
C) 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.
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