As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number of fatal accidents per 1000 licenses and the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Data collected over a one-year period follow.

a- At the 5% level of significance, is there a significant relationship between the two variables? Why or why not?

b- What is the value of the coefficient of determination for this simple linear regression model? Provide a brief interpretation of this value.

c- Use the information from the ANOVA table to compute the standard error of estimate, a.k,a, residual standard error. This value must match the residual standard error in the regression summary.

d- What is the point estimate of the expected number of fatal accidents per 1000 licenses if there are 10% drivers under age in a city?

e- Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. What is the estimate of the standard deviation for this confidence interval?

f- Suppose we want to develop a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21. Compute the t value and the margin of error needed for this confidence interval.

Can you Please show the solution with R code too

g- Provide a 95% confidence interval for the average number of fatal accidents per 1000 licenses for all the cities with 10% of drivers under age 21 and a practical interpretation to this confidence interval.

h- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. What is the estimate of the standard deviation for this prediction interval?

i- Suppose we want to develop a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21. Compute the margin of error needed for this prediction interval.

j- Provide a 95% prediction interval for the number of fatal accidents per 1000 licenses for a city with 10% of drivers under age 21 and a practical interpretation to this prediction interval.

Percent Under 21: 13 12 8 12 11 17 18 8 13 8 9 16 12 9 10 9 11 12 14 14 11 17 8 16 15 9 8 14 8 15 10 10 14 18 10 14 16 12 15 13 9 17

Fatal Accidents per 1000 2.962 0.708 0.885 1.652 2.091 2.627 3.83 0.368 1.142 0.645 1.028 2.801 1.405 1.433 0.039 0.338 1.849 2.246 2.855 2.352 1.294 4.1 2.19 3.623 2.623 0.835 0.82 2.89 1.267 3.224 1.014 0.493 1.443 3.614 1.926 1.643 2.943 1.913 2.814 2.634 0.926 3.256