Solve the following using R. Show all of your work and explain your work and/or answers when necessary. Driving fatalities and speed limits. In 1987, the federal government set the speed limit on interstate highways at 65 mph in most areas of the United States. In 1995, federal restrictions were eliminated so that states assumed control of setting speed limits on interstate highways. The datafile Speed contains the variables FatalityRate, the number of interstate fatalities per 100 million vehicle-miles of travel, Year, and an indicator variable StateControl that is 1 for the years 1995–2007 and zero for earlier years in the period 1987–1994. Here are the first few rows of data:
__Year FatalityRate StateControl__
__1987 2.41 0__
__1988 2.32 0__
__1989 2.17 0__
__1990 2.08 0__
__1991 1.91 0__
TO REITERATE, ABOVE IS JUST THE FIRST FEW ROWS OF DATA. ALL OF THE DATA IS STORED IN THE R FILE Speed .
Therefore the first two lines of your code in R should be:
library(Stat2Data)
data(Speed)
a. Fit a regression of fatality rate on year. What is the slope of the least squares line?
b. Examine a residual plot. What is remarkable about this plot?
c. Fit the multiple regression of fatality rate on year, state control, and the interaction between year and state control. Is there a significant change in the relationship between fatality rate and year starting in 1995?
d. What are the fitted equations relating fatality rate to year before and after 1995?