Researchers are interested in determining the relationship between crashes on rural two-lane highways and lane and shoulder widths. Use the data set “Crashes_rural 2ln highways.” Note that right lane...

Researchers are interested in determining the relationship between crashes on rural two-lane highways and lane and shoulder widths. Use the data set “Crashes_rural 2ln highways.” Note that right lane and right shoulder actually represent the widths of them, respectively. a. Construct the histogram of the variable “Total crashes for 3 years.” What characteristics do you observe from the distribution? b. Plot total crashes for three years (Y) vs. right lane (X). Also, plot total crashes for three years (Y) vs. right shoulder (X). Is there any pattern in the plot? Does the relationship between two variables (X and Y) look linear? c. Fit the normal linear regression model to total crashes for three years with right lane and right shoulder included as predictors. Do you think the model fits the data well? Create appropriate diagnostic plots. What assumptions seem to be violated? d. Fit the normal linear regression model to total crashes for three years with right lane and right shoulder, logAADT, and loglength3 included as predictors. Create appropriate diagnostic plots. What assumptions seem to be violated?