For this problem you will be using the data set ex2018 from the "Sleuth3" package. Read the help(ex2018) file for this data set. It mentions that vehicle age is a surrogate variable. A surrogate variable is a replacement for a variable that is hard to measure with one that is easy to measure. So they are using vehicile age as a proxy for tire age.

1 (a) Test if the fatal accidents of Ford cars are more likely to be due to tire failure while accounting for age of the car and number of passengers. Explain the results, including why it is important to control for number of passengers and age of the car.

(b) Using the model you have fit in the previous problem, make predictions for the probability that the tires were the cause of a fatal accident for the following types of cars. Discuss these predictions and connect them to the conclusions you found earlier.

i. A one year old Ford car with two passengers.

ii. A one year old Other car with two passengers.

(c) Use 10 folds cross validation to create an ROC plot comparing the model you fit in part (a) to a model with only VehicleAge and Passengers. Provide a description of the ROC plot and explain how the results support or contradict your earlier findings. 2. For the following plots state whether you think the time series