Write out your answers to questions in complete sentences. Include all relevant R code and output, without anything extraneous. Instead of importing in an external.csv dataset to analyze, we'll use a dataset that exists in an R package for this problem. Follow these steps to import the necessary dataset: Run this code to open the "car" package, which contains the dataset: > library(car) > my_eid <- Wong 3. The Wong dataset contains data from a study by Wong, Monette, and Weiner (2001) on sample of patients who fell into comas after sustaining traumatic brain injuries. After waking, Wong and colleagues administered various intelligence tests. The "duration" variable records how many days each patient was in a coma. You want to see if there is a change in performance IQ scores ("piq") as duration increased. a. Make a scatterplot for this analysis. Why is a linear regression not appropriate? b. Create a new variable in the data frame called "log_duration" that is the natural log of each duration value plus 1 (so that duration values of zero are defined). You may use the code template below, changing the "UPDATE" portions as needed > UPDATE <- log(UPDATE + 1) c. Assuming this data is a random sample of the population and the observations are independent, conduct an analysis to see if log-duration can predict piq.