1. For this question, we will use the cornnit data set from the faraway package. Be sure to install and load the faraway package first, and then load the data set. The data explore the relationship between corn yield (bushels per acre) and nitrogen (pounds per acre) fertilizer application in a study carried out in Wisconsin.
(a) What is the response variable and predictor for this study? Create a scatterplot of the data, and interpret the scatterplot.
(b) Fit a linear regression without any transformations. Create the corresponding residual plot. Based only on the residual plot, what transformation will you consider first? Be sure to explain your reason.
(c) Create a Box Cox plot for the profile loglikelihoods. How does this plot aid in your data transformation?
(d) Perform the necessary transformation to the data. Re fit the regression with the transformed variable(s) and assess the regression assumptions. You may have to apply transformations a number of times. Be sure to explain the reason be- hind each of your transformations. Perform the needed transformations until the regression assumptions are met. What is the regression equation that you will use?
Note: in part 2d, there are a number of solutions that will work. You must clearly document your reasons for each of your transformations.