Data set: Arsenic
Karagas, Morris, Weiss, Spate, Baskett, and Greenberg collected toenail clippings of several individuals along with samples of each person’s regular drinking water. 6 In this pilot study, the researchers attempted to determine if arsenic concentrations in people’s toenails could be used to determine the level of arsenic in their water. Each of the 21 individuals in this study had a private well. High arsenic concentrations are related to cancer, and several studies have found a positive correlation between arsenic concentrations of drinking water and toenail samples.
a. Create a scatterplot and regression line to predict ArsWater from ArcToe. There are extreme outliers along both the X and Y axes. However, 6 of the 21 water samples contained no arsenic, and taking the logarithm of ArsWater is not possible.
b. Create a scatterplot and regression line to predict log(ArsWater + 1) from log(ArcToe). Create the appropriate residual plots and evaluate the validity of the model. While the transformations are helpful, model assumptions are still violated.
c. Try using a few more variables or transformations to create a better model. This is an example where you are unlikely to find a satisfactory simple regression model.