Consider the Chernobyl Fallout data set in the file "ex1111.csv". The file contains data on cesium concentrations (inBq/Kg) in soil and mushrooms at 17 wooded locations in Umbria (central Italy), from August 1986 to November 1989. Researchers want to investigate the cesium transfer from contaminated soil to plants following the Chernobyl nuclear plant accident in 1986. Specifically, they want to describe the distribution of the mushroom cesium concentration as a function of the soil concentration.

1. Construct a scatter-plot forMushroomvsSoiland discuss any relevant features. Add the simple regression line to your plot as a reference and discuss if a simple regression line seem to be a good model for this data. Explain.
2. Use R to fit a simple linear regression model forMushroomvsSoiland print the summary output for the model. Based only on this output, do you see evidence of association between cesium concentrations in soil and mushrooms? Explain.
3. Construct the residual plot for the model in part 2 and comment on the results. Do you see any indication of possible influential observations?
4. Construct the Cook's distance and the standardized residuals plots and use these plots to identify any possible influential observations.
5. Now remove observation 17 from the data set and re-fit the simple linear regression model. Produce the output and residual plot for this model and compare your results to the output and residual plot in parts 2 and 3.
6. Now consider the entire data set, and fit the linear regression model for the transformed variableslog(Mushroom) vslog(Soil). Produce the output and residual plot for this model and compare your results to the output and residual plot in parts 2 and 3.
7. Which approach (dropping one observation or log-transforming the data) was more appealing to you in this situation? Explain.