Consider the data on species diversity in the Galapagos Islands in the file "galapagos.csv". The data set contains 30 rows, one for each island, and 7 variables. You will use the number of plant species (Species) as the response, and construct a model using the area of the island (Area), the elevation of the island (Elevation), the distance from the nearest island (Nearest), the distance from Santa Cruz Island (Scruz), and the area of the adjacent island (Adjacent) as predictors.

1. Fit the model
2. (Species|predictors) =0+1Area+2Elevation+3Nearest+4Scruz+5Adjacent
3. and print the summary output. Based on this output, which variables seem to do a better job explaining the mean number of of plant species? Explain.
4. Construct a plot for the residuals vs. fitted values and comment on the results (any signs of patterns or trends, non-constant variance, unusual observations?)
5. We have seen that when dealing multiple predictors, sometimes is a good idea to check the residuals versus each explanatory variable. Construct a plot of the residuals vs area of the island. Do you see any unusual observations? If so, identify them and explain what is unusual about them.
6. Construct the plots for leverage, Cook's distance and standardized residuals for this model and in each case identify any potential influential observations.
7. Remove any potential influential observations found in problem 4 and re-fit the model. Report any changes that you observe in the output and how these changes (if any) may change your conclusions from problem 1.
8. How you would deal with the influential observations in this problem? Explain.