4.7 Magellanic penguins, continued. Here are the data for the study of Magellanic penguins in Example 3.6 and Exercise 4.5. The values in italics correspond to the two years with highly unusual climatic conditions that the researchers excluded from their analysis.

Percent starved Percent fledged Percent starved Percent fledged Percent starved Percent fledged Percent starved Percent fledged 39.5 40.8 54.0 20.3 27.4 27.1 47.2 34.7 20.9 43.7 66.0 24.2 38.3 27.8 29.0 37.1 25.9 45.5 28.1 54.2 32.4 57.3 18.6 66.4 44.0 45.8 55.3 26.0 39.0 44.4 39.2 42.6 66.0 1.7 16.8 55.7 28.6 58.2 46.0 32.8 86.4 6.8 46.9 27.2 11.8 60.5 20.9 11.2 69.8 8.6 40.8 26.9 28.6 31.4 34.0 10.5

a. Are the two outliers (values in italics) influential for the correlation? Obtain r with and without these two data points.

b. Are the two outliers influential for regression? Obtain the equation of the least-squares regression line with and without these two data points. Add both regression lines to the same scatterplot, as in Figure 4.4(a).

c. What are the two excluded data points? Are they outliers in the x direction? In the y direction? Are they outliers of the relationship?

Explain how this is relevant to your conclusions in parts a and b.