Exercise 1.34 introduces data on total enrollments in mathematics courses at a small liberal arts college where the academic year consists of two semesters, one in the fall and another in the spring. Data for Fall 2001 to Spring 2012 are stored in MathEnrollment.

(a) In exercise 1.34 the data for 2003 were found to be unusual due to special circumstances. Remove the data from 2003 and fit a regression model for predicting spring enrollment (Spring) from fall enrollment (Fall). Prepare the appropriate residual plots and comment on the slight problems with the conditions for inference. In particular, make sure that you plot the residuals against order (or AYear) and comment on the trend.

(b) Even though we will be able to improve on this simple linear model in the next chapter, let's take a more careful look at the model. What percent of the variability in spring enrollment is explained by using a simple linear model with fall enrollment as the predictor?

(c) Provide the ANOVA table for partitioning the total variability in spring enrollment based on this model.

(d) Test for evidence of significant linear association between spring and fall enrollments.

(e) Provide a 95% confidence interval for the slope of this model. Does your interval contain zero? Why is that relevant?