The SAT2010 data file on the text CD contains combined average SAT scores for each of the 50 states and Washington D.C., and also the corresponding participation rate of each state. Let’s consider using the explanatory variable x = participation rate (in %) to predict the response variable y = combined average score. The regression equation is ŷ = 1718 - 3.36x.
a. Use the regression equation to predict the combined average score for the states with the smallest and largest participation rates.
b. West Virginia has a participation rate of 16% and a combined average score of 1522. Calculate the residual associated with West Virginia and comment on its value in the context of the problem.
c. The correlation between combined average SAT scores and participation rate is -0.877. What factor(s) or characteristic(s) of the students taking the SAT might contribute to this very strong negative relationship?