Run a regression of testscr on str and avginc, where testscr and str are as above, and avginc is a measure of the average household income in the school district.
a. What is the correlation between str and avginc. Does this correlation suggest the model specification suffers from serious multicolinearity?
b. What is the estimated effect of str on testscr?
c. Now create a scatterplot of testscr on avginc, and use OLS to fit a straight line to the data. Do you think this simple regression equation suffers from specification bias? If so, how?
d. What is the probability that all the population slope coefficients are actually zero, but the coefficients we estimated are different from zero due merely to random sampling variability? In other words, what is the probability that the R2 is actually zero? Explain how one conducts an F test to test such a hypothesis.