12.69 A consulting group offers courses in financial management for executives. At the end of these courses participants are asked to provide overall ratings of the value of the course. For a sample of 25 courses, the following regression was estimated by least squares:

yn = 42.97 + 0.38x1 + 0.52x2 - 0.08x3 + 6.21x4 R2 = 0.569 10.292 10.212 10.112 10.3592 where yn = average rating by participants of the course x1 = percentage of course time spent in group discussion sessions x2 = money, in dollars, per course member spent on preparing course material x3 = money, in dollars, per course member spent on food and drinks x4 = dummy variable taking the value 1 if a visiting guest lecturer is brought in and 0 otherwise The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

a. Interpret the estimated coefficient on x4.

b. Test, against the alternative that it is positive, the null hypothesis that the true coefficient on x4 is 0.

c. Interpret the coefficient of determination, and use it to test the null hypothesis that, taken as a group, the four independent variables do not linearly influence the dependent variable.

d. Find and interpret a 95% confidence interval for b2.