# Question

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. To assess the impact of various factors on ratings, the model

Y = β0 + β1X1 + β2X2 + β3X3 + ε

was fitted for 25 such courses, where

Y = average rating by participants of the course

X= = percentage of course time spent in group discussion sessions

X2 = amount of money (in dollars) per course member spent on the preparation of subject matter material

X3 = amount of money per course member spent on the provision of non-course-related material (food, drinks, and so forth)

Part of the SAS computer output for the fitted regression is shown next.

R@Square = 0.579

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 5% level, the null hypothesis that, taken together, the three independent variables do not linearly influence the course rating.

d. Find and interpret a 90% confidence interval for β1.

e. Test the null hypothesis

H0: β2 = 0

against the alternative

H0: β2 > 0

and interpret your result.

f. Test at the 10% level the null hypothesis

H0: β3 = 0

against the alternative

H0: β2 ≠ 0

and interpret your result.

Y = β0 + β1X1 + β2X2 + β3X3 + ε

was fitted for 25 such courses, where

Y = average rating by participants of the course

X= = percentage of course time spent in group discussion sessions

X2 = amount of money (in dollars) per course member spent on the preparation of subject matter material

X3 = amount of money per course member spent on the provision of non-course-related material (food, drinks, and so forth)

Part of the SAS computer output for the fitted regression is shown next.

R@Square = 0.579

a. Interpret the estimated regression coefficients.

b. Interpret the coefficient of determination.

c. Test, at the 5% level, the null hypothesis that, taken together, the three independent variables do not linearly influence the course rating.

d. Find and interpret a 90% confidence interval for β1.

e. Test the null hypothesis

H0: β2 = 0

against the alternative

H0: β2 > 0

and interpret your result.

f. Test at the 10% level the null hypothesis

H0: β3 = 0

against the alternative

H0: β2 ≠ 0

and interpret your result.

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