# Question

Based on 107 students’ scores on the first examination in a course on business statistics, the following model was estimated by least squares:

where

y` = student’s actual score on the examination

x1 = student’s expected score on the examination

x2 = hours per week spent working on the course

x3 = student’s grade point average

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

a. Interpret the estimate of β1.

b. Find and interpret a 95% confidence interval for β2.

c. Test, against a two-sided alternative, the null hypothesis that β3 is 0, and interpret your result.

d. Interpret the coefficient of determination.

e. Test the null hypothesis that β1 = β1 = β3 = 0.

f. Find and interpret the coefficient of multiple correlation.

g. Predict the score of a student who expects a score of 80, works 8 hours per week on the course, and has a grade point average of 3.0.

where

y` = student’s actual score on the examination

x1 = student’s expected score on the examination

x2 = hours per week spent working on the course

x3 = student’s grade point average

The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

a. Interpret the estimate of β1.

b. Find and interpret a 95% confidence interval for β2.

c. Test, against a two-sided alternative, the null hypothesis that β3 is 0, and interpret your result.

d. Interpret the coefficient of determination.

e. Test the null hypothesis that β1 = β1 = β3 = 0.

f. Find and interpret the coefficient of multiple correlation.

g. Predict the score of a student who expects a score of 80, works 8 hours per week on the course, and has a grade point average of 3.0.

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