A statistics professor investigated some of the factors that affect an individual student's final grade in her course. She proposed a multiple regression model where y = β1x1 + β2x2 + β3x3 + e
y is the final grade (out of 100 points), x1 is the number of lectures skipped, x2 is the number of late assignments, and x3 is the midterm exam score (out of 100). The professor recorded the data for 50 randomly selected students. The computer output is shown below.
The REGRESSION EQUATION IS
^y = 41.6 - 3.18x1 - 1.17x2 + .63x3
Predictor Coef S. E t
Constant 41.6 17.8 2.337
x1 -3.18 1.66 -1.916
x2 -1.17 1.13 -1.035
x3 0.63 0.13 4.846
Sc = 13.74 R^2 = 30.0%
ANALYSIS OF VARIANCE
Source of Variation df SS MS F
Regression 3 3716 1238.667 6.558
Error 46 8688 188.870
Total 49 12404
a) What is the coefficient of determination? What does this statistic tell you?
b) Does this data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final grade?
c) Does this data provide enough evidence to conclude at the 5% significance level that the final grade and the number of skipped lectures are linearly related?
d) Does this data provide enough evidence at the 1% significance level to conclude that the final grade and the midterm exam score are positively linearly related?