IV It has been hypothesized that overall academic success fo

IV. It has been hypothesized that overall academic success for college freshmen as measured by grade point average (GPA) is a function of IQ scores (X SUB 1) , hours spent studying each week (X sub 2) , and one\'s high school average (x sub 3) . Suppose the regression equation is: Y-hat = -6.9 + 0.055X1 + 0.107X2 + 0.00833X3 . The multiple standard error is 6.313 and R2 = 0.826. a. What is the predicted GPA for a student with an IQ of 108, 32 hours spent studying per week and a high school average of 82? b. Assuming other independent variables are held constant, what effect on the GPA will there be if the number of hours spent studying per week increases from 32 to 36? c. Which independent variable has the smallest affect on GPA? d. For which independent variable does a unit change have the greatest effect on the GPA?

Solution

What is the predicted GPA for a student with an IQ of 108, 32 hours spent studying per week and a high school average of 82?

Y = -6.9 + 0.055*108 + 0.107*32 + 0.00833*82

Y = 3.14706

Assuming other independent variables are held constant, what effect on the GPA will there be if the number of hours spent studying per week increases from 32 to 36?

Y = -6.9 + 0.055*108 + 0.107*36 + 0.00833*82

Y = 3.57506

increase but not so much

Which independent variable has the smallest affect on GPA?

one\'s high school average (x sub 3), because it has the coefficient more lower

For which independent variable does a unit change have the greatest effect on the GPA?

hours spent studying each week (X sub 2)

because it has the greatest coefficient in the regression equation