It has been hypothesized that overall academic success for college freshmen as measured by grade point average is a function of IQ scores (X1) hours spent studying each week (X2), and one's high school average (x3). Suppose the regression equation is Y (this is Y hat)=6.9+0.055x1 (the 1 is subscripted)+0.107x2 ( the 2 is subscripted)+0.0853X3 (the 3 is subscripted). The multiple standard error is 6.313 and R^2=0.826. A. What is the predicted GPA for a student with a IQ of 108, 32 hours spent studying per week and a high school average of 82?
B. Which independent variable has the smallest affect on GPA?
C. For which independent variable does a unit change have the greatest effect on the GPA?

23.2586 ; IQ ; hours spent studying per week

Step-by-step explanation:

Given the regression model:

y = 6.9+0.055x1 +0.107x2 + 0.0853X3.

IQ scores = (X1)

Hours spent studying each week = (X2),

one's high school average = (x3)

The multiple standard error is 6.313 and R^2=0.826.

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

X1 = 108 ; X2 = 32 ; X3 = 82

y = 6.9 + 0.055(108) + 0.107(32) + 0.0853(82)

y = 23.2586

B.

The Independent variable with the smallest effect on GPA is the variable with the smallest Coefficient, which is IQ with a Coefficient of 0.055

C.

The Independent variable whiae unit change has the greatest effect on GPA is X2, hours spent studying per week as it has the highest Coefficient of all independent variables with a Coefficient value of 0.107.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get