Question

a. Construct a regression model using all three independent variables. Let y be the final exam scores,x1 be the GPAs, x2 be the number of hours spent studying, and x3be the number of absences during the semester.

b.Calculate the multiple coefficient of determination

c.Test the significance of the overall regression model using significance=0.10

d.Calculate the adjusted multiple coefficent of determination

Score   GPA   Hours   Absences
67   2.53   3.0   0
68   2.25   4.0   3
69   2.60   2.5   1
71   3.11   0.5   0
75   3.08   6.0   4
76   2.74   3.5   6
76   3.36   1.5   0
78   2.98   3.0   3
78   2.99   2.0   3
80   2.83   2.5   2
80   2.79   4.5   0
83   3.46   7.0   1
82   3.24   3.0   1
83   3.14   3.0   4
83   3.19   5.5   0
85   2.96   2.0   0
83   2.71   4.0   1
84   3.19   4.5   3
84   3.73   2.0   0
85   3.56   3.5   2
85   2.91   6.0   1
85   3.06   6.5   1
86   3.16   5.0   3
88   3.90   7.5   4
87   3.54   4.0   0
90   3.34   6.5   1
88   3.66   5.0   0
89   2.88   3.5   1
91   3.41   6.0   1
92   3.20   4.5   2
91   3.80   7.0   0
91   3.92   6.0   2
92   3.99   5.0   0
91   3.59   6.5   1
93   2.97   4.0   2
93   3.27   6.5   0
97   2.88   3.5   0
100   3.74   5.0   1
101   3.48   6.5   1
101   3.00   7.0   0

Answer 1

a) The estimated regression equation is :

b) The multiple coefficient of determination R² = 47.70%

c) To test the significance of the overall regression model,

i.e. against H₁ : at least one of them is not zero

The value of the F statistic = 10.95 and P-value = 0

Since P-value < 0.10, so we reject H₀ at 10% level of significance and we can conclude that overall model is significant.

d) The adjusted multiple coefficient of determination =