The students in a training program have taken four tests along with a final exam, with the scores shown in the table. The data are also in file XR17071.
|
Student
|
Test 1
|
Test 2
|
Test 3
|
Test 4
|
Final Exam
|
|
1
|
59
|
65
|
53
|
65
|
62
|
|
2
|
69
|
77
|
57
|
76
|
78
|
|
3
|
79
|
74
|
81
|
86
|
82
|
|
4
|
87
|
88
|
83
|
90
|
96
|
|
5
|
92
|
89
|
97
|
92
|
94
|
|
6
|
65
|
69
|
60
|
66
|
68
|
|
7
|
71
|
70
|
68
|
81
|
78
|
|
8
|
93
|
87
|
85
|
95
|
94
|
|
9
|
83
|
92
|
89
|
90
|
91
|
|
10
|
71
|
68
|
69
|
74
|
77
|
|
11
|
64
|
61
|
74
|
74
|
73
|
|
12
|
76
|
82
|
79
|
78
|
86
|
|
13
|
65
|
75
|
67
|
77
|
79
|
|
14
|
90
|
88
|
75
|
94
|
89
|
|
15
|
69
|
68
|
74
|
76
|
72
|
|
16
|
85
|
81
|
99
|
79
|
96
|
a. Construct the correlation matrix for these variables. Does it appear that multicollinearity could be a problem if all of the independent variables are used in estimating y 5 final exam score? In a stepwise regression, which independent variable would be the first one introduced into the equation, and why?
b. With y = final exam score and the independent variables as shown above, apply stepwise regression analysis to these data.
c. Describe each step of the stepwise regression in terms of the variable introduced, the regression equation after its introduction, and the proportion of variation in y that has been explained.
d. Using only the independent variables introduced during the stepwise regression, carry out a conventional multiple regression analysis on the data. What, if any, additional information does your computer statistical package provide that was not given in the printout for the stepwise regression?