Question:
Consider the following data set:
|
Y1
|
Y2
|
X1
|
X2
|
X3
|
X4
|
|
125
|
113
|
13
|
18
|
25
|
11
|
|
158
|
115
|
39
|
18
|
59
|
30
|
|
207
|
126
|
52
|
50
|
62
|
53
|
|
182
|
119
|
29
|
43
|
50
|
29
|
|
196
|
107
|
50
|
37
|
65
|
56
|
|
175
|
135
|
64
|
19
|
79
|
49
|
|
145
|
111
|
11
|
27
|
17
|
14
|
|
144
|
130
|
22
|
23
|
31
|
17
|
|
160
|
122
|
30
|
18
|
34
|
22
|
|
175
|
114
|
51
|
11
|
58
|
40
|
|
151
|
121
|
27
|
15
|
29
|
31
|
|
161
|
105
|
41
|
22
|
53
|
39
|
|
200
|
131
|
51
|
52
|
75
|
36
|
|
173
|
123
|
37
|
36
|
44
|
27
|
|
175
|
121
|
23
|
48
|
27
|
20
|
|
162
|
120
|
43
|
15
|
65
|
36
|
|
155
|
109
|
38
|
19
|
62
|
37
|
|
230
|
130
|
62
|
56
|
75
|
50
|
|
162
|
134
|
28
|
30
|
36
|
20
|
|
153
|
124
|
30
|
25
|
41
|
33
|
Where:
Y1 - A measure of success in graduate school.
Y2 - Score of grad school on a major review paper.
X1 - A measure of intellectual ability.
X2 - A measure of "work ethic."
X3 - A second measure of intellectual ability.
X4 - A measure of spatial ability.
Write down the linear equation for both regressions
Which factors seems to have significant impact on success in graduate school
Which factors have significant impact on school ranking?
Are those the same factors? How do you interpret the discrepancy?