Question

The data from data421.dat contains information on 78 seventh-grade students. We want to know how well each of IQ score and self-concept score predicts GPA using least-squares regression. We also want to know which of these explanatory variables predicts GPA better. Give numerical measures that answer these questions. (Round your answers to three decimal places.)
find:(Regressor: IQ) R 2   
find: (Regressor: Self-Concept) R 2 
  

 obs  gpa     iq      gender  concept
1       7.94    103     2       54
2       8.292   111     2       73
3       4.643   114     2       39
4       7.47    115     2       69
5       8.882   111     1       47
6       7.585   115     2       76
7       7.65    111     2       63
8       2.412   92      2       30
9       6       100     1       41
10      8.833   115     2       53
11      7.47    116     1       57
12      5.528   96      1       41
13      7.167   105     2       61
14      7.571   116     1       59
15      4.7     80      1       64
16      8.167   116     1       58
17      7.822   102     1       64
18      7.598   123     1       41
19      4       93      2       53
20      6.231   101     1       48
21      7.643   101     2       67
22      1.76    85      2       37
24      6.419   101     1       60
26      9.648   115     2       86
27      10.7    135     1       80
28      10.58   132     2       80
29      9.429   111     2       59
30      8       110     2       73
31      9.585   115     2       70
32      9.571   125     1       74
33      8.998   106     1       44
34      8.333   117     1       73
35      8.175   115     2       57
36      8       117     2       57
37      9.333   125     1       63
38      9.5     125     2       92
39      9.167   89      2       65
40      10.14   120     1       82
41      9.999   113     1       89
43      10.76   124     2       77
44      9.763   107     2       64
45      9.41    121     2       67
46      9.167   110     2       72
47      9.348   105     2       73
48      8.167   123     2       77
50      3.647   89      2       29
51      3.408   102     1       44
52      3.936   93      2       56
53      7.167   113     2       44
54      7.647   105     2       59
55      .53     104     2       53
56      6.173   91      2       41
57      7.295   113     2       59
58      7.295   109     1       53
59      8.938   99      1       54
60      7.882   120     1       76
61      8.353   139     2       70
62      5.062   89      2       56
63      8.175   119     2       55
64      8.235   130     2       67
65      7.588   121     2       45
68      7.647   119     2       59
69      5.237   101     1       67
71      7.825   109     2       67
72      7.333   95      1       48
74      9.167   110     2       56
76      7.996   110     2       66
77      8.714   123     1       26
78      7.833   108     1       70
79      4.885   112     2       36
80      7.998   124     1       46
83      3.82    86      2       78
84      5.936   102     1       76
85      9       108     1       68
86      9.5     100     1       72
87      6.057   93      2       76
88      6.057   110     1       43
89      6.938   100     2       54

Answer 1

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(Regressor: IQ) R 2  = 0.3935(Regressor: Self-Concept) R 2  = 0.2771