Question

The data from data105.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.)
(Regressor: IQ) R ² =

(Regressor: Self-Concept) R ²  =

obs     gpa     iq      gender  concept
1       7.94    101     2       44
2       8.292   120     2       57
3       4.643   114     2       49
4       7.47    106     2       68
5       8.882   116     1       82
6       7.585   107     2       58
7       7.65    101     2       73
8       2.412   81      2       22
9       6       109     1       39
10      8.833   110     2       66
11      7.47    99      1       75
12      5.528   104     1       47
13      7.167   101     2       59
14      7.571   104     1       71
15      4.7     108     1       44
16      8.167   106     1       44
17      7.822   105     1       73
18      7.598   104     1       76
19      4       95      2       41
20      6.231   102     1       46
21      7.643   111     2       52
22      1.76    119     2       44
24      6.419   111     1       48
26      9.648   104     2       60
27      10.7    115     1       44
28      10.58   138     2       50
29      9.429   115     2       59
30      8       108     2       69
31      9.585   115     2       56
32      9.571   118     1       49
33      8.998   121     1       63
34      8.333   119     1       60
35      8.175   123     2       69
36      8       96      2       40
37      9.333   108     1       53
38      9.5     111     2       70
39      9.167   131     2       47
40      10.14   126     1       76
41      9.999   112     1       67
43      10.76   122     2       91
44      9.763   134     2       87
45      9.41    103     2       65
46      9.167   116     2       67
47      9.348   101     2       83
48      8.167   112     2       74
50      3.647   95      2       56
51      3.408   73      1       47
52      3.936   80      2       33
53      7.167   121     2       50
54      7.647   111     2       61
55      .53     81      2       27
56      6.173   106     2       46
57      7.295   117     2       74
58      7.295   112     1       69
59      8.938   98      1       68
60      7.882   102     1       51
61      8.353   114     2       58
62      5.062   116     2       56
63      8.175   123     2       50
64      8.235   91      2       64
65      7.588   102     2       38
68      7.647   115     2       44
69      5.237   105     1       40
71      7.825   86      2       75
72      7.333   111     1       57
74      9.167   116     2       50
76      7.996   106     2       40
77      8.714   118     1       68
78      7.833   114     1       71
79      4.885   102     2       65
80      7.998   131     1       55
83      3.82    98      2       31
84      5.936   111     1       57
85      9       117     1       56
86      9.5     111     1       53
87      6.057   97      2       58
88      6.057   110     1       43
89      6.938   121     2       43

Answer 1

Will be using excel to solve above problem

-> Considering both IQ and Concept in start:

So, R² (For Both) = 0.4785 or 47.85%

-> Considering only IQ

R²(IQ) = 0.3095 or 30.95%

-> Considering Only Concept

R² (Concept) = 0.3088 or 30.88%

Looks Like together they result in better performance