Question

The data from data47.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    111     2       68
2       8.292   115     2       65
3       4.643   106     2       61
4       7.47    112     2       70
5       8.882   117     1       65
6       7.585   105     2       70
7       7.65    97      2       66
8       2.412   90      2       39
9       6       105     1       49
10      8.833   138     2       57
11      7.47    101     1       71
12      5.528   107     1       61
13      7.167   114     2       46
14      7.571   112     1       68
15      4.7     98      1       46
16      8.167   103     1       81
17      7.822   121     1       65
18      7.598   106     1       67
19      4       114     2       57
20      6.231   108     1       71
21      7.643   117     2       76
22      1.76    81      2       55
24      6.419   103     1       39
26      9.648   112     2       50
27      10.7    130     1       67
28      10.58   116     2       59
29      9.429   123     2       44
30      8       94      2       78
31      9.585   116     2       54
32      9.571   126     1       64
33      8.998   97      1       63
34      8.333   106     1       60
35      8.175   110     2       74
36      8       123     2       62
37      9.333   91      1       91
38      9.5     111     2       54
39      9.167   103     2       52
40      10.14   110     1       67
41      9.999   124     1       98
43      10.76   116     2       79
44      9.763   125     2       71
45      9.41    109     2       71
46      9.167   103     2       70
47      9.348   116     2       80
48      8.167   121     2       71
50      3.647   95      2       50
51      3.408   98      1       46
52      3.936   97      2       48
53      7.167   87      2       71
54      7.647   119     2       71
55      .53     60      2       44
56      6.173   107     2       71
57      7.295   107     2       55
58      7.295   114     1       71
59      8.938   121     1       59
60      7.882   112     1       60
61      8.353   114     2       56
62      5.062   116     2       67
63      8.175   116     2       65
64      8.235   114     2       74
65      7.588   110     2       50
68      7.647   100     2       85
69      5.237   107     1       52
71      7.825   114     2       47
72      7.333   86      1       58
74      9.167   109     2       36
76      7.996   98      2       72
77      8.714   116     1       60
78      7.833   103     1       62
79      4.885   101     2       39
80      7.998   105     1       46
83      3.82    79      2       36
84      5.936   108     1       33
85      9       99      1       78
86      9.5     106     1       47
87      6.057   107     2       60
88      6.057   94      1       64
89      6.938   115     2       44

Answer 1

R2 is highlihted in yellow in the pics: The linear regression linear for best ft is run and results are below:

a) Regression with Self concept

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.438798403
R Square	0.192544038
Adjusted R Square	0.181919617
Standard Error	1.899003434
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	65.35462429	65.35462429	18.12278016	5.85433E-05
Residual	76	274.0722671	3.606214041
Total	77	339.4268914
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	3.179726112	1.0250894	3.10190127	0.002698498	1.138083631
Self concept	0.069786405	0.016392999	4.257085877	5.85433E-05	0.037136917

b)Regression with IQ:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.618195085
R Square	0.382165163
Adjusted R Square	0.374035757
Standard Error	1.6611258
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	129.7171332	129.7171332	47.0102212	1.63509E-09
Residual	76	209.7097582	2.759338924
Total	77	339.4268914
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-4.040199423	1.685855661	-2.396527482	0.019009996	-7.397871967
IQ	0.106700673	0.015562201	6.856400018	1.63509E-09	0.075705864

c) The regression with IQ yeild a R2 of 0.3821 which is more than 0.1925 for Self concept.

The R2 determines which is a better predictor. The higher it is the more predictive power the regressor has.

Hence, IQ is a better predictor.