Question

The data from data95.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 :

Which variable is the better predictor?

IQSelf Concept    

obs     gpa     iq      gender  concept
1       7.94    105     2       59
2       8.292   122     2       63
3       4.643   87      2       43
4       7.47    105     2       55
5       8.882   91      1       46
6       7.585   109     2       72
7       7.65    108     2       78
8       2.412   90      2       43
9       6       102     1       58
10      8.833   113     2       60
11      7.47    132     1       71
12      5.528   94      1       12
13      7.167   103     2       67
14      7.571   101     1       70
15      4.7     119     1       31
16      8.167   117     1       65
17      7.822   124     1       51
18      7.598   104     1       51
19      4       98      2       47
20      6.231   117     1       35
21      7.643   111     2       59
22      1.76    88      2       36
24      6.419   109     1       36
26      9.648   115     2       62
27      10.7    123     1       77
28      10.58   127     2       61
29      9.429   113     2       63
30      8       112     2       59
31      9.585   112     2       87
32      9.571   130     1       90
33      8.998   122     1       57
34      8.333   131     1       77
35      8.175   93      2       45
36      8       97      2       62
37      9.333   119     1       80
38      9.5     116     2       68
39      9.167   114     2       53
40      10.14   134     1       86
41      9.999   117     1       51
43      10.76   123     2       43
44      9.763   119     2       61
45      9.41    125     2       68
46      9.167   126     2       65
47      9.348   119     2       69
48      8.167   131     2       54
50      3.647   75      2       59
51      3.408   87      1       52
52      3.936   109     2       27
53      7.167   89      2       57
54      7.647   104     2       34
55      .53     75      2       18
56      6.173   110     2       47
57      7.295   108     2       71
58      7.295   101     1       51
59      8.938   118     1       63
60      7.882   100     1       76
61      8.353   117     2       60
62      5.062   96      2       35
63      8.175   113     2       52
64      8.235   101     2       43
65      7.588   122     2       65
68      7.647   112     2       55
69      5.237   118     1       42
71      7.825   121     2       52
72      7.333   112     1       46
74      9.167   130     2       57
76      7.996   95      2       69
77      8.714   112     1       59
78      7.833   119     1       68
79      4.885   91      2       42
80      7.998   117     1       54
83      3.82    115     2       44
84      5.936   113     1       49
85      9       103     1       69
86      9.5     130     1       61
87      6.057   107     2       52
88      6.057   117     1       50
89      6.938   109     2       46

Answer 1

Using IQ as predictor

in Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.646809885
R Square	0.4184
Adjusted R Square	0.4107
Standard Error	1.6117
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	142.0037	142.0037	54.6657	0.0000
Residual	76	197.4232	2.5977
Total	77	339.4269
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-3.8983	1.5452	-2.5228	0.0137	-6.9759
iq	0.1027	0.0139	7.3936	0.0000	0.0751

R^2 = 0.4184

Using Self-concept as predictor

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.6256
R Square	0.3914
Adjusted R Square	0.3834
Standard Error	1.6487
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	132.8474	132.8474	48.8742	0.0000
Residual	76	206.5795	2.7182
Total	77	339.4269
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2.4952	0.7324	3.4067	0.0011	1.0364
concept	0.0884	0.0126	6.9910	0.0000	0.0632

R^2 = 0.3914

we see that R^2 is larger with IQ as predictor

hence IQ is is the better predictor

Please rate