Question

This data 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.)
A. (Regressor: IQ) R ²
  

B. (Regressor: Self-Concept) R ²
  

obs     gpa     iq      gender  concept
1       7.94    118     2       38
2       8.292   136     2       62
3       4.643   88      2       26
4       7.47    111     2       58
5       8.882   106     1       60
6       7.585   97      2       54
7       7.65    120     2       56
8       2.412   76      2       23
9       6       113     1       51
10      8.833   101     2       68
11      7.47    119     1       54
12      5.528   118     1       64
13      7.167   100     2       71
14      7.571   100     1       53
15      4.7     112     1       34
16      8.167   122     1       40
17      7.822   113     1       58
18      7.598   101     1       58
19      4       101     2       35
20      6.231   98      1       50
21      7.643   100     2       50
22      1.76    85      2       46
24      6.419   110     1       56
26      9.648   111     2       79
27      10.7    97      1       65
28      10.58   114     2       71
29      9.429   117     2       56
30      8       123     2       84
31      9.585   116     2       72
32      9.571   128     1       57
33      8.998   139     1       39
34      8.333   115     1       74
35      8.175   106     2       72
36      8       114     2       57
37      9.333   88      1       56
38      9.5     115     2       84
39      9.167   125     2       51
40      10.14   131     1       64
41      9.999   117     1       67
43      10.76   131     2       83
44      9.763   108     2       57
45      9.41    130     2       69
46      9.167   124     2       66
47      9.348   118     2       51
48      8.167   110     2       56
50      3.647   104     2       52
51      3.408   80      1       41
52      3.936   92      2       54
53      7.167   110     2       40
54      7.647   113     2       46
55      .53     80      2       33
56      6.173   111     2       71
57      7.295   122     2       72
58      7.295   104     1       61
59      8.938   125     1       70
60      7.882   142     1       62
61      8.353   106     2       54
62      5.062   92      2       51
63      8.175   120     2       54
64      8.235   118     2       59
65      7.588   96      2       57
68      7.647   116     2       50
69      5.237   106     1       50
71      7.825   110     2       58
72      7.333   116     1       68
74      9.167   108     2       70
76      7.996   99      2       49
77      8.714   99      1       87
78      7.833   111     1       40
79      4.885   107     2       57
80      7.998   116     1       76
83      3.82    99      2       43
84      5.936   107     1       46
85      9       132     1       54
86      9.5     116     1       53
87      6.057   111     2       31
88      6.057   91      1       46
89      6.938   103     2       36

Answer 1

R-squared:

or   

A) Regression IQ vs GPA

R-squared value= 0.374249187 or 37.4249187%

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.611759092
R Square	0.374249187
Adjusted R Square	0.366015624
Standard Error	1.671733473
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	127.0302382	127.0302382	45.45409711	2.67861E-09
Residual	76	212.3966532	2.794692805
Total	77	339.4268914
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95.0%
Intercept	-3.029035627	1.565273638	-1.935147666	0.056692745	-6.146548211	0.088476956
iq	0.095188115	0.014118749	6.741965375	2.67861E-09	0.06706819	0.12330804

B) Regression Concept Vs GPA:

R-squared value: 0.339685078 or 33.9685078%

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.582825083
R Square	0.339685078
Adjusted R Square	0.330996724
Standard Error	1.717283049
Observations	78
ANOVA
	df	SS	MS	F	Significance F
Regression	1	115.29825	115.29825	39.09659627	2.16209E-08
Residual	76	224.1286413	2.94906107
Total	77	339.4268914
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	2.408983738	0.828789495	2.906629188	0.004784947	0.758306427	4.059661049
concept	0.089587157	0.014327693	6.252727107	2.16209E-08	0.061051083	0.11812323

Both variables are statistically significant for predictions. R-squared value of IQ vs GPA is 0.374249 compare with Concept Vs GPA of 0.339685078. More variance was covered by IQ than Concept variable.