The data from data257.dat contains information on 78 seventh-grade students. We want to know how well...

The data from data257.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.)

gpa     iq      gender  concept
1       7.94    125     2       41
2       8.292   115     2       69
3       4.643   122     2       28
4       7.47    128     2       50
5       8.882   121     1       51
6       7.585   110     2       69
7       7.65    94      2       68
8       2.412   74      2       42
9       6       82      1       59
10      8.833   126     2       63
11      7.47    107     1       55
12      5.528   108     1       52
13      7.167   101     2       58
14      7.571   103     1       81
15      4.7     111     1       40
16      8.167   115     1       61
17      7.822   106     1       64
18      7.598   111     1       68
19      4       99      2       33
20      6.231   97      1       53
21      7.643   117     2       59
22      1.76    92      2       19
24      6.419   102     1       72
26      9.648   121     2       44
27      10.7    136     1       43
28      10.58   122     2       60
29      9.429   116     2       55
30      8       112     2       64
31      9.585   129     2       63
32      9.571   113     1       73
33      8.998   137     1       60
34      8.333   129     1       69
35      8.175   119     2       60
36      8       87      2       61
37      9.333   122     1       71
38      9.5     102     2       53
39      9.167   117     2       68
40      10.14   130     1       49
41      9.999   114     1       64
43      10.76   108     2       57
44      9.763   109     2       80
45      9.41    112     2       66
46      9.167   113     2       53
47      9.348   115     2       76
48      8.167   121     2       59
50      3.647   103     2       47
51      3.408   102     1       50
52      3.936   102     2       48
53      7.167   117     2       34
54      7.647   115     2       49
55      .53     90      2       15
56      6.173   112     2       51
57      7.295   100     2       52
58      7.295   119     1       74
59      8.938   113     1       64
60      7.882   107     1       57
61      8.353   120     2       58
62      5.062   79      2       34
63      8.175   113     2       56
64      8.235   93      2       48
65      7.588   91      2       42
68      7.647   122     2       44
69      5.237   107     1       54
71      7.825   121     2       91
72      7.333   108     1       66
74      9.167   117     2       67
76      7.996   110     2       49
77      8.714   110     1       62
78      7.833   106     1       65
79      4.885   106     2       62
80      7.998   126     1       83
83      3.82    101     2       53
84      5.936   100     1       52
85      9       104     1       56
86      9.5     113     1       83
87      6.057   109     2       60
88      6.057   104     1       62
89      6.938   119     2       48

(Regressor: IQ) R ²

⁼

(Regressor: Self-Concept) R ²

⁼

Expert Solution

IQ

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.576383433
R Square	0.332217862
Adjusted R Square	0.323431255
Standard Error	1.726965757
Observations	78

ANOVA
	df	SS	MS	F	Significance F
Regression	1	112.7636762	112.7636762	37.80957304	3.34928E-08
Residual	76	226.6632152	2.982410726
Total	77	339.4268914

	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-3.363963213	1.76894641	-1.901676159	0.061003464	-6.887125326
iq	0.097946234	0.015928939	6.148948938	3.34928E-08	0.066221002

Concept

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.545796308
R Square	0.29789361
Adjusted R Square	0.288655368
Standard Error	1.770792974
Observations	78

ANOVA
	df	SS	MS	F	Significance F
Regression	1	101.1131019	101.1131019	32.24570326	2.36652E-07
Residual	76	238.3137895	3.135707757
Total	77	339.4268914

	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	2.704030958	0.858895432	3.148265618	0.002347232	0.993392452
concept	0.08333309	0.014675117	5.678530027	2.36652E-07	0.054105062

R^2 of IQ = 0.332217

R^2 of concept = 0.297893

orchestra answered 2 years ago

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