Question

Please give numerical measures not percentage and round to the three decimal places. Thank you.

The data from data349.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 Incorrect: (Regressor: Self-Concept) R 2 29% IWhich variable is the better predictor? IQ

Self Concept

obs     gpa     iq      gender  concept
1       7.94    112     2       50
2       8.292   101     2       44
3       4.643   95      2       46
4       7.47    102     2       51
5       8.882   94      1       60
6       7.585   108     2       61
7       7.65    106     2       51
8       2.412   79      2       47
9       6       117     1       64
10      8.833   113     2       34
11      7.47    104     1       57
12      5.528   105     1       44
13      7.167   90      2       45
14      7.571   98      1       61
15      4.7     121     1       48
16      8.167   114     1       70
17      7.822   114     1       64
18      7.598   117     1       63
19      4       105     2       44
20      6.231   113     1       34
21      7.643   113     2       62
22      1.76    94      2       18
24      6.419   103     1       49
26      9.648   111     2       70
27      10.7    137     1       72
28      10.58   125     2       41
29      9.429   110     2       77
30      8       101     2       58
31      9.585   124     2       72
32      9.571   133     1       58
33      8.998   109     1       49
34      8.333   110     1       50
35      8.175   108     2       29
36      8       105     2       82
37      9.333   124     1       42
38      9.5     84      2       72
39      9.167   119     2       55
40      10.14   101     1       62
41      9.999   107     1       53
43      10.76   119     2       73
44      9.763   134     2       65
45      9.41    123     2       62
46      9.167   125     2       89
47      9.348   101     2       82
48      8.167   97      2       67
50      3.647   102     2       54
51      3.408   77      1       31
52      3.936   98      2       56
53      7.167   101     2       38
54      7.647   103     2       70
55      .53     73      2       35
56      6.173   101     2       34
57      7.295   104     2       54
58      7.295   122     1       58
59      8.938   110     1       83
60      7.882   106     1       48
61      8.353   118     2       58
62      5.062   99      2       48
63      8.175   112     2       35
64      8.235   100     2       67
65      7.588   102     2       57
68      7.647   94      2       62
69      5.237   97      1       44
71      7.825   119     2       61
72      7.333   116     1       54
74      9.167   126     2       44
76      7.996   105     2       53
77      8.714   116     1       48
78      7.833   105     1       45
79      4.885   90      2       55
80      7.998   118     1       60
83      3.82    104     2       22
84      5.936   107     1       52
85      9       121     1       59
86      9.5     102     1       75
87      6.057   89      2       46
88      6.057   113     1       44
89      6.938   111     2       58

Answer 1

Here I am using the R software to solve it.

R-Code

aa=read.table("C:/Users/DELL/OneDrive/Desktop/New Text Document.txt",header=T)

summary(lm(gpa~iq,data=aa))

summary(lm(gpa~concept,data=aa))

OUTPUT:

Call:
lm(formula = gpa ~ iq, data = aa)

Residuals:
Min 1Q Median 3Q Max
-4.3301 -0.8448 0.2547 0.8282 4.4138

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.34605 1.68258 -1.989 0.0503 .
iq 0.10038 0.01555 6.457 9.1e-09 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.698 on 76 degrees of freedom
Multiple R-squared: 0.3542, Adjusted R-squared: 0.3457
F-statistic: 41.69 on 1 and 76 DF, p-value: 9.098e-09

Call:
lm(formula = gpa ~ concept, data = aa)

Residuals:
Min 1Q Median 3Q Max
-5.3295 -0.8105 -0.0631 1.1373 4.2335

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.01832 0.81114 3.721 0.000378 ***
concept 0.08118 0.01441 5.635 2.83e-07 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.775 on 76 degrees of freedom
Multiple R-squared: 0.2947, Adjusted R-squared: 0.2854
F-statistic: 31.75 on 1 and 76 DF, p-value: 2.829e-07

Conclusion: R-squared for iq = 35.42% and R-squared for concept = 29.47%

So the variable "iq" is better predictor to predict GPA. As both the p-value is < 0.05, both regression coefficients are significant we would say the better predictor by R-squared value.