Question

The data from data217.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 ANSWER 1}


(Regressor: Self-Concept) R ^{2 : ANSWER 2}

Which variable is the better predictor?

IQSelf Concept Answer 3

obs     gpa     iq      gender  concept
1       7.94    118     2       66
2       8.292   104     2       60
3       4.643   83      2       47
4       7.47    120     2       55
5       8.882   90      1       67
6       7.585   104     2       59
7       7.65    104     2       75
8       2.412   107     2       58
9       6       114     1       55
10      8.833   107     2       101
11      7.47    116     1       59
12      5.528   91      1       73
13      7.167   120     2       38
14      7.571   114     1       57
15      4.7     117     1       35
16      8.167   114     1       58
17      7.822   123     1       53
18      7.598   132     1       56
19      4       90      2       49
20      6.231   111     1       68
21      7.643   125     2       92
22      1.76    74      2       35
24      6.419   118     1       48
26      9.648   123     2       74
27      10.7    118     1       103
28      10.58   112     2       67
29      9.429   103     2       64
30      8       123     2       82
31      9.585   125     2       59
32      9.571   121     1       50
33      8.998   117     1       60
34      8.333   122     1       70
35      8.175   108     2       63
36      8       111     2       77
37      9.333   118     1       55
38      9.5     125     2       61
39      9.167   127     2       45
40      10.14   129     1       83
41      9.999   140     1       46
43      10.76   126     2       74
44      9.763   124     2       56
45      9.41    127     2       51
46      9.167   122     2       69
47      9.348   107     2       71
48      8.167   124     2       84
50      3.647   97      2       43
51      3.408   125     1       22
52      3.936   88      2       25
53      7.167   118     2       70
54      7.647   123     2       50
55      .53     80      2       37
56      6.173   95      2       64
57      7.295   105     2       57
58      7.295   99      1       58
59      8.938   124     1       80
60      7.882   103     1       50
61      8.353   101     2       36
62      5.062   92      2       69
63      8.175   117     2       75
64      8.235   118     2       67
65      7.588   114     2       39
68      7.647   113     2       43
69      5.237   109     1       53
71      7.825   97      2       61
72      7.333   99      1       61
74      9.167   129     2       70
76      7.996   120     2       63
77      8.714   103     1       45
78      7.833   111     1       41
79      4.885   108     2       67
80      7.998   98      1       65
83      3.82    102     2       56
84      5.936   101     1       48
85      9       118     1       37
86      9.5     115     1       50
87      6.057   108     2       32
88      6.057   105     1       63
89      6.938   107     2       49

Answer 1

EXCEL PROCEDURE

predecure 1:

data -> data analytics -> regression
Y range: GPA
X range: IQ
ok

output 1:

precedure 2:

data -> data analytics -> regression
Y range: GPA
X range: concept
ok

output 2:

ANALYSIS

(Regressor: IQ) R 2 -> 0.379 -> from output 1 -> there is 37.9% variation in GPA which is explained by IQ -> ANSWER 1
(Regressor: Self-Concept) R 2 -> 0.198 -> from output 2 -> there is 19.8% variation in GPA which is explained by concept -> ANSWER 2

Which variable is the better predictor -> IQSelf -> R2 for IQ has higher value as comapred to Concept. the R2 explains % of variation in dependent variable which is explained by all independent variables in the model -> Answer 3