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Homework 4
Covers Chapters 7
Use the Project Talent data set.
1.
Perform a multiple regression by regressing Math on Gender, SES, Sociability,
Reading, and Mechanical Reasoning entering the predictors in this order.
a.
What is the interpretation of the ttests for SES and Sociability?
Be sure to
include the null and alternative hypothesis being tested, the degrees of freedom, the p
value, and your conclusion and decision about Ho at a 10% level of significance.
SES
Ho: B
2
= 0
Ha: B
2
≠ 0
tstat: 1.63
DF: 19
pvalue: 0.119
Decision/Conclusion: Since pvalue is greater than 0.10 we would not reject Ho.
Plausible that the addition of SES makes no significant linear contribution to
prediction of Math Achievement when Gender, Sociability, Reading, and
Mechanical Reasoning are in the model.
Sociability
Ho: B
3
= 0
Ha: B
3
≠ 0
tstat:  0.11
DF: 19
pvalue: 0.912
Decision/Conclusion: Since pvalue is greater than 0.10 we would not reject Ho.
Plausible that the addition of Sociability makes no significant linear contribution to
prediction of Math Achievement when Gender, SES, Reading, and Mechanical
Reasoning are in the model.
Regression Analysis: Math versus Gender, SES, Social, Reading, Mech
The regression equation is
Math =  19.4  0.63 Gender + 0.231 SES  0.050 Social + 0.237 Reading
+ 1.28 Mech
Predictor
Coef
SE Coef
T
P
Constant
19.36
14.14
1.37
0.187
Gender
0.635
3.101
0.20
0.840
1
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View Full DocumentSES
0.2312
0.1415
1.63
0.119
Social
0.0501
0.4476
0.11
0.912
Reading
0.2370
0.1826
1.30
0.210
Mech
1.2820
0.4641
2.76
0.012
b.
State the null and alternative hypotheses being tested by the ANOVA table in
output.
Include the Fstatistic, pvalue, and your decision and conclusion about Ho.
Ho: All slopes equal 0
Ha: Not all slopes equal 0
Fstat: 8.83
pvalue: 0.000
Decision/Conclusion: Reject Ho and conclude at least one slope does not equal 0.
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
5
1769.93
353.99
8.83
0.000
Residual Error
19
761.91
40.10
Total
24
2531.84
Source
DF
Seq SS
Gender
1
401.28
SES
1
582.95
Social
1
48.57
Reading
1
431.08
Mech
1
306.04
c.
Create an ANOVA table that shows the contributions of each of these
predictors using the Sequential Sum of Squares from output.
The addition of these sum
of squares should equal the SSR (Sum of Squares Regression) found in the ANOVA table
of your output.
Source
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 '08
 SENTURK,DAMLA
 Regression Analysis

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