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Homework 4 - 9 Questions
Covers Chapters 6 and 7
Open Project Talent data set located in the Homework 4 folder. Below is data relating to
six variables for 25 students randomly selected from the Project Talent data bank. This
information was collected from high school seniors as part of a comprehensive survey
and follow-up of over 400,000 high school students. A short description of each of the
variables is as follows:
Gender
Reading Comprehension
Mechanical Reasoning
Sociability Inventory
Coded (0) Males and (1) Females
Total correct out of 48 items
Total correct out of 20 items
Total of 12 self-reported items, the higher the score the
more sociable the person
Socioeconomic Status
Based on 9 self-reported items such as income, value of
home, books in home, father’s occupation, parent’s
education, Standard score with mean of 100 and SD of 10.
The higher the score the higher the status
Mathematics Test
Total correct out of 54 items covering arithmetic and high
school mathematics.
School Size is interpreted as follows:
1 = number of students is less than 100
2 = number of students is from 100 to 399
3 = number of students is 400 or more
1. Perform a multiple regression by regressing Math on Gender, SES, Sociability,
Reading, and Mechanical Reasoning entering the predictors in this order. NOTE that
School Size is NOT included.
a. What is the multiple regression equation?
b. What are the degrees for freedom for the slope tests?
c. What is the interpretation of the slope for Reading?
d. What is the interpretation of the t-tests for SES and Sociability? Be sure to
include the null and alternative hypothesis being tested, the degrees of freedom, the pvalue, and your conclusion and decision about Ho at a 10% level of significance.
SES
Ho:
Ha:
t-stat:
DF:
1
p-value:
Decision/Conclusion:
Sociability
Ho:
Ha:
t-stat:
DF:
p-value:
Decision/Conclusion:
e. Compute the partial coefficient of determination (i.e. partial R2) and partial
correlation for adding Mechanical Reasoning to model already containing Gender, SES,
Sociability and Reading. Be sure to correctly identify the direction of this correlation.
Partial R2:
Interpretation:
Partial r:
f. Compute the 95% confidence interval for the correlation between Reading and
Sociability. Remember to transform your interval back from the Fisher’s value to the
population correlation using Table B8.
2. From the ANOVA table output:
a. What are the null and alternative hypotheses being tested?
b. What is the value of the F test statistic?
c. What are the degrees of freedom for this test?
Numerator DF =
and Denominator DF =
d. What is the p-value of this F test?
e. Using α of 0.05, what would be the decision and conclusion of this test?
3. How much of the variation in Math scores is explained by this combination of the five
predictors?
2
4. What is the coefficient of determination after adjusting for the number of predictors in
the model?
5. You want to estimate (use Minitab) the Math scores for 4 individuals with the
following variable values:
Gender
0
0
1
1
SES
86
97
95
104
Social
5
7
8
10
Reading
23
31
33
37
Mech
8
11
13
15
a. What are the predicted math scores for each of these individuals?
b. Find the 90% family-wise Bonferroni simultaneous confidence intervals for
these predicted Math scores and include the interpretation.
6. Create a probability plot of the residuals.
a. What are the appropriate hypotheses for this test?
b. What is the Anderson-Darling test statistic and p-value?
c. What is the conclusion of this test at a 5% level of significance?
7. Do a check of equal variances by performing a Breusch-Pagan Test and White's Test.
Include: a) the null and alternative hypotheses, b) the test statistic c) p-value and DF of the
test, and d) your decision based on a 0.05 level of significance.
Breusch-Pagan Test
a)
b)
c)
d)
3
White's Test
a)
b)
c)
d)
8. From the Breusch-Pagan test there is one predictor that is more correlated with the
residuals than the other predictors. Provide a scatterplot of the residuals (from full
model) against this predictor. What conclusion do you draw from a visual inspection of
this plot?
9. Find the standard deviations for Math and the five predictors. Using these statistics
and the slope estimates find the standardized regression model. Follow up 1: Which
predictor variable provides the greatest relative contribution to the estimation of Math
scores? Follow up 2: Interpret the standardized slope for this variable.
Standard Deviations:
Standardized regression equation:
Follow up 1:
Follow up 2:
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