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 t-tests 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:
Ha:
t-stat:
DF:
p-value:
Decision/Conclusion:
Sociability
Ho:
Ha:
t-stat:
DF:
p-value:
Decision/Conclusion:
b. State the null and alternative hypotheses being tested by the ANOVA table in output. Include the F-statistic, p-value, and your decision and conclusion about Ho.
Ho:
Ha:
F-stat:
p-value:
Decision/Conclusion:
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.
d. For each of the Sequential SS conduct the partial F test for that variable. Be sure to include the null and alternative hypotheses being tested, the degrees of Freedom, the p-value from both the F-table in text (this will be a range) and by using Calc > Probability Distributions in Minitab, and your conclusion and decision about Ho at 10% level of significance.. Note that this will include five (5) partial F tests.
Gender
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
SES
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
Sociability
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
Reading
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
Mechanical Reasoning
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
e. Compute by hand the partial coefficient of determination (i.e. partial R2) and partial correlation for adding Reading to model already containing Gender, SES, and Sociability. Be sure to correctly identify the direction of this correlation.
Partial R2:
Interpretation:
Partial r:
f. Repeat part e using Minitab to find the partial correlation and paste your Minitab output of this correlation below.
g. Conduct the partial F test to determine whether Gender, SES, and Sociability together account for a significant amount of variability in Math Achievement. Be sure to include the null and alternative hypothesis being tested, the degrees of Freedom, the p-value from both the F-table in text (this will be a range) and by using Calc > Probability Distributions in Minitab, and your conclusion and decision about Ho.
Ho:
Ha:
F-stat:
DF:
p-value from table: p-value from Minitab:
Decision/Conclusion:
h. Use Minitab > Basic Statistics > Correlation to get the correlation matrix of the six variables. Copy and past your output. Which variable has the strongest relationship with Math Achievement? The weakest?
Strongest:
Weakest:
i. Compute the test statistic to determine whether the correlation between Reading and Sociability in the population is equal to zero with a two-tailed test and alpha of 5%. Use Minitab Calc > Probability Distributions to get p-value. Check your conclusion (i.e. p-value) to that found in the correlation matrix.
Ho:
Ha:
t-stat:
DF:
p-value:
Decision/Conclusion:
j. 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.
k. How would you interpret the correlation between Gender and Mechanical Reasoning (remember that Males were coded as 0 and Females as 1). How could we have made this correlation positive?
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