Homework 4 - 6 Questions
Covers Chapter 6
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 Coded (0) Males and (1) Females
Reading Comprehension Total correct out of 48 items
Mechanical Reasoning Total correct out of 20 items
Sociability Inventory 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 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:
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. You want to estimate (use Minitab) the Math scores for 4 individuals with the following variable values:
Gender / SES / Social / Reading / Mech0 / 86 / 5 / 23 / 8
0 / 97 / 7 / 31 / 11
1 / 95 / 8 / 33 / 13
1 / 104 / 10 / 37 / 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.
4. 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?
5. 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)
White's Test
a)
b)
c)
d)
6. 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?
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