Chapter 9: Multiple Regression.
- Consider the
Calc.xls data from Chapter 8,
which were collected to see how performance in freshman calculus
is related to various predictors. What was the best individual predictor
of the first semester calculus score? Was it a very successful predictor?
What does multiple regression aim to calculate?
- Assume the analysis presented in the book and consider a male student
who did not take calculus in high school, scored 30 on his ACT Math exam, scored
23 on his algebra placement test, had a 4.0 grade in second-year high school algebra,
and was ranked in the 90th percentile in hos high-school graduation class. What would
you predict his calculus score to be? Why. Explain your answer.
- Is there a difference between male and female students regarding performance
in first-year college calculus?
- How could you reduce the number of predictors (assuming there are non-significant variables).
- Name and briefly describe the four common plots that can help
you assess the success of the regression. How does the use of each one of
them translate into conclusions with respect to the example discussed here?
(That is, consider questions such as these: Does it appear that the range of
values is narrower for large values of predicted calculus score? What does
plotting the residuals vs. predicted values tell us? Same questions for the
plotting of residuals against the predictor variables. Is there any normality
assumption you need to test? Does the assumption seem reasonable in our case here?)
- Some of the female faculty at a junior college felt underpaid, and they
sought statistical help in proving their case. The college collected data for the
variables that influence salary for 37 females and 44 males. The data are stored in
Discrim.xls. You are to find out if the female faculty have been treated
unfairly or not. What do you do and what are your most exhaustive conclusions? Provide
a summary with explanations.
- Is there a discrepancy between the male faculty and female faculty? What is
its average value? Is there a variable that has a greatest influence on this average
discrepancy? How do you know? Explain.