Statistical Applications ACTIVITY 9: Inference and prediction in multiple regression
Why
The purpose of finding a regression line is description of the relation between the predictors
and the response in the population. The regression equation gives the best linear fit to the data
(sample) and the coefficient of determination (R2) measures the closeness of that fit to the data,
not to the population. The two main issues for “usefulness” are determining whether the data
indicate a linear relation in the population (and determining which predictors are useful) and (if
so) estimating the rate of change of the response (based on the different predictors) and using
the equation to predict means and individual values.
LEARNING OBJECTIVES
1. Work as a team, using the team roles
2. Gain experience with linear regression concepts
3. Learn how to determine if a regression equation gives evidence of a linear relation in a population
4. Learn to identify (statistically) significant predictors in a regression situation
5. Learn to use the regression line for prediction
CRITERIA
1. Success in completing the exercises.
2. Success in answering questions about the model
3. Success in working as a team
RESOURCES
1. The “Multiple Regression” handout from Monday
2. Your Text - especially sections 15.5 and 15.6 and the table of data on p. 688
3. Your Calculator
4. 40 minutes
PLAN
1. Select roles, if you have not already done so, and decide how you will carry out steps 2 and 3 (5
minutes)
2. Work through the exercises given here - be sure everyone understands all results (30 minutes)
3. Assess the team’s work and roles performances and prepare the Reflector’s and Recorder’s reports
including team grade (5 minutes).
4. Be prepared to discuss your results.
EXERCISE The table given in Case problem 3 (p687-688 in your text) gives information on a sample of
48 national universities, showing graduation rate (percent of entering first-year students who graduate
from the school), percent of classes that are under 20 (students), the student-faculty ratio (# students per
faculty member) and the alumni/ae giving rate (percent of alumni/ae who donate to the university). A
national fundraising organization wishes to see if graduation rate, % of classes under size 20 and student-
faculty ratio can be used to effectively predict the alumni/ae giving rate. The Minitab printout of the
regression calculation is given below.
1. Using the regression model for predicting % giving based on all three predictors, answer the questions
below (very little calculation is required - mostly explanation).
(a) Give the regression equation (with context, of course) for predicting alumni/ae giving rate based
on these three predictors.
(b) What does the equation give as the predicted giving rate for New York University (graduation
rate 72%, 63% of classes under 20, student-faculty ratio 13)? What is the residual?
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