Statistical Applications ACTIVITY 8: Inference for Linear regression
Why
For any set of points there is a line of best fit, with a slope and an intercept (just as any set
of numbers has a mean and a standard deviation). for most really data, though, the point of
collecting the data is to draw conclusions about a population from which the data were drawn.
We want to extend the tools of inference (estimation — with confidence — and testing for
significance) to the relation between variables - particularly the slope, which gives (ideally) the
rate of change of (the mean of) the response as the predictor changes.
LEARNING OBJECTIVES
1. Work as a team, using the team roles
2. Gain experience with linear regression concepts
3. Be able to use and interpret tests of significance for linear regression.
4. Be able to find and intepret confidence interval estimates for the slope of a regression line.
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 “Simple Linear Regression” handout from last week - especially the sections on testing the
regression coefficient, on confidence intervals for β1, on the F-test.
2. Your Text - especially sections 14.4 - 14.5 and the statistical tables
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
1. A sales manager collected the following data on annual sales and years of experience for 10 salespeople:
Years of Annual Sales
Salesperson Experience ($1000s)
1 1 80
2 3 97
3 4 92
4 4 102
4 6 103
6 8 111
7 10 119
8 10 123
9 11 117
10 13 136
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