# Using an Applet to Demonstrate Sampling Distributions of Regression Coefficients

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

## Summary

## Learning Goals

- Recognize that even if there is no linear relationship between two variables the slope from a sample regression line can be non-zero.
- Explain that the slope and intercept of a regression line are random quantities and will vary from sample to sample.
- Explain that the sampling distribution of the slope (and intercept) of the regression line have a normal distribution.

## Context for Use

Prerequisites for this activity:

- Students should have some understanding of the concept of fitting simple linear regression models. That is, the idea that a scatterplot leads to a sample slope and a sample intercept.
- Also, the general concept of a sampling distribution is assumed. It might not be appropriate to introduce sampling distributions in this setting.

## Description and Teaching Materials

By teaming a hands-on activity with the use of an applet the instructor can help students better understand the idea of a sampling distribution in the regression setting.

- Instructor's detailed instructions. Instructors detailed Instructions (Microsoft Word 90kB Oct15 06)
- Student worksheet. In Class Activity (Microsoft Word 86kB Jul6 06)
- Sampling Distributions of Regression Coefficients Applet
- Instructor's guide to applet use. Applet Instructions (Microsoft Word 196kB Jul6 06)

## Teaching Notes and Tips

A little bit of careful planning will make this demonstration go smoothly.

- Students should bring a calculator to class to aide in regression line calculations. Although it may not be necessary, it streamlines the activity process.
- Students will work in groups of five on a worksheet. Worksheets should be pre-numbered to facilitate calling on the groups.
- As the students are calculating their regression lines, the instructor should prepare histograms on the board or a transparency for the sample intercepts and slopes.
- The instructor should open the applet while the students are working.

## Assessment

Assessments over this topic should be focused on the students understanding of the sampling distribution of the coefficients. Students should be asked to explain why a confidence interval or hypothesis test is needed for a regression parameter. Many students in basic regression courses or advanced introductory classes can calculate the confidence intervals and hypothesis tests but not explain their meaning. Questions that ask for calculations of intervals and tests should be followed with questions that ask for explanations of their meaning.

## References and Resources

- Sampling Distributions of Regression Coefficients Applet
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