Stat 100 Project 2 Notes to the Instructor

Purpose: We want the students to be able to create a respectable graph of data and add a regression line to it. We also want them to experiment with the regression tool to learn how it behaves.

Instructions:

The instructions may seem long, but they are very detailed. The actual work is not that much; the student only has to create one chart and experiment with it. I expect that most students will skim the instructions to get a general idea of what to do and only read in detail if a problem arises.

Questions:

1. Using the equation for the regression line or just by reading from the graph, what would be your estimate for the chirp burst rate at 80 degrees F?

Goal: can the student read a chart reasonably accurately? (Few will use the equation.)

2. Use the formula for the regression line to estimate the chirp burst rate at 40 degrees F.

Goal: to see if the student understands the equation. If the student gets a wild answer and does not notice that it is strange, we should point this out in the grading.

3. Do you think this last estimate would be a valid conclusion? What might be wrong?

Goal: the student should recognize that regression estimate may fail if we try to extrapolate too far. In this case, based on the first recipe (count chirps in 14 seconds and add 40), the student could recognize that the cricket is not chirping at all at 40 degrees.

4. What is the value of the correlation coefficient R ? (Note we are given R2, not R.) Is R positive or negative, and why?

Goal: the student should recognize that R is positive because the regression line has positive slope. They should also notice that the spreadsheet reports R2 not R, which is a very common error in past years.

5. What does R tell us about how well the regression line fits the data (qualitatively)?

Goal: the student should note that the magnitude of R is reasonably close to 1 (it is approximately 0.835), indicating a reasonable, but not perfect fit.

Suggested Grading (ten points total):

Five points for the chart – deduct points for hiding the data, poor chart appearance, errors, etc.

One point for each question. Grading can be as fine as half-points.