Sampling Distribution of Slopes (Topic 9.2)

Chapter 12 - Day 1

Learning Targets
  • Identify statistics and parameters for linear regression.

  • Use the sampling distribution of slopes to evaluate a claim.

Activity: Does Seat Location Matter? Part 1
Answer Key:

Today we start learning about inference for slope. The calculations for this are not difficult. In fact, we’d say they’re easier than the calculations for all the other inference procedures. But the conceptual thinking behind these procedures can be tough for students. We went back and forth trying to decide if we should take the time to create a sampling distribution for slope, and we decided it was worth it. So to start the chapter, today we are going to use simulation and random assignment to create many LSRLs and find the slope of each.

Before teaching this lesson you will need to make sets of 30 notecards that have each individual score written on them. Then explain to students that last year you were curious to see if the row a student sat in affected their grades. So you randomly assigned the students to rows and then recorded their score on the final exam. The data is given. The students should be able to complete the entire first page without teacher input.

Discuss the slope and ask students if they are convinced that row impacts score on the final exam. Some will say yes, some will say no. Steer the discussion to the idea that we need to find out how likely it is that this slope occurs purely by chance if row has no effect on exam score. Pass out the sets of cards and give students time to complete the random assignment and to find the slope of each LSRL. Add the slopes to the dotplot on the board and use them to estimate a p-value.

You can extend the simulation by using the Two Quantitative Variables applet to do many, many random assignments.

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