Regression Revisited

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 Teaching Tips

• You might want to review (and review with your students) the section on two variables early in the course. In that unit, we were concerned with describing relations between two variables. Now we're interested in inferring relations that exist in populations based on a sample.

• There are (at least) two purposes for regression. One is prediction: for a given x value, how well can I predict the y-value that I'll see? The other purpose is to estimate the value of the slope and, in particular, to see if it is non-zero.

• Use examples where many of the x values are the same. (The Tootsie Pops activity in the Data Collection and Analysis section is often a good example.) Students need to see scatter plots where multiple y values correspond to the same x value to absorb the idea of responses having a distribution for each x value.

• By-hand computations of the slope, let alone the standard error of the slope, are unpleasant and distracting. Students should practice interpretation rather than computation.

•  Make sure they see examples of output from several different statistical software programs (such as Minitab).  They will be expected to interpret computer output on the AP exam.

• A good exercise for students, to help them learn to read regression output tables, is to give them incomplete tables and ask them to re-construct the missing output.

• As with all previous inference procedures, you must check certain conditions before you proceed; otherwise, the confidence interval/hypothesis test calculations performed by the computer are worthless. You can check three of the underlying conditions for hypothesis tests of a slope:

(1) Are the data linear? Look at the residual plot for curvature or other violations of linearity.
(2) Is the variance constant across all x values? Look at the residual plot for fanning or bulging.
(3) Is the distribution of the responses normal? Look at a normal quantile plot of the residuals.