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Regression
Posted:
Mar 27, 1996 2:33 PM


This is a partial answer to Tim Brown's question about inference in regression. The AP course outline calls for inference on the slope of the least squares line, and the formula for the standard error of the slope is given. The student should be able to use this standard error formula to construct confidence intervals and test statistics with regard to slope. (An example will appear in the Teacher's Guide.)
Students will not be able to derive the formula for the standard error, but they should understand what it measures and that it make sense. What happens, for example, if the xvalues are close together in one case and spread far apart in another? They should also understand that the tvalues used in the inference procedures come from an assumption about the normality of the residuals (which should always be plotted).
Simulation is a great tool for motivating the behavior of slopes in repeated sampling. But, be careful to note that the usual regression setting calls for a fixed set of xvalues, with random y's. (This is different from the usual correlation setting in which x and y values can both be random.)
Hope this helps.
Dick Scheaffer



