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Topic: Regression
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Richard Scheaffer

Posts: 440
Registered: 12/6/04
Posted: Mar 27, 1996 2:33 PM
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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 x-values are close together in one case and spread far
apart in another? They should also understand that the t-values 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 x-values, 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

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