Confidence Intervals for the Slope of a Regression Model

AP Statistics· difficulty 4/5

SE of the slope is given by SE(b) = s / (s_x * sqrt(n-1)) where s is residual SD and s_x is the standard deviation of x.

If s_x (spread of x) doubles, what happens to SE(b)?

Explanation

Per the formula SE(b) = s/(s_x * sqrt(n-1)), doubling s_x halves SE(b). More x-spread improves slope precision.

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