At the x value where the probability of success is some value p , the line drawn tangent to the logistic regression curve has slope p(1 p) a Explain why the slope is 4 when p 0 5 b Show that the slope is weaker at other p values by evaluating this at p 0 1, 0 3, 0 7, and 0 9 What does the slope app...

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At the x value where the probability of success is some value p , the line drawn

Question:

At the x value where the probability of success is some value p , the line drawn tangent to the logistic regression curve has slope βp(1 - p).
a. Explain why the slope is β / 4 when p = 0.5.
b. Show that the slope is weaker at other p values by evaluating this at p = 0.1, 0.3, 0.7, and 0.9. What does the slope approach as p gets closer and closer to 0 or 1? Sketch a curve to illustrate.