In logistic regression (with one predictor in this case), we use the logistic function p(x) = e (?0+?1x) 1 + e (?0+?1x) = 1 1 + e ?(?0+?1x) , which implies that 0

(a) Show that p(x) 1 ? p(x) = e (?0+?1x) , where the left-hand side is called the odds ratio. Therefore, log p(x) 1 ? p(x) = ?0 + ?1x.

(b) Show that the slope of the logistic regression curve p(x) = 1/(1 + e ?(?0+?1x) ) can be written as ?1p(x)(1 ? p(x)). Hint: differentiate p(x) with respect to x, and then substitute for expressions that equal p(x) and 1 ? p(x).

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