Question

Suppose the probability π(x)π(x) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in metres) from the target is well-fitted by a logistic regression equation with
log(π(x)/[1−π(x)])=6.4−0.11xlog⁡(π(x)/[1−π(x)])=6.4−0.11x
Please answer below to 3 significant digits.

Part a)
For this prediction model, what is the probability of reaching the target from a distance of 44 metres.

Part b)
At what distance is the probability of reaching the target equal to 0.6?

Answer 1

a)

e probability of reaching the target from a distance of 44 metres =e^6.4-0.11x/(1+e^6.4-0.11x)=0.8264

b)

distance =(1/0.11)*(6.4-ln(0.6/0.4))=54.4958