Question

Suppose the probability 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(T(x)/1) 6.8-0.11a 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 31 metres. Part b) At what distance is the probability of reaching the target equal to 0.6?

Answer 1

SOLUTION:

From given data,

Suppose the probability π(x) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in meters) from the target is well-fitted by a logistic regression equation with log( π(x) / [1−π(x)] )=6.7−0.13 x

log( π(x) / [1−π(x)] )=6.7−0.13 x

here from above :

Part a) For this prediction model, what is the probability of reaching the target from a distance of 34 metres.

$\pi$(x) =e ^{6.7−0.13 x} / (1 + e ^{6.7−0.13 x} )

hence at x=34 meters

$\pi$(34) =e ^{6.7−0.13 *34} / (1 + e ^{6.7−0.13 *34})

$\pi$(34)= 0.907

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

for x=(1/0.13)*(6.7- ln ($\pi$(x) / (1-$\pi$(x)))

hence for $\pi$(x)=0.6

x=13*(6.7- ln (0.6 / (1-0.6))

= 13 * 6.29453489

x = 81.8289

value of x = 81.8289

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