A campaign manager conducts a survey to gauge voter support for Rand Paul. She g

Question

A campaign manager conducts a survey to gauge voter support for Rand Paul. She gathers data on the age of registered voters (x) and whether the person supports Rand Paul (Y=1) or not (Y=0). An analysis yields the following logistic equation:

ln(p/(1-p))= -.224-.012x

where p is the probability of a someone supporting Rand Paul.

a.) find the estimated probability that a 21 year old will support Rand Paul.

b.) Compare the odds of support for Rand Paul between two people who are 10 years apart in age and give your answer in a complete sentence.

c) At what age is the expected probability of supporting Rand Paul equal to 0.5?

Explanation / Answer

we are given that

ln(p/(1-p))= -.224-.012x

so taking exp on both the sides

p/(1-p) = exp(-.224-.012*x) ,

where x = age , so x = 21

p/(1-p) = exp(-.224-.012*21) =0.6212

p = 0.6212 - 0.6212p

p = 0.6212/1.6212 = 0.3831

b)

who are 10 years apart

p/(1-p) = exp(-.224-.012*x) , if x = 1

p= 0.789/1.789 = 0.44

and another with x = 11

p/(1-p) = exp(-.224-.012*11) = 0.70

p = 0.70 / 1.70 = 0.411

so odds are 0.44/0.411 = 1.070 , so 2 people who are 10 years apart in age , the younger person is 7% more likely to vote for paul rand

c) again using the same equation

p/(1-p) = exp(-.224-.012*x) , and putting p = 0.5

ln(p/(1-p))= -.224-.012*x

we know ln1 = 0

0.224 = -0.12*x, x = 1.8666

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