A medical researcher is interested in assessing the probability of some symptoms of coronary heart disease being present at a given age. For this reason, he uses the following data collected on 100 individuals. The response variable is CHD which is 1 if coronary heart disease is present and 0 otherwise. The following linear probability model and logit model have been estimated: Linear probability: = - 0.53796 + 0.02181Age
Logit: = Using the logit model, what is the estimated probability of coronary heart disease for a 60-year-old individual?
A) 0.4581
B) 0.3219
C) 0.7706
D) 0.7946

Question

A medical researcher is interested in assessing the probability of some symptoms of coronary heart disease being present at a given age. For this reason, he uses the following data collected on 100 individuals.  The response variable is CHD which is 1 if coronary heart disease is present and 0 otherwise. The following linear probability model and logit model have been estimated: Linear probability:  = - 0.53796 + 0.02181Age
Logit:  =  Using the logit model, what is the estimated probability of coronary heart disease for a 60-year-old individual?
A) 0.4581 
B) 0.3219 
C) 0.7706 
D) 0.7946

Quizplus · Accepted Answer

Using the logit model: 
11ea8309_a9aa_0f05_b223_8de8a415023c_TB6618_11 = 11ea8309_a9aa_0f06_b223_fdd811fdbd50_TB6618_11

We can rearrange it to calculate the estimated probability of CHD: 
11ea8309_a9aa_0f06_b223_fdd811fdbd50_TB6618_11 = -5.018 + 0.0827Age

For Age = 60: 
11ea8309_a9aa_0f06_b223_fdd811fdbd50_TB6618_11 = -5.018 + 0.0827(60) = -0.072

Then, we use the formula for odds to probability conversion:

Probability = odds / (1 + odds)

odds = exp(-0.072) = 0.930

Probability = 0.930 / (1 + 0.930) = 0.7946

Therefore, the estimated probability of coronary heart disease for a 60-year-old individual is 0.7946 or approximately 79.46%.

The correct answer is D.

A Medical Researcher Is Interested in Assessing the Probability of Some