As part of a study of the association between smoking and risk of squamous cell carcinoma, a logistic regression model was estim
ated as:
logit(probability of having squamous cell carcinoma) = -4.84 + 4.6*(SMOKER)
where SMOKER=0 for non-smoker and 1 for smoker. What is the predicted probability of a smoker having squamous cell carcinoma?
1 answer:
Answer:
0.44
Step-by-step explanation:
Given the estimated logistic regression model on risk of having squamous cell carcinoma
-4.84 + 4.6*(SMOKER)
SMOKER = 0 (non-smoker) ; 1 (SMOKER)
What is the predicted probability of a smoker having squamous cell carcinoma?
exp(-4.84 + 4.6*(SMOKER)) / 1 + exp(-4.84 + 4.6*(SMOKER))
SMOKER = 1
exp(-4.84 + 4.6) / 1 + exp(-4.84 + 4.6)
exp^(-0.24) / (1 + exp^(-0.24))
0.7866278 / 1.7866278
= 0.4402863
= 0.44
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