By NEAS - 7/2/2024 2:16:22 PM
MS Module 15 Logistic regression odds ratio practice exam questions
[Module 15 for the 2nd edition of the textbook and Module 21 for the 3rd edition of the textbook.]
(The attached PDF file has better formatting.)
A probability Y is related to the independent variable X by logistic regression:
Y = probability(x) = exp(β0 + β1 x) / (1 + exp(β0 + β1 x) )
● When X = 5.4, the probability Y is 31%
● When X = 6.2, the probability Y is 39%
Question 15.1: Odds ratio
At X = 5.4, what is the odds ratio of Y?
Answer 15.1: 31% / (1 – 31%) = 0.449
(odds ratio = probability / (1 – probability)
Question 15.2: Odds ratio
At X = 6.2, what is the odds ratio of Y?
Answer 15.2: 39% / (1 – 39%) = 0.639
(odds ratio = probability / (1 – probability)
Question 15.3: Multiplicative change in the odds ratio
What is the multiplicative change in the odds ratio, or exp(β1), when x increases by 1 unit?
Answer 15.3: (0.639 / 0.449)(1/(6.2 – 5.4) ) = 1.554
(the multiplicative change in the odds ratio, or exp(β1), when x increases by 1 unit, =
(odds at point X2 / odds at point X1)(1 / (value of X2 – value of X1) )
Question 15.4: Odds ratio
At X = 6.9, what is the odds ratio of Y?
Answer 15.4: 0.639 × 1.554(6.9 – 6.2) = 0.870
(odds ratio at point X3 = odds ratio at point X2 × (multiplicative change in odds ratio)(value of point X3 – value of point X2)
Question 15.5: Probability of Y
At X = 6.9, what is the probability of Y?
Answer 15.5: 0.870 / (1 + 0.870) = 46.52%
(probability = odds ratio / (1 + odds ratio)
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