MS Module 15 Logistic regression probability of success 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.)
[The practice problems in the 24 modules explain the statistical procedures; the practice exam questions in this thread shows what you will be asked on the final exam.]
A statistician uses a logistic regression model:
● The independent variable X is a quantitative predictor.
● The dependent variable Y is 1 if the observation is a success and 0 otherwise.
The estimate of β1 is -0.21
The odds of success at X = 1.8 are 0.4493
Question 15.1: Probability of success
What is the probability of success at X = 1.8?
Answer 15.1: 0.4493 / (1 + 0.4493) = 31.00%
(probability = odds ratio / (1 + odds ratio)
Question 15.2: Multiplicative change in the odds ratio
What is the multiplicative change in the odds ratio when x increases by 1 unit?
Answer 15.2: e-0.21 = 0.8106
(the multiplicative change in the odds ratio when x increases by 1 unit = exp(β1)
Question 15.3: Odds of success
What are the odds of success at X = 2.7?
Answer 15.3: 0.4493 × 0.8106(2.7 – 1.8) = 0.3719
(odds ratio at point X3 = odds ratio at point X2 × (multiplicative change in odds ratio)(value of point X3 – value of point X2)
Question 15.4: Probability of success
What is the probability of success at X = 2.7?
Answer 15.4: 0.3719 / (1 + 0.3719) = 27.11%
(probability = odds ratio / (1 + odds ratio)
Question 15.5: Odds of success
What are the odds of success at X = 0?
Answer 15.5: 0.4493 × 0.8106(0 – 1.8) = 0.6557
(odds ratio at point X3 = odds ratio at point X2 × (multiplicative change in odds ratio)(value of point X3 – value of point X2)
Question 15.6: Probability of success
What is the probability of success at X = 0?
Answer 15.6: 0.6557 / (1 + 0.6557) = 39.60%
(probability = odds ratio / (1 + odds ratio)
Question 15.7: β0
What is β0?
Answer 15.7: ln(0.6557) = -0.4221
(β0 = ln(odd ratio at X = 0) )
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