Question

Mr. King performed logistic regression for his manufacturing project. The actual observed odd ratio for his project is 3/2. However, his predicted odds ratio is 2/3. Please help Mr. King to calculate the absolute difference between observed probability and estimated/predicted probability.

Answer 1

Odds ratio = Probability of event / Probability of non-events

Probability of non-events = 1 - Probabiloty of events

So odds ratio = Probability of event / ( 1 - Porbability of events)

Given our observed odds ratio = 3/2

Let the obersved probability be Po

So 3/2 = Po  / 1 - Po

3 * ( 1 - Po) = 2 * Po

3 - 3Po  = 2Po

5Po  = 3

So Po = 3/5

The obersved probability be 3/5

Given our predicted (estimated) odds ratio = 2/3

Let the predicted or estimated probability be Pe

So 2/3 = Pe  / 1 - Pe

2 * ( 1 - Pe) = 3 * Pe

2 - 2Pe  = 3Pe

5Pe  = 2

So Pe = 2/5

The predicted or estimared probability be 2/5

The difference between observed probability (Po) and estimated/predicted probability (Pe) = 3/5 -2/5 = 1/5

The difference between observed probability (Po) and estimated/predicted probability (Pe) is 1/5