Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. The outcome is measured with a dichotomous variable (in which there are only two possible outcomes).
π(x)=eα+βx1+eα+βx
Where −
Response - Presence/Absence of characteristic.
Predictor - Numeric variable observed for each case
β=0⇒ P (Presence) is the same at each level of x.
β>0⇒ P (Presence) increases as x increases
β=0⇒ P (Presence) decreases as x increases.
Problem Statement:
Solve the logistic regression of the following problem Rizatriptan for Migraine
Response - Complete Pain Relief at 2 hours (Yes/No).
Predictor - Dose (mg): Placebo (0), 2.5,5,10
Dose | #Patients | #Relieved | %Relieved |
---|---|---|---|
0 | 67 | 2 | 3.0 |
2.5 | 75 | 7 | 9.3 |
5 | 130 | 29 | 22.3 |
10 | 145 | 40 | 27.6 |
Solution:
Having α=−2.490and{\beta = .165}, we've following data:
Dose(x) | π(x) |
---|---|
0 | 0.03 |
2.5 | 0.09 |
5 | 0.23 |
10 | 0.29 |