5 Logistic Regression

Logistic Regression is mainly used when we have to work on probability. It outputs values between 0 and 1. So 0.5 is cutoff point and anything below 0.5 goes to class 0 and rest to class 1.

Logistic is also called Sigmod. Shown in function below.

\[ \phi (z) = \frac{1}{1 + e^{-z}} \]

this always outputs b/w 0 and 1.

5.0.1 Difference between logistic and linear equations

linear model: $ y = b_0 + b_1x $

where as logistic is shown in equation below (also same as \(\phi (z)\) eq above) :

\[ p = \frac{1}{1 + e^{-(b_0 + b_1 x)}} \]

5.0.2 Model Evaluation

Use confusion matrix to evaluate classification model.

Classifiaction model is when we classify our predisctions against test data.

Confusion matrix puts predictions and tests together to compare.

n=165	Predicted=NO	Predicted=YES
Actual: NO	TN = 50	FP = 10	60
Actual: YES	FN = 5	TP = 100	105
55	110

False Positive FP is Type 1 error FN is Type 2 error

5.0.3 Accuracy:

Correct: (TP + TN) / total = 150/165 = 0.91

Our model is 91% correct,

Wrong: (FP + FN)/100 = 15/165 = 0.09

Our mode is 9% wrong.