Logistic RegressionwithMathematicalExamplesonit.pdf
- 1. L O G I S T I C R E G R E S S I O N ( B I N A R Y C L A S S I F I C A T I O )
- 2. N E E D O F L O G I S T I C R E G R E S S I O N • In linear regression, dependent variable is continuous. • If we add an outlier in our dataset, the best fit line in linear regression shifts to fit that point.
- 3. • The predictive values may be out of range (may exceed 1 or go below 0).
- 4. L O G I S T I C R E G R E S S I O N • Supervised Machine Learning technique. • Used for solving the binary classification problems. • Predicts the output of a categorical dependent variable. • Outcome must be categorical or discrete value. It can be either Yes or No.
- 5. L O G I S T I C F U N C T I O N • Also called Sigmoid Function. • Maps any real value into another value within a range of 0 and 1. • It forms a curve like the ‘S’ shape. This S-shaped curve is called the Sigmoid or Logistic function. • Use the concept of threshold value, defines the probability of either 0 or 1.
- 6. • Equation of sigmoid function is: where, y= dependent variable e= Euler’s constant (value: 2.178) x= independent variable
- 7. D E R I V AT I O N O F S I G M O I D F U N C T I O N • Equation of best-fit line in linear regression is: • Take ‘odds’ of P:
- 8. • Take the ‘log of odds’: • Multiply by exponent on both sides:
- 11. E X A M P L E • Predict whether or not the patient has diabetes on the base of blood glucose level.
- 13. A P P L I C A B L E I N W H I C H F I E L D S : • Spam or not spam emails. • Fraud detection. • Disease diagnosis.
- 14. D R A W B A C K S • Logistic regression fails to predict a continuous outcome. • Not works well for cases where the dataset is not linearly separable. • May not be accurate when the dataset is too small.
- 15. T H A N K Y O U !