Logistic Regression

1. Overview

We can predict categorical outcomes through a logistic regression yes or no will buy or won't buy 0 or 1.

2. Introduction

Not only is this linear regression an awful fit but it also predicts values which are consist of only 0 and 1 which fall outside the natural domain of admission. This regression doesn't even know that our values are bounded between 0 and 1. The first assumption of the OLS was linearity and it has violated our data is non-linear. Thus we must use non-linear approaches.

When the score is relatively low. The probability of getting admitted is zero when the score is relatively high. When the score is relatively high, the probability of getting admitted is 1 or 100% a score in between 1600 and 1750 is uncertain. We would call this curve a logistic regression curve.

2.1 Logistic Model Formula

$$p(X)=\frac{e^{\beta_{0}+\beta_{1}x_{1}+\cdots +\beta_{k}x_{k}}}{1+e^{\beta_{0}+\beta_{1}x_{1}+\cdots +\beta_{k}x_{k}}}$$

2.2 Logit Formula

$$log(odds)=\beta_{0}+\beta_{1}x_{1}+\cdots +\beta_{k}x_{k}$$

Linear regression is the basis of logistic regression given that the model is not very different.

3. Reference

https://en.wikipedia.org/wiki/Logistic_regression