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Role of Log Odds in Logistic Regression
Introduction
Logistic Regression is a statistical method to predict a dependent data variable based on the relationship between one or more independent variables. It makes use of log odds and with the help of a logistic function, it predicts the probability of an event occurring. It is a classification method.
What are Log Odds and Why are they Useful for Logistic Regression?
Logistic regression is used to predict binary outcomes. For example, in an election, whether a candidate will win or not, whether SMS is spam or ham, etc.
Odds are the ratio of the probability of success to failure. It is given as
$$\mathrm{Odds \:=\: p\: / \:1 p}$$
where p = odds of success, 1 â€“ p = odds of failure
log of odds will be given by
$\mathrm{Log \:of\: odds\: = \:log \:(p\: /\: 1  p)}$ (1)
The above equation (1) is the logit function represented as
Fitting this equation to a line, we get
$\mathrm{log\frac{p}{1p}\:=\:\beta_0x\:+\:\beta_1x}$ [ logistic regression equation] (2)
$\mathrm{p\:=\:\frac{e^{\beta_0x\:+\:\beta_1x}}{1\:+\:e^{\beta_0x\:+\:\beta_1x}}}$ (3)
odds of failure can be written as
$\mathrm{1p\:=\:\frac{1}{1\:+\:e^{\beta_0x\:+\:\beta_1x}}}$ (4)
The log odds ratio can be written as
$\mathrm{p/1p\:=\:\frac{1}{1\:+\:e^{\beta_0x\:+\:\beta_1x}}\:=\:e^{\beta_0x\:+\:\beta_1x}}$ (5)
which is the equation of logistic regression.
Odds Ratio Example in Python
Let us take the following data.
country1 
country2 


cheetah 
8 
2 
lion 
1 
5 
Example
from scipy.stats import fisher_exact as fe odds_ratio, p_value = fe([[8, 2], [1, 5]]) print(odds_ratio)
Output
20.0
Advantages of log odds
Log odds convert the Logistic Regression which is a probabilitybased model to a Likelihoodâ€“based model.
Logistic Regression parameters are determined by Maximum Likelihood Estimation (MLE)
They are very useful in solving problems of win or lose, fraud or nonfraud, span not spanlike scenarios.
Conclusion
Log odds are used in Logistic Regression when we want a non binary result. Log odds make the Logistic regression work both for regression and classification model