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In Logistic regression, the final values we achieve are associated with Probability. Then why do we need Logit/Log of odds? We can directly use probability.

Is Logit used to get the equation of a best fit line?

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The Log of Odds is used for interpretation purposes if we want to compare Logisitic Regression to Linear Regression. Unlike linear regression, $\beta_0 + \beta_1X$ does not directly give you the estimated value of your response variable. It gives the estimated log of odds, here's a short derivation that you already may have seen: $$p = \frac{e^{\beta_0+\beta_1X}}{1+e^{\beta_0+\beta_1X}}$$ $$\frac{p}{1-p}=e^{\beta_0+\beta_1X}$$ $$ ln(\frac{p}{1-p}) = \beta_0+\beta_1X$$

This is different from linear regression which takes the following form: $$ \hat y = \beta_0 + \beta_1X$$

If $\beta_0+\beta_1X$ doubles, $\hat y$ doubles in the case of linear regression but probability does not double, the log of odds does.

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