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ln(p1−p)=β0+β1X

The equation of line in the above equation denotes that the log of odds is linearly related to the predictor variables.

Why is log of odds linearly related to the predictor variables, but not the plain odds?

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For understanding this first we will have to look at the maths of logistic regression.

The equation of linear regression is given by : P(y|x;w) = Sigmoid(wTx + b)

Now if we take log on both sides and folow the match in the image below, it clearly show why log of odds linearly related to the predictor variables

enter image description here

After step 6, shown in above image if you take log on both sides, it becomes log of odd

    i.e ***ln(p/1-p) is linearly related wTx +b***

Image Ref : https://ayearofai.com/rohan-6-follow-up-statistical-interpretation-of-logistic-regression-e78de3b4d938

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