Logistic Regression Step by Step Implementation

From Theory to Practice

Say we are doing a classic prediction task, where given a input vector with $n$ variables:

And to predict 1 response variable $y$ (may be the sales of next year, the house price, etc.), the simplest form is to use a linear regression to do the prediction with the formula:

Where $W$ is a column vector with $n$ dimension. Say now our question changed a bit, we hope to predict a probability, like what’s the probability of raining tomorrow? In this sense, this…