With the data from Codecademy University, we want to predict whether each student will pass their final exam. Recall that in linear regression, we fit a line of the following form to the data:

$y = b_{0} + b_{1}x_{1} + b_{2}x_{2} +\cdots + b_{n}x_{n}$

where

• y is the value we are trying to predict
• b_0 is the intercept of the regression line
• b_1, b_2, … b_n are the coefficients
• x_1, x_2, … x_n are the predictors (also sometimes called features)

For our data, y is a binary variable, equal to either 1 (passing), or 0 (failing). We have only one predictor (x_1): num_hours_studied. Below we’ve fitted a linear regression model to our data and plotted the results. The best fit line is in red.

We see that the linear model does not fit the data well. Our goal is to predict whether a student passes or fails; however, a best fit line allows predictions between negative and positive infinity.