10. Video: What Defines A Line?

A line is commonly identified by an intercept and a slope.

The intercept is defined as the predicted value of the response when the x-variable is zero.

The slope is defined as the predicted change in the response for every one unit increase in the x-variable.

We notate the line in linear regression in the following way:

$\hat{y} = b_0 + b_1x_1$

where

$\hat{y}$ is the predicted value of the response from the line.

$b_0$ is the intercept.

$b_1$ is the slope.

$x_1$ is the explanatory variable.

$y$ is an actual response value for a data point in our dataset (not a prediction from our line).