Interpreting the Coefficients

The slope of the fitted line has useful meaning on its own. It represents the predicted change in the output per unit change in the input.

The magnitude of the change depends on the units of the coefficients. Of course, coefficients of the fitted line are in the same units as the training data and so our inputs to the fitted line must be in these units. The y-axis and the y-intercept are in the units of our observed values. The slope is in units of observed values / units of feature values (rise over run). So if we are predicting the prices of houses in dollars using the houses’ floor space in square feet, the then y-intercept in in dollars and the slope is in dollars/square feet.