Using the Least-Squares Regression Line to Predict Values of the Outcome Variable, y

The LSRL allows us to a predict value of the y variable, given a value of the x-variable. To do this we just substitute the given x value into the equation for the LSRL.
The LSRL does NOT allow us to predict the change in the y-value for a specific individual who currently has a particular y value if the x-value for that individual is changed.
The slope of the LSRL is the estimated difference in y-values for two different individuals whose x-values differ by one.

Interpreting the y-intercept of the LSRL

If the data contain both positive and negative x-values, then the y-intercept is the estimated outcome when the value of the explanatory variable x is 0.
If the x-values are all positive or all negative, then the y-intercept does not have a useful interpretation. (This is so in the video below, although the presenter fails to point this out!) The reason is that the intercept corresponds to a x-value of 0, which is outside the range of the data. In general, we do not interpret values outside the range of the data.

Interpreting the Slope of the LSRL

If the x-values of two points on the line differ by 1, then their y-values will differ by an amount equal to the slope of the line.
If the values of the explanatory variable, x, for two individuals differ by 1, then their predicted values for y will differ by $LaTeX: b_1,\:$ the slope of the LSRL. If instead, the the values of the explanatory variable, x, for two individuals differ by an amount , then their predicted values for y will differ by

Examples

Here are some video examples of finding the LSRL and using the LSRL to predict a value as well as interpreting the slope and y-intercept of the LSRL. (Although, as stated above, in the case of the example used in the video using the LSRL and interpreting the y-intercept is an unreliable use of the LSRL in the case of the example chosen.)