This gives a second regression line. The two lines are symmetric with respect to the SD line. Study Notes Recall that the regression line predicts the average y value associated with a given x value. Note that is also necessary to get a measure of the spread of the y values around that average. To construct the r.m.s. error, you first need to determine the residuals.
Residuals are the difference between the actual values and the predicted values.
They can be positive or negative as the predicted value under or over estimates the actual value. Squaring the residuals, averaging the squares, and taking the square root gives us the r.m.s error. You then use the r.m.s. error as a measure of the spread of the y values about the predicted y value. These approximations assume that the data set is football-shaped. Squaring the residuals, et cetera, to compute the r.m.s.