The vertical distance from a data point to the regression li

The vertical distance from a data point to the regression line is called the

Solution

the rms of the vertical residuals is a measure of the typical vertical distance from the data to the regression line, that is, the typical error in estimating the value of Y by the height of the regression line. A bit of algebra[+]

shows that the rms of the verticalresiduals from the regression line (the rms error of regression) is

(1r2)×SDY

The rms error of regression is always between 0 and SDY. It is zero when r=±1 and SDY when r=0. (Try substituting r=1 and r=0 into the expression above.) When r=±1, the regression line accounts for all of the variability of Y, and the rms of the vertical residuals is zero. When r=0, the regression line does not \"explain\" any of the variability of Y: The regression line is a horizontal line at height mean(Y), so the rms of the vertical residuals from the regression line is the rms of the deviations of the values of Y from the mean of Y, which is, by definition, the SD of Y. When r is not zero, the regression line accounts for some of the variability of Y, so the scatter around the regression line is less than the overall scatter in Y.

so the answer is rms