Is the Regression Line too Shallow?
Number of Points in the Cloud
Target Correlation of Cloud
Show SD Line and Regression Line
For some values of the correlation, the regression line does not appear to pass through the cloud of points as well as the SD line does. Try various correlations and see for yourself!
But the regression line does a better job of predicting y-values from x-values. To see this look at a vertical slice of the cloud:
Show a Slice of the Cloud
The big point in the green slice indicates the mean y-value for all points in the slice. Which line comes closer to it? Try some other slices, too.
Choose a New Slice
To form an overall impression of how the regresion line is doing, look at the means for all of the slices at once:
Show Means of All Slices