# Outliers change the sign of linear relation

I have a scatter plot with Hgb A1C as the explanatory variable ('x' axis) and FPG ('y' axis)as the result variable. There is a positive linear relationship but it is weak. There is 1 outlier in the y direction. There is 1 outlier in the x direction. When each of these points is removed, r changes in opposite directions. I am trying to explain why this is happening, in simple language.

Would it make sense to say: When the outlier in the y direction is removed, r increases because an outlier that normally falls a distance away from the regression line would decrease the size of the correlation coefficient.

When the outlier in the x direction is removed, r decreases because an outlier that normally falls near the regression line would increase the size of the correlation coefficient.

Does this make sense?

• Yes, I think you're quite right. And overplotting regression lines on four scatterplots (all points, only Y outlier removed, only X outlier removed, and both outliers removed) should illustrate. – Assad Ebrahim Oct 6 '12 at 4:16 