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?