What are the residuals from a bivariate fit orthogonal?

Question

In the Fit Y by X platform, I have fit a regression with the 'Fit orthogonal' option in the dropdown menu. I'm wondering what are the residuals from this model (if I were to click Save Residuals). I want to have the orthogonal residuals -- that is, the distance of each point to the regression line when that distance is perpendicular to the regression line (rather than the standard residual, being a vertical distance to the regression line).

So, are the residuals from the orthogonal fit the orthogonal or vertical distance to the line?

If vertical, could someone please tell me if there's an easy way to get the orthogonal distances?

MRB3855 · Accepted Answer

Hi @JayBee911   As far as I can see, there is precious little detail in JMP documentation wrt the residuals in question. However, it should be easy to verify if JMP is using residuals in the vertical direction via calculating them yourself from the equation: Y[observed] - (b0 + b1*X[observed] ). My guess is that JMP shows those, the vertical ones. If you want the residuals, defined as the orthogonal distances from the line to the points, you’ll probably need to dust off your trigonometry hat.

https://davegiles.blogspot.com/2014/11/orthogonal-regression-first-steps.html

Edit: It turns out JMP calculates the vertical residuals (I verified with my own data), which makes sense since you are trying to predict Y from X. However, if you want the orthogonal residuals (the ones used when minimizing the sum of squared residuals to estimate b0 and b1), you'll need to follow the method in the link above.