Your free utility indeed found the same simple Deming regression fit for your example with replicates as the commercial add-in Analyse-it® finds. Analyse-it® also calculates and plots the confidence intervals.

For your example, the ordinary Least Squares assumption that either Machine A or Machine B has no measurement error has negligible impact on the maximum likelihood estimator for the line, but gives an artificially tight confidence interval on the slope that is only ~57% of the more realistic interval calculated by Deming regression.

Yes, Analyse-It is a very good statistics add-in for Excel, although I haven’t needed the Method Evaluation edition with simple & weighted Deming regression.

With respect to simple Deming Regression, Jon’s numbers looked right when I checked over a year ago. When r² is very high, OLS, rOLS, diagonal regression, and Deming regression all give very similar regression lines.

Deming Regression is a special case of total least squares, which tends to be beyond what most people (possibly even Jon) care to attempt in Excel. Advanced regression techniques eventually deserve specialized tools beyond spreadsheets, and if one doesn’t want to buy commercial statistics software, then R may be a good Open Source choice. Its PCA or MethComp packages reportedly support Deming among other regression techniques.

Dale

Your follow-up comment is posted under a different article, Deming Regression Utility.

I will look into this when I have a chance. Unfortunately it’s not as high priority as other things. But I will get to it, because I don’t like inaccuracies here.

Can you share the data set that led to this result?

What 30-day trial software are you referring to?

The confidence interval information isn’t buried in the calculations. I didn’t implement the algorithms for these quantities.