# Orthogonal (Deming) Regression

Click **SigmaXL > Templates & Calculators > Basic MSA Templates > Orthogonal (Deming) Regression** to access the Orthogonal (Deming) Regression template.

The following example is given in **SigmaXL > Help > Template Examples > MSA > Orthogonal (Deming) Regression**.

Notes:

- Orthogonal (Deming) Regression differs from the simple linear regression in that it accounts for errors in observations on both the x- and the y- axis. Use it to compare the same parts on two measurement systems.
- Enter your Measurement data in the X and Y columns. The X and Y column headings may be modified. This template has a maximum sample size of 1000. Rows with missing data will be deleted.
- Enter
**Measurement Variance Ratio (Y/X)**. A value of 1 assumes equal variance. This ratio is assumed to be constant. - The variances for this ratio may be estimated from separate Gage R&R studies or from data replicates. Note that you cannot simply use the variances from the data.
- Enter
**Confidence Level**and**H0: Slope =**. Typically H0: Slope = 1, so you are expecting a p-value > alpha, i.e., fail to reject H0. - Click the
**Orthogonal Regression Report**button to produce the regression report and scatterplot with orthogonal best fit line. - Residuals are given in the report and include Predicted (Raw Y) Residuals, Standardized (Raw Y) Residuals, X Fit Residuals, Y Fit Residuals and Deming Optimized Residuals. See [2] for formulas.
- Model Summary includes Pearson Correlation Squared and Generalized R-Square [1].
- See SigmaXL Workbook Appendix Orthogonal (Deming) Regression for formula details.
- SigmaXL must be initialized and appear on the menu in order for this template to function.

**REFERENCES**

- Bossé, M., Marland, E., Rhoads, G., Sanqui, J.A. & BeMent, Z. (2022), “Generalizing R2 for deming regressions”, Communications in Statistics - Theory and Methods, DOI: 10.1080/03610926.2022.2059678
- NCSS Procedures, “Deming Regression”, https://www.ncss.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Deming_Regression.pdf. Note that the error variance ratio is defined as Variance(X)/Variance(Y).
- Wikipedia “Deming Regression”, https://en.wikipedia.org/wiki/Deming_regression.

**ACKNOWLEDGEMENT**

Special thanks to the authors of “Generalizing R2 for deming regressions”, Michael Bossé, Eric Marland, Gregory Rhoads, Jose Almer Sanqui & Zack BeMent, for providing R code used to validate Generalized R-Square.

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