# Deming regression

Deming regression is an errors-in-variables model that fits a line describing the relationship between two variables. Unlike ordinary linear regression, it is suitable when there is measurement error in both variables.

Deming regression (Cornbleet & Gochman, 1979) finds the line of best fit by minimizing the sum of the distances between the measured values and the regression line, at an angle specified by the variance ratio. It assume both variables are measured with error. The variance ratio of the errors in the X / Y variable is required and assumed to be constant across the measuring interval. If you measure the items in replicate, the measurement error of each method is estimated from the data and the variance ratio calculated.

In the case where the variance ratio is equal to 1, Deming regression is equivalent to orthogonal regression. When only single measurements are made by each method and the ratio of variances is unknown, a variance ratio of 1 is sometimes used as a default. When the range of measurements is large compared to the measurement error this can be acceptable. However in cases where the range is small the estimates are biased and the standard error underestimated, leading to incorrect hypothesis tests and confidence intervals (Linnet, 1998).

Weighted Deming regression (Linnet, 1990) is a modification of Deming regression that assumes the ratio of the coefficient of variation (CV), rather than the ratio of variances, is constant across the measuring interval.

Confidence intervals for parameter estimates use a t-distribution and the standard errors are computed using a Jackknife procedure (Linnet, 1993).

**Related information**

- What is Analyse-it?
- What's new?
- Administrator's Guide
- User's Guide
- Statistical Reference Guide
- Distribution
- Compare groups
- Compare pairs
- Contingency tables
- Correlation and association
- Principal component analysis (PCA)
- Factor analysis (FA)
- Item reliability
- Fit model
- Method comparison / Agreement
- Correlation coefficient
- Scatter plot
- Fit Y on X
- Ordinary linear regression
- Deming regression
- Passing-Bablok regression
- Fitting ordinary linear regression
- Fitting Deming regression
- Fitting Passing-Bablok regression
- Linearity
- Residual plot
- Checking the assumptions of the fit
- Average bias
- Estimating the bias between methods at a decision level
- Testing commutability of other materials
- Difference plot (Bland-Altman plot)
- Fit differences
- Plotting a difference plot and estimating the average bias
- Limits of agreement (LoA)
- Plotting the Bland-Altman limits of agreement
- Mountain plot (folded CDF plot)
- Plotting a mountain plot
- Partitioning and reducing the measuring interval
- Agreement measures for binary and semi-quantitative data
- Chance corrected agreement measures for binary and semi-quantitative data
- Agreement plot
- Estimating agreement between two binary or semi-quantitative methods
- Study design
- Study design for qualitative methods
- Measurement systems analysis (MSA)
- Reference interval
- Diagnostic performance
- Survival/Reliability
- Control charts
- Process capability
- Pareto analysis
- Study Designs
- Bibliography

Version 6.10

Published 21-Jul-2022