# Ordinary linear regression

Ordinary linear regression fits a line describing the relationship between two variables assuming the X variable is measured without error.

Ordinary linear regression finds the line of best fit by minimizing the sum of the vertical distances between the measured values and the regression line. It, therefore, assumes that the X variable is measured without error.

Weighted linear regression is similar to ordinary linear regression but weights each item to take account of the fact that some values have more measurement error than others. Typically, for methods that exhibit constant CV the higher values are less precise and so weights equal to 1 / X² are given to each observation.

Although the assumption that there is no error in the X variable is rarely the case in method comparison studies, ordinary and weighted linear regression are often used when the X method is a reference method. In such cases the slope and intercept estimates have little bias, but hypothesis tests and confidence intervals are inaccurate due to an underestimation of the standard errors (Linnet, 1993). We recommend the use of correct methods such as Deming regression.

- 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 6.15

Published 18-Apr-2023