What is orthogonal regression?

Orthogonal regression examines the linear relationship between two continuous variables: one response (Y) and one predictor (X). Orthogonal regression is often used in clinical chemistry and laboratory settings when you want to know if two instruments or two methods are measuring the same thing. Unlike simple linear regression, both the response and predictor in orthogonal regression contain measurement error. In simple regression, only the response variable contains measurement error.

If you use least squares regression to analyze data when x and y both contain measurement error, the slope may be biased, therefore impacting the validity of your results.

Orthogonal regression provides the line that "best" fits the data. This line can then be used to:

·    Determine whether two testing methods are equivalent

·    Examine how the response variable changes as the predictor variable changes

·    Predict the value of a response variable (Y) for the predictor variable (X)

In orthogonal regression, the best fitting line is the one that minimizes the weighted orthogonal distances from the plotted points to the line. If the error variance ratio is 1, the weighted distances are Euclidean distances.

In orthogonal regression, the following assumptions must be met:

·    Both the predictor and the response contain a fixed unknown quantity denoted as x and y, respectively, and an error component.     

·    The error terms are independent.

·    The error terms have means of zero and constant variances.

·    The predictor and response are linearly related.