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.