An orthogonal fit function is a linear regression equation that minimizes the orthogonal distance between each data point and the regression line. In comparison, the ordinary least squares model estimates a linear function that minimizes the sum or squared errors.

In the illustration below, the red lines between each point and the regression line show the distance measure used for estimating a linear equation. The plot on the left uses orthogonal distances to determine the best fit line. The plot on the right uses ordinary least squares regression to estimate the slope and intercept of the line. The two methods yield different parameter estimates for the line.

The orthogonal fit allows for measurement error in the independent (X) variables as well as the dependent (Y) variables. It is also called Total Least Squares regression or Errors in Variables regression.