Major Axis Regression

Major Axis Regression (MAR) and Reduced Major Axis Regression are common methods for handling the problem of natural variability in both x and y.  

MAR is a method that minimizes a different loss function than in Ordinary Least Squares (OLS) regression. OLS minimizes the sum of the squared deviation about the predicted values, (observed-predicted)^2. MAR minimizes the sums of squares of the perpendicular distance between each point and the regression line.

STATISTICA provides the option to specify a custom loss function in Nonlinear Estimation. From the Statistics menu, select Advanced Linear/Nonlinear Models - Nonlinear Estimation to display the Nonlinear Estimation Startup Panel.

On the Quick tab, select User-specified regression, custom loss function. and click the OK button to display the User-Specified Regression, Custom Loss dialog.

In this dialog, click the Function to be estimated & loss function button to display the Estimated function and loss function dialog. Here you can specify the regression equation to be estimated and the loss function.

For simple linear regression, Y = b0 + b1*x, the loss function for MAR is (y - (b0 + b1*x))^2/(1 + b1^2).