Implementing deming regression

In this recipe, we will implement deming regression, which means we will need a different way to measure the distance between the model line and data points.

Deming regression goes by several names. It is also known as total regression, orthogonal distance regression (ODR), and shortest-distance regression.

Getting ready

If least squares linear regression minimizes the vertical distance to the line, deming regression minimizes the total distance to the line. This type of regression minimizes the error in both y and x values.

See the following diagram for a comparison:

Figure 8: Difference between regular linear regression and deming regression; linear regression on the left minimizes the vertical...