Mathematics    

Multiple Regression

If y is a function of more than one independent variable, the matrix equations that express the relationships among the variables can be expanded to accommodate the additional data.

Suppose we measure a quantity y for several values of parameters and . The observations are entered as

A multivariate model of the data is

Multiple regression solves for unknown coefficients ,, and , by performing a least squares fit. Construct and solve the set of simultaneous equations by forming the regression matrix, X, and solving for the coefficients using the backslash operator.

The least squares fit model of the data is

To validate the model, find the maximum of the absolute value of the deviation of the data from the model.

This is sufficiently small to be confident the model reasonably fits the data.


  Linear-in-the-Parameters Regression Case Study: Curve Fitting