Statistics Toolbox

ridge

Parameter estimates for ridge regression.

Syntax

b = ridge(y,X,k)

Description

b = ridge(y,X,k) returns the ridge regression coefficients b for the linear model y = X+, where:

• X is an n-by-p matrix
• y is the n-by-1 vector of observations
• k is a scalar constant (the ridge parameter)

The ridge estimator of is .

When k = 0, b is the least squares estimator. For increasing k, the bias of b increases, but the variance of b falls. For poorly conditioned X, the drop in the variance more than compensates for the bias.

Example

This example shows how the coefficients change as the value of k increases, using data from the hald dataset.

load hald;
b = zeros(4,100);
kvec = 0.01:0.01:1;
count = 0;
for k = 0.01:0.01:1
count = count + 1;
b(:,count) = ridge(heat,ingredients,k);
end
plot(kvec',b'),xlabel('k'),ylabel('b','FontName','Symbol')

See Also
regress, stepwise

regstats

robustdemo