RidgeRegStd

Ridge regression is a variant of MLR which provides a solution to problems caused by collinear predictors x_i in the MLR equation:

The method RidgeRegStd calculates the ridge regression model after standardizing the independent data InData. Thus when applying this ridge regression model the means and standard deviations returned in the parameters Means and StdDevs have to be used to standardize the unknown data prior to calculating the estimated response.

The matrix InData contains the values of the independent variables x_i, the vector OutData contains the values of the dependent variable y. The parameter Lambda is the ridge parameter which must be greater or equal zero (in most cases the optimum value will be in the range between zero and 0.1).

The function returns TRUE if the result is valid. In this case the coefficients a₁ to a_n of the solution are the vector elements Coeff[1] to Coeff[n], respectively. The constant term a₀ is contained in Coeff[n+1].

Numerical instabilities which may arise from near-singular equations are indicated by returning a TRUE value in the variable parameter NearSingular. In this case the calculated coefficients should not be used.

The vector DeltaCoeff reflects the uncertainties of the estimated parameters in vector Coeff. In order to get the standard deviation of the parameters, DeltaCoeff has to be multiplied by the standard error of the residuals. The standard error can be calculated by

with n = number of rows of InData, k = number of columns of InData, and the Y_i being the actual and the estimated OutData.

Hint 1:

RidgeRegStd uses singular value decomposition to obtain the solution.

Hint 2:

The vectors Coeff, DeltaCoeff, Means, and StdDevs are automatically adjusted to the required size.