# ogre

0th

Percentile

##### Ordinary Generalized Ridge Regression Estimator

This function can be used to find the Ordinary Generalized Ridge Regression Estimated values and corresponding scalar Mean Square Error (MSE) value. Further the variation of MSE can be determined graphically.

Keywords
~kwd1, ~kwd2
##### Usage
ogre(formula, k, data = NULL, na.action, ...)
##### Arguments
formula
in this section interested model should be given. This should be given as a formula.
k
a single numeric value or a vector of set of numeric values. See Example.
data
an optional data frame, list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called.
na.action
if the dataset contain NA values, then na.action indicate what should happen to those NA values.
...
currently disregarded.
##### Details

Since formula has an implied intercept term, use either y ~ x - 1 or y ~ 0 + x to remove the intercept. Use plot so as to obtain the variation of scalar MSE values graphically. See Examples.

##### Value

• If k is a single numeric values then ogre returns the Ordinary Generalized Ridge Regression Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value. If k is a vector of set of numeric values then ogre returns all the scalar MSE values and corresponding parameter values of Ordinary Generalized Ridge Regression Estimator.

##### References

Arumairajan, S. and Wijekoon, P. (2015) ] Optimal Generalized Biased Estimator in Linear Regression Model in Open Journal of Statistics, pp. 403--411 Hoerl, A.E. and Kennard, R.W. (1970) Ridge Regression Biased estimation for non orthogonal problem, 12, pp.55--67.

plot

• ogre
##### Examples
## Portland cement data set is used.
data(pcd)
k<-0.01
ogre(Y~X1+X2+X3+X4-1,k,data=pcd)
# Model without the intercept is considered.

## To obtain the variation of MSE of
# Ordinary Generalized Ridge Regression Estimator.
data(pcd)
k<-c(0:10/10)
plot(ogre(Y~X1+X2+X3+X4-1,k,data=pcd),
main=c("Plot of MSE of Ordinary Generalized Ridge Regression
points(smse[1,],pch=16,cex=0.6)