# rid: Ordinary Ridge Regression Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

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

## Usage

 `1` ```rid(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 ‘Examples’. `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 `rid` returns the Ordinary 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 `rid` returns all the scalar MSE values and corresponding parameter values of Ordinary Ridge Regression Estimator.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Hoerl, A.E. and Kennard, R.W. (1970) Ridge Regression Biased estimation for non orthogonal problem, 12, pp.55–67.

`plot`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```## Portland cement data set is used. data(pcd) k<-0.01 rid(Y~X1+X2+X3+X4-1,k,data=pcd) # Model without the intercept is considered. ## To obtain the variation of MSE of Ordinary Ridge Regression Estimator. data(pcd) k<-c(0:10/10) plot(rid(Y~X1+X2+X3+X4-1,k,data=pcd), main=c("Plot of MSE of Ordinary Ridge Regression Estimator"), type="b",cex.lab=0.6,adj=1,cex.axis=0.6,cex.main=1,las=1,lty=3,cex=0.6) mseval<-data.frame(rid(Y~X1+X2+X3+X4-1,k,data=pcd)) smse<-mseval[order(mseval[,2]),] points(smse[1,],pch=16,cex=0.6) ```