# rls: Restricted Least Square Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

## Description

This function can be used to find the Restricted Least Square Estimated values and corresponding scalar Mean Square Error (MSE) value.

## Usage

 `1` ```rls(formula, r, R, delt, data, na.action, ...) ```

## Arguments

 `formula` in this section interested model should be given. This should be given as a `formula`. `r` is a j by 1 matrix of linear restriction, r = Rβ + δ + ν. Values for `r` should be given as either a `vector` or a `matrix`. See ‘Examples’. `R` is a j by p of full row rank j ≤ p matrix of linear restriction, r = Rβ + δ + ν. Values for `R` should be given as either a `vector` or a `matrix`. See ‘Examples’. `delt` values of E(r) - Rβ and that should be given as either a `vector` or a `matrix`. 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.

In order to find the results of Restricted Least Square Estimator, prior information should be specified.

## Value

`rls` returns the Restricted Least Square Estimated values, standard error values, t statistic values,p value and corresponding scalar MSE value.

## Author(s)

P.Wijekoon, A.Dissanayake

## References

Hubert, M.H. and Wijekoon, P. (2006) Improvement of the Liu estimator in the linear regression medel, Chapter (4-8)

## Examples

 ```1 2 3 4 5 6``` ```## Portland cement data set is used. data(pcd) r<-c(2.1930,1.1533,0.75850) R<-c(1,0,0,0,0,1,0,0,0,0,1,0) delt<-c(0,0,0) rls(Y~X1+X2+X3+X4-1,r,R,delt,data=pcd) # Model without the intercept is considered. ```

### Example output

```\$`*****Restricted Least Square Estimator*****`
Estimate Standard_error t_statistic pvalue
X1   2.1930         0.0000     11.8365  0.000
X2   1.1533         0.0000     24.0560  0.000
X3   0.7585         0.0000      4.7551  0.001
X4   0.4864         0.0197          NA     NA

\$`*****Mean square error value******`
MSE
4e-04
```

lrmest documentation built on May 29, 2017, 9:02 a.m.