Constrained least squares {cols} | R Documentation |

## Constrained least squares

### Description

Constrained least squares.

### Usage

```
cls(y, x, R, ca)
```

### Arguments

`y` |
The response variables, a numerical vector with observations. |

`x` |
A matrix with independent variables, the design matrix. |

`R` |
The R vector that contains the values that will multiply the beta coefficients. See details and examples. |

`ca` |
The value of the constraint, |

### Details

This is described in Chapter 8.2 of Hansen (2019). The idea is to inimise the sum of squares of the residuals under the constraint `R^T \beta = c`

. As mentioned above, be careful with the input you give in the x matrix and the R vector.

### Value

A list including:

`bols` |
The OLS (Ordinary Least Squares) beta coefficients. |

`bcls` |
The CLS (Constrained Least Squares) beta coefficients. |

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

Hansen, B. E. (2022). Econometrics, Princeton University Press.

### See Also

### Examples

```
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
R <- c(1, 1, 1, 1)
cls(y, x, R, 1)
```

*cols*version 1.1 Index]