Fits an increasing monotonic regression of y on x.

### No options

### Parameters

`Y` = variates |
Y-values of the data points |
---|---|

`X` = variates |
X-values of the data points; default is to assume that the x-values are monotonically increasing |

`RESIDUALS` = variates |
Variate to save the residuals from each fit |

`FITTEDVALUES` = variates |
Variate to save the fitted values from each fit |

### Description

Monotonic regression plays a key role in non-metric multidimensional scaling, which is available in Genstat via the `MDS`

directive. However, it can be useful in its own right, so the method has been made accessible by the `MONOTONIC`

directive. A monotonic regression through a set of points is simply the line that best fits the points subject to the constraint that it never decreases: of course the line need not be straight, in fact it rarely will be. If you need a monotonically decreasing line, you can simply subtract all the y-values from their maximum, find the monotonically increasing regression, and then back-transform the data and fitted line, and change the sign of the residuals.

The `MONOTONIC`

directive has no options. It has four parameters: `Y`

to specify the y-values, `X`

for the x-values, `RESIDUALS`

to save the residuals, and `FITTEDVALUES`

to save the fitted values. The x-values need not be supplied, in which case the directive assumes that the y-values are in increasing order of the x-values. In common with the other regression directives, the variates to save the residuals and fitted values need not be declared in advance.

Options: none.

Parameters: `Y`

, `X`

, `RESIDUALS`

, `FITTEDVALUES`

.

### Action with `RESTRICT`

`MONOTONIC`

ignores any restrictions on the variates.

### See also

Directives: `MDS`

, `FIT`

, `FITCURVE`

, `FITNONLINEAR`

.

Commands for: Multivariate and cluster analysis, Regression analysis.

### Example

" Example 1:4.5.2 " VARIATE [VALUES=2,6,4,4, 9,1,12,15,13,18] X & [VALUES=1,5,3,6,10,0,11,14,16,18] Y MONOTONIC Y=Y; X=X; FITTED=Fvals LPGRAPH [TITLE='Monotonic regression'; NROWS=25; NCOLUMNS=61]\ Fvals,Y; X; METHOD=line,point SORT X,Y MONOTONIC Y; RESIDUALS=Res; FITTED=Fvals PRINT X,Y,Fvals,Res