# Functional R-squared

### Description

Calculates the functional R-squared for a fitted FDboost-object

### Usage

1 2 | ```
funRsquared(object, overTime = TRUE, breaks = object$yind, global = FALSE,
...)
``` |

### Arguments

`object` |
fitted FDboost-object |

`overTime` |
per default the functional R-squared is calculated over time
if |

`breaks` |
an optional vector or number giving the time-points at which the model is evaluated. Can be specified as number of equidistant time-points or as vector of time-points. Defaults to the index of the response in the model. |

`global` |
logical. defaults to |

`...` |
currently not used |

### Details

`breaks`

should be set to some grid, if there are many
missing values or time-points with very few observations in the dataset.
Otherwise at these points of t the variance will be almost 0
(or even 0 if there is only one observation at a time-point),
and then the prediction by the local means *μ(t)* is locally very good.
The observations are interpolated linearly if necessary.

Formula to calculate R-squared over time, `overTime=TRUE`

:

*R^2(t) = 1 - ∑_{i}( Y_i(t) - \hat{Y}_i(t))^2 / ∑_{i}( Y_i(t) - \bar{Y}(t) )^2 *

Formula to calculate R-squared over subjects, `overTime=FALSE`

:

*R^2_i = 1 - \int (Y_i(t) - \hat{Y}_i(t))^2 dt / \int (Y_i(t) - \bar{Y}_i )^2 dt *

### Value

Returns a vector with the calculated R-squared and some extra information in attributes.

### Note

`breaks`

cannot be changed in the case the `bsignal()`

is used over the same domain
as the response! In that case you would have to rename the index of the response or that
of the covariates.

### References

Ramsay, J., Silverman, B. (2006). Functional data analysis. Wiley Online Library. chapter 16.3