This function is deprecated. Use `regr_cc_sof`

.
This function builds a data frame needed
to plot the scalar-on-function regression control chart,
based on a fitted function-on-function linear regression model and
proposed in Capezza et al. (2020).
If `include_covariates`

is `TRUE`

,
it also plots the Hotelling's T2 and
squared prediction error control charts built on the
multivariate functional covariates.

```
regr_cc_sof(
object,
y_new,
mfdobj_x_new,
y_tuning = NULL,
mfdobj_x_tuning = NULL,
alpha = 0.05,
parametric_limits = FALSE,
include_covariates = FALSE,
absolute_error = FALSE
)
```

- object
A list obtained as output from

`sof_pc`

, i.e. a fitted scalar-on-function linear regression model.- y_new
A numeric vector containing the observations of the scalar response variable in the phase II data set.

- mfdobj_x_new
An object of class

`mfd`

containing the phase II data set of the functional covariates observations.- y_tuning
A numeric vector containing the observations of the scalar response variable in the tuning data set. If NULL, the training data, i.e. the data used to fit the scalar-on-function regression model, are also used as the tuning data set. Default is NULL.

- mfdobj_x_tuning
An object of class

`mfd`

containing the tuning set of the multivariate functional data, used to estimate the control chart limits. If NULL, the training data, i.e. the data used to fit the scalar-on-function regression model, are also used as the tuning data set. Default is NULL.- alpha
If it is a number between 0 and 1, it defines the overall type-I error probability. If

`include_covariates`

is`TRUE`

, i.e., also the Hotelling's T2 and SPE control charts are built on the functional covariates, then the Bonferroni correction is applied by setting the type-I error probability in the three control charts equal to`alpha/3`

. In this last case, if you want to set manually the Type-I error probabilities, then the argument`alpha`

must be a named list with three elements, named`T2`

,`spe`

and`y`

, respectively, each containing the desired Type I error probability of the corresponding control chart, where`y`

refers to the regression control chart. Default value is 0.05.- parametric_limits
If

`TRUE`

, the limits are calculated based on the normal distribution assumption on the response variable, as in Capezza et al. (2020). If`FALSE`

, the limits are calculated nonparametrically as empirical quantiles of the distribution of the residuals calculated on the tuning data set. The default value is`FALSE`

.- include_covariates
If TRUE, also functional covariates are monitored through

`control_charts_pca`

,. If FALSE, only the scalar response, conditionally on the covariates, is monitored.- absolute_error
A logical value that, if

`include_covariates`

is TRUE, is passed to`control_charts_pca`

.

A `data.frame`

with as many rows as the
number of functional replications in `mfdobj_x_new`

,
with the following columns:

* `y_hat`

: the predictions of the response variable
corresponding to `mfdobj_x_new`

,

* `y`

: the same as the argument `y_new`

given as input
to this function,

* `lwr`

: lower limit of the `1-alpha`

prediction interval
on the response,

* `pred_err`

: prediction error calculated as `y-y_hat`

,

* `pred_err_sup`

: upper limit of the `1-alpha`

prediction interval
on the prediction error,

* `pred_err_inf`

: lower limit of the `1-alpha`

prediction interval
on the prediction error.

The training data have already been used to fit the model. An additional tuning data set can be provided that is used to estimate the control chart limits. A phase II data set contains the observations to be monitored with the built control charts.

Capezza C, Lepore A, Menafoglio A, Palumbo B, Vantini S. (2020)
Control charts for
monitoring ship operating conditions and CO2 emissions
based on scalar-on-function regression.
*Applied Stochastic Models in Business and Industry*,
36(3):477--500.
<doi:10.1002/asmb.2507>

```
library(funcharts)
air <- lapply(air, function(x) x[1:100, , drop = FALSE])
fun_covariates <- c("CO", "temperature")
mfdobj_x <- get_mfd_list(air[fun_covariates],
n_basis = 15,
lambda = 1e-2)
y <- rowMeans(air$NO2)
y1 <- y[1:80]
y2 <- y[81:100]
mfdobj_x1 <- mfdobj_x[1:80]
mfdobj_x2 <- mfdobj_x[81:100]
mod <- sof_pc(y1, mfdobj_x1)
cclist <- regr_cc_sof(object = mod,
y_new = y2,
mfdobj_x_new = mfdobj_x2)
plot_control_charts(cclist)
```