# jack.test

##### Jackknife approximate t tests of regression coefficients

Performes approximate t tests of regression coefficients based on jackknife variance estimates.

- Keywords
- htest

##### Usage

```
jack.test(object, ncomp = object$ncomp, use.mean = TRUE)
# S3 method for jacktest
print(x, P.values = TRUE, …)
```

##### Arguments

- object
an

`mvr`

object. A cross-validated model fitted with`jackknife = TRUE`

.- ncomp
the number of components to use for estimating the variances

- use.mean
logical. If

`TRUE`

(default), the mean coefficients are used when estimating the (co)variances; otherwise the coefficients from a model fitted to the entire data set. See`var.jack`

for details.- x
an

`jacktest`

object, the result of`jack.test`

.- P.values
logical. Whether to print \(p\) values (default).

- …
Further arguments sent to the underlying print function

`printCoefmat`

.

##### Details

`jack.test`

uses the variance estimates from `var.jack`

to
perform \(t\) tests of the regression coefficients. The resulting object
has a print method, `print.jacktest`

, which uses
`printCoefmat`

for the actual printing.

##### Value

`jack.test`

returns an object of class `"jacktest"`

, with components

The estimated regression coefficients

The square root of the jackknife variance estimates

The \(t\) statistics

The `degrees of freedom' used for calculating \(p\) values

The calculated \(p\) values

print.jacktest returns the "jacktest" object (invisibly).

##### Warning

The jackknife variance estimates are known to be biased (see
`var.jack`

).
Also, the distribution of the regression coefficient estimates and the
jackknife variance estimates are unknown (at least in PLSR/PCR).
Consequently, the distribution (and in particular, the degrees of
freedom) of the resulting \(t\) statistics is unknown. The present code
simply assumes a \(t\) distribution with \(m - 1\) degrees of
freedom, where \(m\) is the number of cross-validation segments.

Therefore, the resulting \(p\) values should not be used uncritically, and should perhaps be regarded as mere indicator of (non-)significance.

Finally, also keep in mind that as the number of predictor variables increase, the problem of multiple tests increases correspondingly.

##### References

Martens H. and Martens M. (2000) Modified Jack-knife Estimation of
Parameter Uncertainty in Bilinear Modelling by Partial Least Squares
Regression (PLSR). *Food Quality and Preference*, **11**, 5--16.

##### See Also

##### Examples

```
# NOT RUN {
data(oliveoil)
mod <- pcr(sensory ~ chemical, data = oliveoil, validation = "LOO", jackknife = TRUE)
jack.test(mod, ncomp = 2)
# }
```

*Documentation reproduced from package pls, version 2.7-2, License: GPL-2*