The limit of quantification is the x value, where the relative error of the
quantification given the calibration model reaches a prespecified value 1/k.
Thus, it is the solution of the equation $$L = k c(L)$$
where c(L) is half of the length of the confidence interval at the limit L
(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
`inverse.predict`

, and L is obtained by iteration.

```
loq(
object,
...,
alpha = 0.05,
k = 3,
n = 1,
w.loq = "auto",
var.loq = "auto",
tol = "default"
)
```

- object
A univariate model object of class

`lm`

or`rlm`

with model formula`y ~ x`

or`y ~ x - 1`

, optionally from a weighted regression. If weights are specified in the model, either`w.loq`

or`var.loq`

have to be specified.- ...
Placeholder for further arguments that might be needed by future implementations.

- alpha
The error tolerance for the prediction of x values in the calculation.

- k
The inverse of the maximum relative error tolerated at the desired LOQ.

- n
The number of replicate measurements for which the LOQ should be specified.

- w.loq
The weight that should be attributed to the LOQ. Defaults to one for unweighted regression, and to the mean of the weights for weighted regression. See

`massart97ex3`

for an example how to take advantage of knowledge about the variance function.- var.loq
The approximate variance at the LOQ. The default value is calculated from the model.

- tol
The default tolerance for the LOQ on the x scale is the value of the smallest non-zero standard divided by 1000. Can be set to a numeric value to override this.

The estimated limit of quantification for a model used for calibration.

IUPAC recommends to base the LOQ on the standard deviation of the signal where x = 0.

The calculation of a LOQ based on weighted regression is non-standard and therefore not tested. Feedback is welcome.

Examples for `din32645`

```
m <- lm(y ~ x, data = massart97ex1)
loq(m)
#> $x
#> [1] 13.97764
#>
#> $y
#> [1] 30.6235
#>
# We can get better by using replicate measurements
loq(m, n = 3)
#> $x
#> [1] 9.971963
#>
#> $y
#> [1] 22.68539
#>
```