doe_model_anova Function

public function doe_model_anova(mdl, x, y) result(anova)

Computes an analysis of variance (ANOVA) table for a DOE model.

The sums of squares are computed from the data as

$$SS_{tot} = \sum_{i=1}^{m} (y_i - \bar{y})^{2}, \quad SS_{res} = \sum_{i=1}^{m} (y_i - \hat{y}_i)^{2}, \quad SS_{model} = SS_{tot} - SS_{res}$$

with $R^{2} = 1 - SS_{res} / SS_{tot}$, $MS = SS / df$, and $F = MS_{model} / MS_{res}$.

The model is treated as nested within the null (intercept-only) model. With $p =$ count(mdl%map) parameters, the degrees of freedom are $p - 1$ for the model, $m - p$ for the residual, and $m - 1$ in total. The p-value is the upper tail of the F-distribution with those degrees of freedom. If either the model or residual degrees of freedom is not positive, the F-statistic is reported as zero with a p-value of one. A perfect fit (zero residual) gives a p-value of zero.

Arguments

Type	Intent	Optional	Attributes		Name
class(doe_model),	intent(in)			::	mdl	The DOE model to analyze.
real(kind=real64),	intent(in),		dimension(:,:)	::	x	The M-by-N matrix containing the M values of each of the N factors at which to evaluate the model.
real(kind=real64),	intent(in),		dimension(:)	::	y	The M-element array containing the observed responses. This array must have the same number of rows as x.

Return Value type(doe_anova_table)

A doe_anova_table object containing the ANOVA table.