Fit the full linear model of the response y on every column of x, and a reduced model on the columns of x indexed by keep, both by least squares, and test the null hypothesis that the columns the reduced model leaves out add nothing to it. keep holds column indices or a logical mask; left out or empty, the reduced model has no predictors and the test is of every column of x together. Both models include a constant term unless 'Intercept' is false. y must be a vector with one element per row of x, and neither may contain missing values.

The test decision is returned in h, which is 1 when the null hypothesis is rejected at the significance level alpha and 0 otherwise, and the p-value in p. stats is a structure with the following fields:

The degrees of freedom come from the ranks of the two designs. Cohen’s f^2 is taken, as Cohen defines it, from the noncentrality of the F statistic, lambda = f^2 (df1 + df2 + 1): the point estimate from max (F df1 (df2 - 2) / df2 - df1, 0), unbiased for the noncentrality before its truncation at zero, and the interval by inverting the noncentral F distribution. Where the interval would need a noncentrality above 10^5, where ncfcdf loses accuracy, it is NaN.

The following Name/Value pairs are accepted:

The same tests, and any linear hypothesis on the coefficients, are available from a fitted LinearModel through its coefTest method.

See also: regression_ttest, regress, fitlm

Source Code: regression_ftest