Statistics: regression_ftest

### Function Reference: `regression_ftest`

statistics: [h, pval, stats] = regression_ftest (y, x, fm)
statistics: […] = regression_ftest (y, x, fm, rm)
statistics: […] = regression_ftest (y, x, fm, rm, Name, Value)
statistics: […] = regression_ftest (y, x, fm, [], Name, Value)

F-test for General Linear Regression Analysis

Perform a general linear regression F test for the null hypothesis that the full model of the form `y = b_0 + b_1 * x_1 + b_2 * x_2 + … + b_n * x_n + e`, where n is the number of variables in x, does not perform better than a reduced model, such as `y = b'_0 + b'_1 * x_1 + b'_2 * x_2 + … + b'_k * x_k + e`, where k < n and it corresponds to the first k variables in x. Explanatory (dependent) variable y and response (independent) variables x must not contain any missing values (NaNs).

The full model, fm, must be a vector of length equal to the columns of x, in which case the constant term b_0 is assumed 0, or equal to the columns of x plus one, in which case the first element is the constant b_0.

The reduced model, rm, must include the constant term and a subset of the variables (columns) in x. If rm is not given, then a constant term b’_0 is assumed equal to the constant term, b_0, of the full model or 0, if the full model, fm, does not have a constant term. rm must be a vector or a scalar if only a constant term is passed into the function.

Name-Value pair arguments can be used to set statistical significance. `"alpha"` can be used to specify the significance level of the test (the default value is 0.05). If you want pass optional Name-Value pair without a reduced model, make sure that the latter is passed as an empty variable.

If h is 1 the null hypothesis is rejected, meaning that the full model explains the variance better than the restricted model. If h is 0, it can be assumed that the full model does NOT explain the variance any better than the restricted model.

The p-value (1 minus the CDF of this distribution at f) is returned in pval.

Under the null, the test statistic f follows an F distribution with ’df1’ and ’df2’ degrees of freedom, which are returned as fields in the stats structure along with the test’s F-statistic, ’fstat’

See also: regression_ttest, regress, regress_gp

Source Code: regression_ftest