

   RRaaiinnbbooww--TTeesstt

        raintest(formula, data=list())

   AArrgguummeennttss::

    formula: a symbolic describtion for the model to be tested

       data: an optional data frame containing the variables in
             the model.  By default the variables are taken
             from the environment which 'raintest' is called
             from

   DDeessccrriippttiioonn::

        `raintest' performs the Rainbow-Tests on linearity.

   DDeettaaiillss::

        The basic idea of the Rainbow-Test is that even if the
        true relationship is nonlinear, over a subsample of
        data given a good linear fit can be achieved.  The null
        hypothesis is rejected whenever the overall fit is sig-
        nificantly inferious to the fit of the subsample. The
        test statistic under H_0 follows a F distribution with
        df1 and df2 degree of freedom. This particular proce-
        dure compares a subsample consisting of all data points
        without the upper and lower quartile (of time index),
        thus 50 data points. If the true relationship is con-
        cave or convex, the null hypothesis should be rejected.

   VVaalluuee::

        A list with class `"htest"' containing the following
        components:

   statistic: the value of the test statistic.

    p.value: the p-value of the test.

     method: a character string indicating what type of test
             was performed.

   data.name: a character string giving the name(s) of the
             data.

   AAuutthhoorr((ss))::

        Torsten Hothorn <hothorn@amadeus.statistik.uni-dort-
        mund.de>

   RReeffeerreenncceess::

        Kraemer, W., Sonnberger, H. (1986): The linear regres-
        sion model under test

   SSeeee AAllssoo::

        `lm'

   EExxaammpplleess::

        x <- c(1:30);
        y <- x^2 + rnorm(30,0,2);
        formular <- y ~ x;
        rain <- raintest(formular);
        qf(0.95, rain$parameter[1], rain$parameter[2]);

