Hello Luiz:
There might be some confusion between tests involving:
(1) A linear combination of coefficients of predictor variables, and
(2) The coefficient of a linearly varying predictor variable.
You are using (1), but I think you really want to use (2).
That is, you should code one input stimulus function (aka, predictor variable)
to represent the hypothesized linear increase. Of course, there should also be
a predictor variable representing a constant response to each condition. And
you may wish to include a variable representing a quadratic response.
So, the model might look something like this:
y(t) = b0 + b1t + c*C(t) + l*L(t) <-- that's l, not 1
where
C(t) = 1 for any of the 4 levels, 0 for null condition
L(t) = 0 for low, 1 for medium, 2 for high, 3 for very high
Or, you could code the L(t) values as: -1.5, -0.5, 0.5, 1.5, depending on how
you want to interpret the constant term. (Note: -2 -1 1 2 is not linear;
however, there is no absolute requirement that the spacing between levels has
to be equal.)
The test for linear dependence then becomes a test for whether the coefficient
l of L(t) (that's l, not 1) is zero or not.
Doug Ward
