[S] Multiple R-squared from lm

Robin Reed (strga@snow.csv.warwick.ac.uk)
Mon, 1 Jun 1998 08:48:39 +0100 (BST)


Suppose we have a data.frame which contains the
response y and a factor, x, with say 4 levels. Then

y ~ . and y ~ -1 + .

are different parametrisations of the same model. The first has an
intercept and 3 columns for the factor and the second has no
intercept but 4 columns for the factor.

In SPLUS, (v3.3 for Windows and v4.5), calling summary
gives the results that the 2 fits have different values for Multiple
R-squared and the F-test for regression. (Other quantities such as s
are the same.) This appears to be caused by the fact that SPLUS
uses the formula for the no-intercept case when evaluating Multiple
R-squared for the second model.
(For the particular dataset that I had, the value of R-squared moved
form 0.66 to 0.98.)

What do people think of this behaviour? I much prefer no
information to misleading information and so I believe it would be
better if SPLUS output no values at all for these quantities in the no-intercept
case.

Robin Reed
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R J Reed R.J.Reed@warwick.ac.uk
Department of Statistics
University of Warwick
Coventry CV4 7AL
United Kingdom
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