Re: When and how to do transformation in multiple regression

From: jim clark (clark_at_uwinnipeg.ca)
Date: 11/25/04 

Date: Thu, 25 Nov 2004 10:34:58 -0600

Hi

> On 24 Nov 2004 11:35:20 -0800, jo_chau@hotmail.com (Jo) wrote:
> > I am doing a project of multiple regression. I've found a best subset
> > for the model. I think it is finished. However, I am told that I
> > should do certain transformation about the data because they are
> > nonlinear. I am confused. I don't know when constructing a multiple
> > regression, how to examine whether the data are linear or not, when I
> > should do the transformation and which technique I should choose.

Focusing on the transformation question, and ignoring the
problems with best subset alluded to by Rich, you can determine
whether a relation between y and x is non-linear by: (a) plotting
y against x and looking for deviations from linear, (b) plotting
residuals of y from a linear regression on x against x to again
look for u-shaped or inverted-u-shaped pattern (assuming
relatively simple deviation from linearity), and/or
(c) regressing y on x and x^2 to see if the x^2 term is
significant (indicating a significant deviation from linearity).

If you conclude that there are systematic deviations from
linearity, then you can transform x using the following
principles. If you have an increasing or decreasing function
that levels off as x increases (i.e., function decelerates), then
you need to compress your scale of x (i.e., move higher values
"closer" to lower values). You do this by raising x to a power
less than 1 (or equivalent transformations), such as square root
transform (power of 1/2), log transform ("power" of 0), or
reciprocal (power of -1). If you have an increasing or
decreasing function that accelerates (gets steeper) as x
increases, then you need to stretch x (i.e., move higher values
"further away" from lower values). You do this by raising x to a
power greater than 1 (or equivalent transformations), such as
squaring (power of 2).

Best wishes
Jim

============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 clark@uwinnipeg.ca
CANADA http://www.uwinnipeg.ca/~clark
============================================================================

Relevant Pages

  • Re: Simple Sagnac
    ... The only reply from you I've seen on the topic of Sagnac ... There is a train on the track of length x', ... those are the equations of transformation between coordinate ... it certainly is a linear transformation. ...
    (sci.physics.relativity)
  • Re: CLT and regression
    ... understand its relationship with regression analyis. ... using a Box-Cox transformation to get them normal: ... transformations often gets you close enough to normality. ... and the estimated weights will ...
    (sci.stat.consult)
  • Re: The Present.
    ... | Sorcerer wrote: ... |> "Given that the equations are linear", which they are not, the lying ... The Galilean transformation is correct when it comes to the y and z ... performing the transformations in three directions at once, ...
    (sci.physics.relativity)
  • Re: Some Beginner SR Questions
    ... that "The Mapping Postulate and the Homogeneity postulate imply that the ... the transformation would not be one-to-one everywhere." ... delta-t are linear functions of delta-x' and delta-t'. ... other expressions involving x' and t. ...
    (sci.physics.relativity)
  • Re: interaction terms in regression model
    ... approach to regression than that in some other disciplines. ... centering constants you use (I'm assuming a two-variable model here... ... two linear and one interaction between those) the "significance" of the ... The "failure to center" ...
    (sci.stat.edu)