Michael Dykes wrote:
So, am i wrong to /assume /that the reasons my professor is asking us to
find a high R^2 & adjusted R^2, low Cp (near what p+1, if i remember
correctly), low PRESS, & AIC is b/c the data is randomly generated (b/c
he has stated that all of the data for *all *of these hw assignments are
randomly generated)? And i am not /exactly /sure to what you are
referring when you say: 'low signal to noise ratios'. Do you mean /low
/R^2 to epsilon_i's? or /low /predictors to epsilon i's? Please excuse
my ignorance in these matters, but I am not only asking these questions
for hw sakes's but for my future, as I hope to study for the actuarial
exams & take the Probability Test sometime either next Spring or Summer
[after taking this professors Calculus-based Prob & Stat sequence in the
coming Fall & Spring Semester].
Thanks again for your help, Professor.
Let me just add that a valid test of whether any of the variables or
interactions is associated with Y is to formulate a model with all the
parameters in it and to use the global F test.
Stepwise techniques such as you are being asked to use are not
scientific. If the true R^2 (which you do not know) is not high, the
low signal:noise ratio makes the data incapable to telling you the
"right" variables to include with any reliability. Unfortunately, most
teachers of statistics do not understand this point, so you might be
graded off for providing the right answer.
Frank
On Thu, Apr 15, 2010 at 8:26 AM, Frank E Harrell Jr
<f.harr...@vanderbilt.edu <mailto:f.harr...@vanderbilt.edu>> wrote:
Michael Dykes wrote:
I have a project due in my Linear Regression class re:
regression on a data
set & my professor gave us a hint that there were *exactly *2 sig
interactions. The data set is attached. We have to find which
predictors are
significant, & which 2 interactions are sig. Also, I nedd some
guidance for
this & selecting the best model. I tried the `full' model, that
being:
z=lm(y~x1+x2+x3+x4+x1*x2+x2*x3...+x3*x4). I then ran an anova(z), &
summary(z). My R^2 & R^2_a were *really* low. I am not sure how
to do PRESS,
AIC & Cp in R yet though. Any help would be appreciated.
Michael this is not really the place for help on homework other than
perhaps on technical roadblocks. Note that the strategy you are
being told to follow is one whose statistical properties have been
severely criticized in the statistical literature. Only with a very
high signal to noise ratio (e.g., high true R^2) can torturing data
lead to a confession to something other than what the analyst wants
to hear. I suppose that in simulated data there is a "true" model
out there waiting to be found, but beware of using this approach
with real data with low signal to noise ratios.
Frank
--
Frank E Harrell Jr Professor and Chairman School of Medicine
Department of Biostatistics Vanderbilt University
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