Hi Don,
Thanks for the response. Comments, clarification, and questions below.
--- You wrote:
On 3 May 2000, Richard M. Barton wrote:
> Suppose Y does not appear to be normally distributed, but Z=ln(Y) does.
>
> I do a linear regression of Z on X, which is dichotomous (0,1).
>
> 1) In simple terms, what does the unstandardized regression
> coefficient b tell me about the relationship between X and Y?
You'd get a more interesting answer if X were continuous, (and
especially, perhaps, if X were a measure of time).
***but X is not...
If you had regressed Y on dichotomous X, you have two predicted values
for Y: a, and a + b. Then b is the difference in means of Y between
the two groups identified by X. (You have in effect performed a t-test.)
***well understood...
Having regressed Z (= ln(Y)) on X, you have two predicted values for Z:
a, and a + b. The corresponding values of Y are e^a and e^a times
e^b. Then e^b is the ratio between the geometric means of Y for the
two groups aforementioned.
***now that was the kind of answer I was looking for: e^b is not a ratio of the
arithmetic means but of the geometric means. Interesting.
> 2) Is {e raised to the b} interpretable in terms of X and Y?
If Y is a time series and X is the time at which Y is observed...
***but they are not...
> 3) Is there some other transformation of b that makes the relationship
> between X and Y easily interpretable?
With dichotomous X, how difficult is the interpretation that one is
carrying out a t-test on Z, and therefore finding an average ratio of
Y|X=1 to Y|X=0 ?
***ah, but it's a ratio of geometric, not arithmetic, means...
and e^a is the geometric mean of the group with a 0 on X, correct?
***My situation is that I'm trying to help a doctoral student who is "statistically
challenged" and who was told by her advisor to do certain analyses without the student
understanding her analyses and without her getting help from her advisor. One
analysis is regressing this Z=ln(Y) variable on a multilevel categorical X1 variable,
which was then transformed to a set of dichotomous dummy variables, each 0-1, each a
comparison of an X1-category to the same X1-reference category. Further complicate
this by adding dummy coded X2, X3,...Xk variables, throw in a couple of continuous
predictors for good measure.
The student seems to understand hazard ratios, so I figured I'd present a simple
version of the problem to the list first and see if I got a response regarding ratios.
I was dropping a line to catch a small fish first, which I'm now using as bait for
the big fish
What is a simple interpretation of a given unstandardized b coefficient in this
situation?
So thank you for your first response, and please consider yourself my chum :-)
rick barton
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
--- end of quote ---
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