Re: Correlation in Simulation

On Jun 17, 1:05 pm, "A.A.A" <ayaf...@xxxxxxxxx> wrote:
Hi,
i am simulating data for multinomial logistic regression. I have two
explanatory variables x1 and x2. The question is:

1-If i generated x1 from normal(0,1) and x2 from uniform(0,1)
separately,would this be equivalent to saying that x1 and x2 are
uncorrelated.

Your method of generating X1 and X2 means that X1 and X2 are
independent of one another. However, the correlation between these two
sets of number will most likely not be exactly 0.

2-Is it logical to assume in a multiple model that x1 and x2 are
uncorrelated?

If you are talking about collecting real data for X1 and X2, it
depends on what X1 and X2 are, but *usually* real data show some
correlation, sometimes they show high correlation. If you have a
designed orthogonal experiment, then X1 and X2 are uncorrelated. If
you can, a priori, based upon first principle knowledge, say that X1
and X2 are independent, then you can make such an assumption.
Otherwise I would not make such an assumption.

3-If i assumed in a multiple model having two x's that x1 and x2 are
uncorrrelated,would this analysis be equivalent to making 2 separate
simple regressions one with y(dependent variable) and x1 and the other
with y and x2?

If X1 and X2 are completely uncorrelated, then the slopes you compute
from separate models would be the same as the slopes you compute from
the combined model, PROVIDED that you center both X1 and X2 before you
compute the regression. Even if you center both X1 and X2, the ANOVA,
F-tests, t-tests and measures of error and measures of fit change
depending on whether you model X1 and X2 together, compared to
modeling X1 and X2 individually.

--
Paige Miller
paige\dot\miller \at\ kodak\dot\com
.

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