[R] solution to a regression with multiple independent variable
John Sorkin
jsorkin at grecc.umaryland.edu
Sun Nov 5 16:38:55 CET 2006
Please forgive a statistics question.
I know that a simple bivariate linear regression, y=f(x) or in R
parlance lm(y~x) can be solved using the variance-covariance matrix:
beta(x)=covariance(x,y)/variance(x). I also know that a linear
regression with multiple independent variables, for example y=f(x,z)
can also be solved using the variance-covariance matrix, but I don't
know how to do this. Can someone help me go from the variance-covariance
matrix to the solution of a regression with multiple independent
variables? It is not clear how one applies the matrix solution b=
(x'x)-1*x'y to the elements of the variance-covariance matrix, i.e. how
one gets the required values from the variance-covariance matrix.
Any help, or suggestions would be appreciated.
Thanks,
John
John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC,
University of Maryland School of Medicine Claude D. Pepper OAIC,
University of Maryland Clinical Nutrition Research Unit, and
Baltimore VA Center Stroke of Excellence
University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
jsorkin at grecc.umaryland.edu
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