Hello John, you can derive these estimators by considering a step-wise approach:
1) Derive the estimators by evaluating a model with demeaned variables, i.e. consider (\tilde{X}'\tilde{x})^-1 \tilde{x}'\tilde{y}, where \tilde{...} refers to the demeaned variables. 2) Obtain the estimate of the intercept, by utilising the "Schwerpunkteigenschaft" of the OLS estimator. HTH, Bernhard >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) >[EMAIL PROTECTED] > >Confidentiality Statement: >This email message, including any attachments, is for the >so...{{dropped}} > >______________________________________________ >R-help@stat.math.ethz.ch mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code. > ***************************************************************** Confidentiality Note: The information contained in this mess...{{dropped}} ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.