Eric, here's my take: On the formula * Assume there are J covariates (X). Then, there should be J+1 coefficients: 1 intercept term (Beta_0) and 1 coefficient (Beta_1, ... Beta_J) for each of the covariates = J+1 coefficients. * [cid:image001.png at 01CAA1D1.CD653800] is the covariance matrix of the beta's * The covariance matrix above has dimensions J+1 by J+1 because there is an intercept (Beta_0), and the usual coefficients (Beta_1, ... , Beta_J) * Each entry in the matrix is a covariance of respective Beta's, i.e., [i+1, j+1] entry in the matrix is cov(Beta_i, Beta_j). The subscript is shifted by one because of the intercept term. * Variance is covariance of a beta with itself, i.e., the j+1 by j+1 entry of the matrix is the variance of Beta_j. These terms can be found along the diagonal * SE of a beta is the square-root of the variance of a beta If you don't have an intercept term, then the equation below should have subscripts j,j Some useful R functions: * t() transposes a matrix * %*% is matrix multiplication, e.g., A%*%B multiples A and B, assuming A and B are matrices with correct dimensions * solve() finds the inverse of a matrix * diag() grabs the diagonals of a square matrix and puts it into a vector. Best regards, Joseph Joseph Poj Gavinlertvatana Doctoral student, Marketing Harvard Business School 203 Wyss Hall, Soldiers Field, Boston, MA 02163 Ph 617.230.5907 Fx 617.496.4397 Txt/Vm 617.910.0563 Em pgavinlertvatana at hbs.edu From: gov2001-l-bounces at lists.fas.harvard.edu [mailto:gov2001-l-bounces at lists.fas.harvard.edu] On Behalf Of Lin, Eric Sent: Saturday, January 30, 2010 4:51 PM To: Class List for Gov 2001/E-2001 Subject: [gov2001] Formula for SE In the following formula for SE of beta: [cid:image002.png at 01CAA1D1.CD653800] What does the subscripted index j+1 stand for? (this is from the gov2000 notes, lecture 8 page 69. Thanks! EXL