SE for Intercept in Multiple LInear Regression

luizvs · August 25th, 2003, 1:11 pm

Does anyone know the formula for standard error of intercept in multiple linear regression?Tx in advance.

mrbadguy · August 27th, 2003, 10:52 am

I know a formula for generic standard deviation or residual but not specifically referred to intercept:given a general linear model for multiple regression:y= b + b1*x1 + b2*x2 +….+bk*xk + epsilononce you have estimated your coefficients bi with least square prediction equation the residual standard deviation Se is:yi – yi= yi – (b+b1xi1+b2xi2…..+bk*xik)the residual is = sum[_] ( yi – yi) ^2=sum[yi-(b + bixi1+b2*xi2+…+bixik)]^2and Se = sqrt ( MS residual) = sqrt [ Ssresidual / n-(k-1)rgds,

Aaron · August 27th, 2003, 12:45 pm

Let n be the number of observations, s be the square root of the sum of the residuals squared divided by n-2, m be the mean of the independent variables, v be the variance of the independent variables and a be the estimated intercept. Then a*[(1 + m^2/v)/n]^-0.5/s has a t distribution with n-2 degrees of freedom under the standard least squares assumptions. So the standard error is s*[(1+m^2/v)/n]^0.5.