formula used by R to compute the t-values in a linear regression
Exactly. My formula holds only for k=1, this is how I generated it. Do you have any references concerning the " rather more careful algorithms"? Thanks, Samuel -----Original Message----- From: peter dalgaard [mailto:pdalgd at gmail.com] Sent: 01 August 2011 14:45 To: Samuel Le Cc: r-help at stat.math.ethz.ch Subject: Re: [R] formula used by R to compute the t-values in a linear regression
On Aug 1, 2011, at 15:27 , Samuel Le wrote:
Hello,
I was wondering if someone knows the formula used by the function lm to compute the t-values.
I am trying to implement a linear regression myself. Assuming that I have K variables, and N observations, the formula I am using is:
For the k-th variable, t-value= b_k/sigma_k
With b_k is the coefficient for the k-th variable, and sigma_k =(t(x) x )^(-1) _kk is its standard deviation.
I find sigma_k = sigma * n/(n*Sum x_{k,i}^2 -(sum x_{k,i}^2))
With sigma: the estimated standard deviation of the residuals,
Sigma = sqrt(1/(N-K-1)*Sum epsilon_i^2)
With:
N: number of observations
K: number of variables
This formula comes from my old course of econometrics.
For some reason it doesn't match the t-value produced by R (I am off by about 1%). I can match the other results produced by R (coefficients of the regression, r squared, etc.).
I would be grateful if someone could provide some clarifications.
AFAICT, your formula only holds for K=1. Otherwise, the formula for sigma_k involves matrix inversion. Also, even for K=1, beware that textbook formulas like SSDx = SSx - (Sx)^2/n involve subtraction of nearly equal quantities and easily loses multiple digits of precision, so software tends to use rather more careful algorithms. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com "D?den skal tape!" --- Nordahl Grieg __________ Information from ESET NOD32 Antivirus, version of virus signature database 6275 (20110707) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com __________ Information from ESET NOD32 Antivirus, version of virus signature database 6275 (20110707) __________ The message was checked by ESET NOD32 Antivirus. http://www.eset.com