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.



Samuel


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