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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