# [R] Definition of t-value

algorithms at gmx.de algorithms at gmx.de
Sat Jan 13 19:20:10 CET 2007

```Hello,

I'd like to ask for the exact definition of the t-value, which R uses in its summaries of a linear model for judging the importance of an independent variable in explaining the dependent variable.
I searched the documentation, some groups, and the web for quite a long time, but the best I could come up with is the following from

Measure of the statistical significance of an independent variable b in explaining the dependent variable y. It is determined by dividing the estimated regression coefficient b by its standard error Sb. That is

t-Value = b/Sb

Thus, the t-statistic measures how many standard errors the coefficient is away from zero. Generally, any t-value greater than +2 or less than - 2 is acceptable. The higher the t-value, the greater the confidence we have in the coefficient as a predictor. Low t-values are indications of low reliability of the predictive power of that coefficient.

My problem is that I do not know how to compute the standard error Sb of some regression coefficient, when I have done nothing more than to use the lm command in this manner:

Out = lm(A~ data\$B + data\$C + data\$D)

Does anyone know in detail, how R computes the t-value displayed in summaries?

Thank you very much,

Peter
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