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What is the meaning of t value and Pr(>|t|) when using summary() function on linear regression model in R?

Coefficients:
                              Estimate Std. Error t value Pr(>|t|)    
(Intercept)                    10.1595     1.3603   7.469 1.11e-13 ***
log(var)                        0.3422     0.1597   2.143   0.0322 *
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The column t value shows you the t-test associated with testing the significance of the parameter listed in the first column. For example the t value of 7.369 refers to the t-test of the (Intercept) 10.1595 divided by the standard error of that estimate 1.3603. Pr(>|t|) gives you the p-value for that t-test (the proportion of the t distribution at that df which is greater than the absolute value of your t statistic). 1.11e-13 is scientific notation. The asterisks following the Pr(>|t|) provide a visually accessible way of assessing whether the statistic met various $\alpha$ criterions.

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I don't quite grok t-test, but wikipedia has a good article about p-value - basically the p-value is the chance that the result you're seeing happened due to random variation. Commonly a p-value of .05 or less (interpreted roughly as "there's a 5% chance or less of this happening just due to random variation") is taken to mean that the result is significant.

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    $\begingroup$ Because these issues have been discussed extensively on this site, I will be brief: (1) the p-value is a probability conditional on assuming the null hypothesis (it's not some unconditional "chance" and it's likely contrafactual) and (2) it is not a chance of "the result you're seeing"--which in this case is practically zero--but rather it's the chance--under the null hypothesis--that your result would fall within a "critical region" for the hypothesis test. Although this may seem like nit-picking, much confusion can arise from misinterpreting loose language. $\endgroup$ – whuber Feb 13 '13 at 23:27
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    $\begingroup$ @whuber - thank you for taking the time to put together a correct and accurate description of p-value. I only barely grasp that myself, honestly, but was purposefully giving a "loose language" answer to help the asker get a basic idea without overwhelming him... seems to me that a lot of statistics are like that - what a statistic actually says is not so use friendly,so people give really rough approximations that are easier to digest. I think it was in "Six Easy Pieces" that Feynman explained physics like that. "This isn't accurate, but it's a useful approximation" $\endgroup$ – Aerik Feb 13 '13 at 23:50
  • $\begingroup$ Unfortunately, loose language leads to a lot of misguided actions taken as a result of a misunderstanding. $\endgroup$ – Glen_b Sep 9 '13 at 10:03

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