15
$\begingroup$

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 *
$\endgroup$
2

2 Answers 2

16
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

$\endgroup$
3
  • 6
    $\begingroup$ 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, 2013 at 23:27
  • 2
    $\begingroup$ @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, 2013 at 23:50
  • 2
    $\begingroup$ Unfortunately, loose language leads to a lot of misguided actions taken as a result of a misunderstanding. $\endgroup$
    – Glen_b
    Sep 9, 2013 at 10:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.