Training a linear model in R, I get something like the following as summary (I think it looks similar in SPSS too).

lm(formula = df.full$diff.err ~ df.full$diff.emo)

    Min       1Q   Median       3Q      Max 
-0.96323 -0.10255 -0.00002  0.10104  0.94691 

                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      1.737e-05  1.647e-03   0.011    0.992    
df.full$diff.emo 8.207e-01  7.924e-03 103.573   <2e-16 ***
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.163 on 10060 degrees of freedom
Multiple R-squared:  0.5161,    Adjusted R-squared:  0.516 
F-statistic: 1.073e+04 on 1 and 10060 DF,  p-value: < 2.2e-16

Under the "Coefficients" section I am given p-values for the intercept and the slope. My question is, what is the name of the test which is (typically) used to obtain these p-values?

I am under the impression, that people online just generally refer to it as "the p-value of the slope/intercept" without discussing where these come from, for example here

Significance of Regression Intercept (R lm model)



  • $\begingroup$ Whether that is true in general about what people say, the output itself tells you that the tests of the coefficients are t-tests and as @gRRRR rightly explains the overall test for the regression is an F test. A good reason for not explaining might be that this is regarded as standard stuff explained in textbooks. After all, many papers refer to means without feeling a need to give an explanation, a formula or a worked example. It's a matter for your field of what (is regarded as) in need of explanation. $\endgroup$
    – Nick Cox
    Commented Dec 8, 2016 at 9:17

1 Answer 1


As the last line of your output suggests, the p-value comes from the F-statistic (it is the probability of getting as high an F-statistic as you got under the null hypothesis), which in turn comes from the F test. There's a detailed discussion of the procedure of evaluating multiple linear regression slope with an F test here


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.