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 Dec 8 '16 at 9:17

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


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