To clarify what I mean, let's say we have these two models


Running anova(fit.1,fit.1.2) will provide an f-statistic for Input2 and the p-value for it's significance. Running summary(fit.1.2) will provide a t-statistic for Input1 and Input2 and the p-value for both. My question is why is the p-value for the f-statistic of Input2 in the ANOVA test equal to the p-value of the t-statistic of Input2 in the t-test? Below, I have attempted to include the output.

> anova(fit.1,fit.1.2)
Analysis of Variance Table
Model 1: Output ~ Input1
Model 2: Output ~ Input1 + Input2
  Res.Df   RSS Df  Sum of Sq  F Pr(>F)
1    498 185.43
2    497 185.38  1    0.0452 0.1212 0.7279

> summary(fit.1.2.3)
lm(formula = Output ~ Input1+Input2)
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.21480    0.05179  23.458   <2e-16
Input1       0.80116    0.02819  28.423   <2e-16
Input2       0.00970    0.02787   0.348    0.728

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.