I got the following outcome. I am confused with the interpretation. When I consider RSS then model 2 is better than model 1. What does that high p value mean? Does in influence my conclusion??

anova(reg4.3,reg4.4, test="Chisq")

Analysis of Variance Table

Model 1: Gas ~ Flow * CODin + A + B + C
Model 2: Gas ~ Flow * CODin + A + B + C + Blue + Green

  Res.Df     RSS Df Sum of Sq Pr(>Chi)
1     60 10034.5     
2     58  9851.3  2    183.21   0.5831
  • $\begingroup$ RSS always improves when you add parameters*, no matter how irrelevant the variable is. $\,\,$ *(well, it can be exactly zero, but that's an event with probability zero under the model assumptions)... so just knowing there's an improvement in RSS doesn't tell you anything. $\endgroup$
    – Glen_b
    May 27, 2014 at 7:28

1 Answer 1


The anova command that you wrote (with test="Chisq") will perform a Likelihood ratio test, where $H_0:$ Model 1 is a preferred model and $H_1:$ Model 2 is a preferred model. Roughly speaking, this test looks at the loglikelihood of models 1 and 2 and see if the increase in the loglikelihood of model 2 (due to adding two more variables i.e. Blue and Green) is significant enough to reject $H_0$ or not. Here since 0.5831>0.05, you don't reject $H_0$. In other words, we don't have enough evidence to reject the hypothesis that model 1 is a preferred model compared to model 2.

Of course, when you add two more variables (regardless of being significant or not), you are actually reducing your RSS and model 2 would be the preferred model. But there is a trade of here, you need to answer this question: Is it worth it to add two more variable to reduce RSS by 183.21? Above Likelihood ratio test is saying that "NO it is not worth it"!


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.