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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
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  • $\begingroup$ 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

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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"!

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