# Anova output Variables meaning [closed]

I have this output from R that I'm trying to understand.

I would gladly appreciate any help!


Model 1: y ~ x + w + x:w
Model 2: y ~ x + w
Res.Df      RSS Df Sum of Sq      F  Pr(>F)
1     40 13452999
2     41 14759878 -1  -1306879 3.8858 0.05564 .


I should add that I'm a novice at using R and from what I can see:

$$F=3.8858$$

Numerator $$df=0$$

Denominator $$df=-1$$

Can a df be negative ?

Why would my $$F$$ and be on the last line?

Is it technically correct if I say that my $$p$$-val$$= 0.05564$$

1-pf(6.9202,0,1)


The above R code gives me nothing coherent.

This is a test to assert the importance of $$\beta_3$$ in the model

• The documentation of the function ANOVA in R says "It is conventional to list the models from smallest to largest, but this is up to the user." I think that answers one of my questions. – Mahamad A. Kanouté Sep 19 at 22:43
• What questions remain? – Peter Flom - Reinstate Monica Sep 20 at 13:04
• Why would F be on the last line ? Is it customary to R ? – Mahamad A. Kanouté Sep 20 at 15:38

This is the output of a call to anova() to compare two models, one with the term x:w and one without. The null hypothesis is that the model without x:w fits better.

This is a $$1$$-$$df$$ test. The numerator $$df = 1$$ and the denominator $$df = 40$$. The code to compute the p-value would be 1-pf(3.8858,1,40), which does indeed give $$0.05564$$. Becuase $$p>.05$$, there is not enough evidence to reject the null hypothesis at a $$.05$$ significance level. The x:w term doesn't significantly add to the model given the data you observed. Note that this p-value should be exactly equal to the p-value on the coefficient of $$\beta_3$$ if x and w are numeric because the test for whether $$\beta_3=0$$ is identical to the model comparison test you just performed.

$$F$$ is on the last line because that's a logical place for it to be to keep the output compact.

• What's your truck for choosing the df ? I see 41 and 40 how do you know which one to pick ? – Mahamad A. Kanouté Sep 20 at 15:40
• This technique has probably been described in statistics textbooks, which would tell you the formula. I figured it out by seeing which df gave me the p-value produced by the test. – Noah Sep 20 at 16:08
• Gotcha ! Indeed I do remember it but it's a bit confusing here as I see Res.Df and Df . Thank you anyway ! – Mahamad A. Kanouté Sep 20 at 16:18