R: In anova.lm (g): ANOVA F-tests for an almost perfect fit are unreliable

Question

I am connecting online manuals with old text to learn R (p. 182 - http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf ). When I use the data from a package from R (as in the sample tutorials), there is no problem. However, when I use data from my text, I always end without an F value and warning.

Take a look:

in data.frame:

car.noise <- data.frame( speed = c("idle", "0-60mph", "over 60"), chrysler = c(41,65,76), bmw = c(45,67,72), ford = c(44,66,76), chevy = c(45,66,77), subaru = c(46,76,64)) 

check the data.frame file:

 car.noise speed chrysler bmw ford chevy subaru 1 idle 41 45 44 45 46 2 0-60mph 65 67 66 66 76 3 over 60 76 72 76 77 64 

melt the data.

 mcar.noise<- melt(car.noise, id.var="speed") 

check molten data.frame

 > mcar.noise speed variable value 1 idle chrysler 41 2 0-60mph chrysler 65 3 over 60 chrysler 76 4 idle bmw 45 5 0-60mph bmw 67 6 over 60 bmw 72 7 idle ford 44 8 0-60mph ford 66 9 over 60 ford 76 10 idle chevy 45 11 0-60mph chevy 66 12 over 60 chevy 77 13 idle subaru 46 14 0-60mph subaru 76 15 over 60 subaru 64 

run anova and get a warning:

 > anova(lm(value ~ variable * speed, mcar.noise)) Analysis of Variance Table Response: value Df Sum Sq Mean Sq F value Pr(>F) variable 4 6.93 1.73 speed 2 2368.13 1184.07 variable:speed 8 205.87 25.73 Residuals 0 0.00 Warning message: In anova.lm(lm(value ~ variable * speed, mcar.noise)) : ANOVA F-tests on an essentially perfect fit are unreliable 

Only 2 explanations I can come up with:

1: wrong coding 2: Text examples are too “perfect” for fitting as they try to show a clear example

Answer 1

You are trying to fit a model that gives a separate value for each variable speed combination. With the data you have, this means that you have no replication at all. It will be like trying to compare two groups when you have only one value from each group.

If you look at the “Remains” line in the anova table, you should notice that you do not have any degrees of freedom, and your sums of squares are 0. You can try to fit the model without interaction, if you think this is appropriate, but you don’t have enough data to fit the interaction model.