Thank you Dr @Rainer for your time,

Here is my result...

Please see the following link:

https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)

Your question is unclear. First you talk about degrees of freedom, an ANOVA, and then a correlation of zero? What does have a correlation of zero to do with degrees of freedom??? These are two completely different things! You can have r = 0 and a very large sample, which in turn means also high df, since df for product moment correlation = N-2. So you would have df = 0 in case of N = 2 (which I guess is not the case). In case of ANOVA df_treat = k-1 (where k is no. of groups), df_error = df_tot(N-1) - df_treat. So, to get df = 0 you have either only one group in an ANOVA or only one participant in each group.

Thank you Dr @Rainer for your time,

Here is my result...

My guess as to what happened is that not all combinations of levels have been observed. E.g. you have two factors each with two levels as follows:

facA=c(a,a,a,b,b,b), facB=c(c,c,c,c,d,d) and the response y=c(4,5,4.3,5,6). I you run this in e.g. SPSS you will get zero degrees of freedom for the interaction effect, since not all combinations have been observed, namely for FacA level A, there is not FacB with level D.

Thank you all of you