[R] factor analysis

[bunny , lautloscrew.com]

Hi there,

i´ve trouble understanding the factanal output of R.
i am running a a FA on a dataset with 10 variables.

i plotted eigenvalues to finde out how many factors to try.
i think the "elbow" is @ 3 factors.
here are my eigenvalues: 2.6372766 1.5137754 1.0188919 0.8986154  
0.8327583 0.7187473 0.6932792 0.5807489 0.5709594 0.5349477
(of the correlation matrix)

i guess this is basically what screeplot does as well.

and here´s my problem:
unfortunately the cumulative variance @ 3 factors is only .357
there are no crossloadings and the interpretation of the factors and  
their loadings definetely make sense so far.

Can i use this factor analysis somehow despite the poor cumulative  
variance of the first three factors ?
changing the rotation didnt help much.

The test of the hypothesis says the following:

Test of the hypothesis that 3 factors are sufficient.
The chi square statistic is 46.58 on 18 degrees of freedom.
The p-value is 0.000244

does this mean the Hnull is that 3 factors are sufficient and i cant  
recject ?


4 factors say:
Test of the hypothesis that 4 factors are sufficient.
The chi square statistic is 10.82 on 11 degrees of freedom.
The p-value is 0.458

Unfortunately ?factanal does not tell me what the Hnull is in this  
case ?

Thx a lot in advance for some advice

matthias