# What is the meaning of the R factanal output?

What does all this mean? I'm a factor analysis 'noob' and although I've read a book, it didn't tell me everything apparently.

Since the chi square statistic is so high and the p-value so low, it would seem that the data is close to being coplanar (2 dimensions) within the 6-dimensional space. Yet that only accounts for 89.4% of the variance (am I interpreting this right?)

Also, I thought factors were orthogonal to each other, so how can both factors have positive loadings for every variable?

And what do the uniquenesses mean?

> factanal(charges[3:8],2)

Call:
factanal(x = charges[3:8], factors = 2)

Uniquenesses:
APT    CHELPG   Natural       AIM Hirshfeld       VDD
0.217     0.250     0.082     0.052     0.005     0.033

Factor1 Factor2
APT       0.609   0.642
CHELPG    0.657   0.564
Natural   0.571   0.769
AIM       0.382   0.896
Hirshfeld 0.910   0.408
VDD       0.844   0.504

Factor1 Factor2
Proportion Var   0.470   0.424
Cumulative Var   0.470   0.894

Test of the hypothesis that 2 factors are sufficient.
The chi square statistic is 77.1 on 4 degrees of freedom.
The p-value is 7.15e-16
>

• @SeanMurphy: Thanks! Now, I understand that factor analysis "factors" (approximately) the 160x6 data matrix into a 160x2 scores matrix and a 2x6 loadings matrix. The output gives me the loadings matrix, but I'm also interested in the scores matrix. How do I get that? Preferably in a form that I can export and/or plot. Commented Oct 26, 2014 at 15:46