A pre-loaded example dataset in R

Main page: https://www.rdocumentation.org/packages/datasets/versions/3.6.2/topics/ability.cov

ability.cov
## $cov
##         general picture  blocks   maze reading   vocab
## general  24.641   5.991  33.520  6.023  20.755  29.701
## picture   5.991   6.700  18.137  1.782   4.936   7.204
## blocks   33.520  18.137 149.831 19.424  31.430  50.753
## maze      6.023   1.782  19.424 12.711   4.757   9.075
## reading  20.755   4.936  31.430  4.757  52.604  66.762
## vocab    29.701   7.204  50.753  9.075  66.762 135.292
## 
## $center
## [1] 0 0 0 0 0 0
## 
## $n.obs
## [1] 112
require(stats)
(ability.FA <- factanal(factors = 1, covmat = ability.cov))
## 
## Call:
## factanal(factors = 1, covmat = ability.cov)
## 
## Uniquenesses:
## general picture  blocks    maze reading   vocab 
##   0.535   0.853   0.748   0.910   0.232   0.280 
## 
## Loadings:
##         Factor1
## general 0.682  
## picture 0.384  
## blocks  0.502  
## maze    0.300  
## reading 0.877  
## vocab   0.849  
## 
##                Factor1
## SS loadings      2.443
## Proportion Var   0.407
## 
## Test of the hypothesis that 1 factor is sufficient.
## The chi square statistic is 75.18 on 9 degrees of freedom.
## The p-value is 1.46e-12
update(ability.FA, factors = 2)
## 
## Call:
## factanal(factors = 2, covmat = ability.cov)
## 
## Uniquenesses:
## general picture  blocks    maze reading   vocab 
##   0.455   0.589   0.218   0.769   0.052   0.334 
## 
## Loadings:
##         Factor1 Factor2
## general 0.499   0.543  
## picture 0.156   0.622  
## blocks  0.206   0.860  
## maze    0.109   0.468  
## reading 0.956   0.182  
## vocab   0.785   0.225  
## 
##                Factor1 Factor2
## SS loadings      1.858   1.724
## Proportion Var   0.310   0.287
## Cumulative Var   0.310   0.597
## 
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 6.11 on 4 degrees of freedom.
## The p-value is 0.191
## The signs of factors and hence the signs of correlations are
## arbitrary with promax rotation.
update(ability.FA, factors = 2, rotation = "promax")
## 
## Call:
## factanal(factors = 2, covmat = ability.cov, rotation = "promax")
## 
## Uniquenesses:
## general picture  blocks    maze reading   vocab 
##   0.455   0.589   0.218   0.769   0.052   0.334 
## 
## Loadings:
##         Factor1 Factor2
## general  0.364   0.470 
## picture          0.671 
## blocks           0.932 
## maze             0.508 
## reading  1.023         
## vocab    0.811         
## 
##                Factor1 Factor2
## SS loadings      1.853   1.807
## Proportion Var   0.309   0.301
## Cumulative Var   0.309   0.610
## 
## Factor Correlations:
##         Factor1 Factor2
## Factor1   1.000   0.557
## Factor2   0.557   1.000
## 
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 6.11 on 4 degrees of freedom.
## The p-value is 0.191