testscores <- matrix(scan(), ncol=5, byrow=T)
 36 58 43 36 37
 62 54 50 46 52
 31 42 41 40 29
 76 78 69 66 81
 46 56 52 56 40
 12 42 38 38 28
 39 46 51 54 41
 30 51 54 52 32
 22 32 43 28 22
 9 40 47 30 24
 32 49 54 37 52
 40 62 51 40 49
 64 75 70 66 63
 36 38 58 62 62
 24 46 44 55 49
 50 50 54 52 51
 42 42 52 38 50
 2 35 32 22 16
 56 53 42 40 32
 59 72 70 66 62
 28 50 50 42 63
 19 46 49 40 30
 36 56 56 54 52
 54 57 59 62 58
 14 35 38 29 20

 
dimnames(testscores) <- list(1:25, c("diffgeom","complex", "algebra", "reals", "statistics"))
testscores
testscores.prc <- princomp(testscores)
testscores.prc

summary(testscores.prc)

summary(testscores.prc, loadings=T)

loadings(testscores.prc)

plot(loadings(testscores.prc))
testscores_cor.prc <- princomp(testscores,cor=T)
summary(testscores_cor.prc, loadings=T)

plot(loadings(testscores_cor.prc))

exam81 <- matrix(scan(), ncol=3, byrow=T)
 1 -2 0
 -2 5 0
 0 0 2
 

covmatrix_exam81 

cov.obj <- list(cov = covmatrix, center = c(0,0,0))
cov.obj
princov <- princomp(covlist = cov.obj)
princov

summary(princov)

summary(princov,loadings=T,correlations=T)
 
plot(testscores.prc, style="lines")

plot(testscores.prc)

testscores.eigen <- testscores.prc$sdev^2
testscores.eigen

mean(testscores.eigen)

testscores.prc$scores

predict(testscores.prc)

 newscores <- matrix(scan(), ncol=5, byrow=T)
 22 50 70 54 30
 22 46 38 52 62
 22 42 50 40 62
 


dimnames(newscores) <- list(1:3, c("diffgeom","complex", "algebra", "reals", "statistics"))
newscores 

predict(testscores.prc, newdata=newscores)




testscores <- matrix(scan(), ncol=5, byrow=T)
 36 58 43 36 37
 62 54 50 46 52
 31 42 41 40 29
 76 78 69 66 81
 46 56 52 56 40
 12 42 38 38 28
 39 46 51 54 41
 30 51 54 52 32
 22 32 43 28 22
 9 40 47 30 24
 32 49 54 37 52
 40 62 51 40 49
 64 75 70 66 63
 36 38 58 62 62
 24 46 44 55 49
 50 50 54 52 51
 42 42 52 38 50
 2 35 32 22 16
 56 53 42 40 32
 59 72 70 66 62
 28 50 50 42 63
 19 46 49 40 30
 36 56 56 54 52
 54 57 59 62 58
 14 35 38 29 20



testscores.fa <- factanal(testscores, factors=2)
testscores.fa

summary(testscores.fa)

loadings(testscores.fa)

1 - testscores.fa$uniquenesses

testscores.fa2 <- factanal(testscores, factors=2, method="mle")
testscores.fa2

factcov <- factanal(covlist = cov.obj)
factcov

plot(loadings(testscores.fa))
biplot(testscores.fa)

newscores <- matrix(scan(), ncol=5, byrow=T)
 22 50 70 54 30
 22 46 38 52 62
 22 42 50 40 62
 


predict(testscores.fa)
predict(testscores.fa, newdata=newscores)