```
#First compare to lm using data input
summary(lm(rating ~ complaints + privileges, data = attitude))
lmCor(rating ~ complaints + privileges, data = attitude, std=FALSE) #do not standardize
z.attitude <- data.frame(scale(attitude)) #standardize the data before doing lm
summary(lm(rating ~ complaints + privileges, data = z.attitude)) #regressions on z scores
lmCor(rating ~ complaints + privileges, data = attitude) #by default we standardize and
# the results are the same as the standardized lm
R <- cor(attitude) #find the correlations
#Do the regression on the correlations
#Note that these match the regressions on the standard scores of the data
lmCor(rating ~ complaints + privileges, data =R, n.obs=30)
#now, partial out learning and critical
lmCor(rating ~ complaints + privileges - learning - critical, data =R, n.obs=30)
#compare with the full regression:
lmCor(rating ~ complaints + privileges + learning + critical, data =R, n.obs=30)
#Canonical correlations:
#The first Kelley data set from Hotelling
kelley1 <- structure(c(1, 0.6328, 0.2412, 0.0586, 0.6328, 1, -0.0553, 0.0655,
0.2412, -0.0553, 1, 0.4248, 0.0586, 0.0655, 0.4248, 1), .Dim = c(4L,
4L), .Dimnames = list(c("reading.speed", "reading.power", "math.speed",
"math.power"), c("reading.speed", "reading.power", "math.speed",
"math.power")))
lowerMat(kelley1)
mod1 <- lmCor(y = math.speed + math.power ~ reading.speed + reading.power,
data = kelley1, n.obs=140)
mod1$cancor
#Hotelling reports .3945 and .0688 we get 0.39450592 0.06884787
#the second Kelley data from Hotelling
kelley <- structure(list(speed = c(1, 0.4248, 0.042, 0.0215, 0.0573), power = c(0.4248,
1, 0.1487, 0.2489, 0.2843), words = c(0.042, 0.1487, 1, 0.6693,
0.4662), symbols = c(0.0215, 0.2489, 0.6693, 1, 0.6915), meaningless = c(0.0573,
0.2843, 0.4662, 0.6915, 1)), .Names = c("speed", "power", "words",
"symbols", "meaningless"), class = "data.frame", row.names = c("speed",
"power", "words", "symbols", "meaningless"))
lowerMat(kelley)
lmCor(power + speed ~ words + symbols + meaningless,data=kelley) #formula mode
#lmCor(y= 1:2,x = 3:5,data = kelley) #order of variables input
#Hotelling reports canonical correlations of .3073 and .0583 or squared correlations of
# 0.09443329 and 0.00339889 vs. our values of cancor = 0.3076 0.0593 with squared values
#of 0.0946 0.0035,
lmCor(y=c(7:9),x=c(1:6),data=Thurstone,n.obs=213) #easier to just list variable
#locations if we have long names
#now try partialling out some variables
lmCor(y=c(7:9),x=c(1:3),z=c(4:6),data=Thurstone) #compare with the previous
#compare complete print out with summary printing
sc <- lmCor(SATV + SATQ ~ gender + education,data=sat.act) # regression from raw data
sc
summary(sc)
lmCor(Pedigrees ~ Sentences + Vocabulary - First.Letters - Four.Letter.Words ,
data=Thurstone) #showing formula input with two covariates
#Do some regressions with real data (rather than correlation matrices)
lmCor(reaction ~ cond + pmi + import, data = Tal.Or)
#partial out importance
lmCor(reaction ~ cond + pmi - import, data = Tal.Or, main="Partial out importance")
#compare with using lm by partialling
mod1 <- lm(reaction ~ cond + pmi + import, data = Tal.Or)
reaction.import <- lm(reaction~import,data=Tal.Or)$resid
cond.import <- lm(cond~import,data=Tal.Or)$resid
pmi.import <- lm(pmi~import,data=Tal.Or)$resid
mod.partial <- lm(reaction.import ~ cond.import + pmi.import)
summary(mod.partial)
#lm uses raw scores, so set std = FALSE for lmCor
print(lmCor(y = reaction ~ cond + pmi - import, data = Tal.Or,std = FALSE,
main = "Partial out importance"),digits=4)
#notice that the dfs of the partial approach using lm are 1 more than the lmCor dfs
#Show how to find quadratic terms
sc <- lmCor(reaction ~ cond + pmi + I(import^2), data = Tal.Or)
sc
#pairs.panels(sc$data) #show the SPLOM of the data
#Consider an example of a derivation and cross validation sample
set.seed(42)
ss <- sample(1:2800,1400)
model <- lmCor(y=26:28,x=1:25,data=bfi[ss,],plot=FALSE)
original.fit <- crossValidation(model,bfi[ss,]) #the derivation set
cross.fit <- crossValidation(model,bfi[-ss,]) #the cross validation set
summary(original.fit)
summary(cross.fit)
predicted <- predict(model,bfi[-ss,])
cor2(predicted,bfi[-ss,26:28]) #these are the correlations of the predicted with observed
#now do it for the correlations matrices - these should be the same
R1 <- lowerCor(bfi[ss,], show=FALSE)
R2 <- lowerCor(bfi[-ss,], show=FALSE)
mod1 <- lmCor(y=26:28,x=1:25,data=R1,plot=FALSE)
original <- crossValidation(model,R1) #the derivation set capitalizes on chance
cross <- crossValidation(model,R2) #the cross validation set -- values are lower
summary(original) #inflated by chance
summary(cross) #cross validated values are better estimates
```

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