library(languageR)


t.test(ratings$meanWeightRating,ratings$meanSizeRating)
t.test(ratings$meanWeightRating,ratings$meanSizeRating,paired=T)
t.test(ratings$meanWeightRating-ratings$meanSizeRating)
sum(ratings$meanWeightRating-ratings$meanSizeRating<0)

par(mfrow=c(1,2))
boxplot(ratings$meanWeightRating,ratings$meanSizeRating,names=c("weight","size"),ylab="mean rating") #p84�¶
boxplot(ratings$meanWeightRating-ratings$meanSizeRating,names="difference",ylab="mean rating difference") #p84‰E
par(mfrow=c(1,1))

shapiro.test(ratings$meanWeightRating-ratings$meanSizeRating)
wilcox.test(ratings$meanWeightRating,ratings$meanSizeRating,paired=T)

plot(ratings$meanWeightRating,ratings$meanWeightRating,xlab="mean weight rating",ylab="mean size rating") #p85�¶

plot(c(-4,4),c(-4,4),xlab="x",ylab="y",type="n") #set up the plot region,p86
abline(2,-2,lty=2) #add the lines
abline(-2,1,lty=3)
abline(h=0) #and add the axes
abline(v=0)
abline(h=-2,col="grey") #and ancillary lines in grey
abline(h=2,col="grey")
abline(v=1,col="grey",lty=2)
abline(v=2,col="grey",lty=2)
plot(ratings$meanWeightRating,ratings$meanWeightRating,xlab="mean weight rating",ylab="mean size rating",col="darkgrey") #p85‰E
abline(0.527,0.926)

ratings.lm=lm(meanSizeRating~meanWeightRating,data=ratings)
ratings.lm
coef(ratings.lm)
abline(ratings.lm)

mvrnormplot.fnc(r=0.9)

summary(ratings.lm)
summary(ratings.lm)$coef
summary(ratings.lm)$coef[ ,3]
summary(ratings.lm)$coef[ ,1]
data.frame(summary(ratings.lm)$coef)$Estimate
cor(ratings$meanSizeRating,ratings$meanWeightRating)
cor.test(ratings$meanSizeRating,ratings$meanWeightRating)
cor.test(ratings$meanSizeRating,ratings$meanWeightRating,method="spearman")

plot(ratings$FreqSingular,ratings$FreqPlural)
abline(lm(FreqPlural~FreqSingular,data=ratings),lty=1)
abline(lm(FreqPlural~FreqSingular,data=ratings[ratings$FreqSingular<500, ]),lty=2)
library(MASS)
abline(lmsreg(FreqPlural~FreqSingular,data=ratings),lty=3)

ratings.lm=lm(meanSizeRating~meanFamiliarity,data=ratings)
round(summary(ratings.lm)$coef,4)
plot(ratings$meanFamiliarity,ratings$meanSizeRating,xlab="mean familiarity",ylab="mean size rating",type="n")
plants=ratings[ratings$Class=="plant", ]
animals=ratings[ratings$Class=="animal", ]
points(plants$meanFamiliarity,plants$meanSizeRating,pch='p',col="darkgrey")
lines(lowess(plants$meanFamiliarity,plants$meanSizeRating),col="darkgrey")
points(animals$meanFamiliarity,animals$meanSizeRating,pch='a')
lines(lowess(animals$meanFamiliarity,animals$meanSizeRating))
plants.lm=lm(meanSizeRating~meanFamiliarity,plants)
abline(coef(plants.lm),col="darkgrey",lty=2)
animals.lm=lm(meanSizeRating~meanFamiliarity,animals)
abline(coef(animals.lm),lty=2)

xvals=seq(-4,4,0.1)
yvals1=0.5+0.25*xvals+0.6*xvals^2
yvals2=2.5+0.25*xvals-0.2*xvals^2
plot(xvals,yvals1,xlab="x",ylab="y",ylim=range(yvals1,yvals2),type="1")
lines(xvals,yvals2,col="darkgrey")

plants.lm=lm(meanSizeRating~meanFamiliarity+I(meanFamiliarity^2),data=plants)
summary(plants.lm)$coef
plot(ratings$meanFamiliarity,ratings$meanSizeRating,xlab="mean familiarity",ylab="mean size rating",type="n")
points(plants$meanFamiliarity,plants$meanSizeRating,pch='p',col="darkgrey")
plants$predict=predict(plants.lm)
plants=plants[order(plants$meanFamiliarity), ]
lines(plants$meanFamiliarity,plants$predict,col="darkgrey")
animals.lm=lm(meanSizeRating~meanFamiliarity+I(meanFamiliarity^2),data=animals)
summary(animals.lm)$coef
points(animals$meanFamiliarity,animals$meanSizeRating,pch='a')
animals$predict=predict(animals.lm)
animals=animals[order(animals$meanFamiliarity), ]
lines(animals$meanFamiliarity,animals$predict)
meanSizeRating~meanFamiliarity+I(meanFamiliarity^2)

library(MASS)
x=mvrnorm(n=1000,mu=c(0,0),Sigma=cbind(c(1,0.8),c(0.8,1)))
head(x)
cor(x[ ,1],x[ ,2])
Sigma=cbind(c(1,0.8),c(0.8,1))
Sigma
cor(x[ ,1],x[ ,2])
cor(x[ ,1],100*x[ ,2])
cor(0.001*x[ ,1],100*x[ ,2])
cov(x[ ,1],x[ ,2])
cov(x[ ,1],100*x[ ,2])
cov(0.003*x[ ,1],100*x[ ,2])

persp(kde2d(x[ ,1],x[ ,2],n=50),
phi=30,theta=20, #angles defining viewing direction
d=10, #strength of perspective
col="lightblue", #color for the surface
shade=0.75,ltheta=-100, #shading for viewing direction
border=NA, #we use shading, so we disable border
expand=0.5, #shrink the vertical direction by 0.5
xlab="x",ylab="y",zlab="density") #add labels
mtext("bivariate standard normal",3,1) #and add titles

n=1000 #number of words
lambdas=rlnorm(n,1,4) #lognormal random numbers
mat=matrix(nrow=n,ncol=2) #define matrix with zeros
for(i in 1:n){ #loop over each word index
mat[i, ]=rpois(2,lambdas[i]) #store Poisson frequencies
}
mat[1:10, ]
mat=log(mat+1)
persp(kde2d(mat[ ,1],mat[ ,2],n=50),phi=30,theta=20,d=10,col="lightblue",shade=0.75,box=T,border=NA,ltheta=-100,expand=0.5,xlab="log X",ylab="log Y",zlab="density")
mtext=("bivariate lognormal-Poisson",3,1)