#R SCRIPT FOR 2008 LINEAR MODELS 02

#READ TABLE AND ASSIGN VARIABLES FROM COLUMNS:
K=read.table("c:/2008LinearModelsData/Toluca.txt")
attach(K)
X=V1
Y=V2

summary(lm(Y~X))

anova(lm(Y~X))

confint(lm(Y~X),level=0.90)

confint(lm(Y~X),level=0.95)

predict.lm(lm(Y~X),interval="confidence",level=0.90)

predict.lm(lm(Y~X),interval="prediction",level=0.90)

cor.test(X,Y, method="pearson",alternative="two.sided",conf.level=0.95)

#COLLECTING INFORMATION FROM THE REGRESSION:
Yh=predict(lm(Y~X))
RESID=resid(lm(Y~X))
CONF=data.frame(predict.lm(lm(Y~X),interval="confidence",level=0.90))
PRED= data.frame(predict.lm(lm(Y~X),interval="prediction",level=0.90))
#CALCULATING WORKING-HOTELLING INTERVAL ALSO:
#FIRST ONE SPECIFIES CONFIDENCE LEVEL ALPHA:
alpha=0.10
#FINDING n:
n=length(X)
#USING qt() FUNCTION TO CALCULATE CRITICAL VALUE C :
C=qt((1-(alpha/2)),(n-2))
C
#USING qf() FUNCTION TO CALCULATE WI CRITICAL VALUE W:
W=sqrt(2*qf(1-alpha,2,(n-2)))
W
#CALCULATING WORKING-HOTELLING INTERVALS:
WH.lwr=Yh-((W/C)*(Yh-CONF$lwr))
WH.upr=Yh+((W/C)*(Yh-CONF$lwr))
WORHOT=data.frame(WH.lwr,WH.upr)
WORHOT
# REPORTING WITHIN A DATAFRAME CALLED "RESULTS":
RESULTS=data.frame(X,Y,Yh,RESID,CONF$lwr,CONF$upr,PRED$lwr,PRED$upr,WH.lwr,WH.upr)
RESULTS

#PLOTTING DATA, REGRESSION LINE, AND INTERVALS:
plot(X,Y,pch=19,col="black")
points(X,Yh,pch=19,col="blue")
abline(lm(Y~X),col="blue")
#segments(X,predict(lm(Y~X)),X,Y,col="red")
points(X,CONF$lwr, pch=24,col="green")
points(X,CONF$upr, pch=25,col="green")
points(X,PRED$lwr, pch=24,col="magenta")
points(X,PRED$upr, pch=25,col="magenta")
points(X,WH.lwr, pch=24,col="brown")
points(X,WH.upr, pch=25,col="brown")