Productivity <- scan(what=list(Lot.Size=0,Hours=0))
80 399 30 121 50 221 90 376 70 361 60 224 120 546
80 352 100 353 50 157 40 160 70 252 90 389 20 113
110 435 100 420 30 212 50 268 90 377 110 421 30 273
90 468 40 244 80 342 70 323

Toluca <- data.frame(Productivity$Lot.Size,Productivity$Hours)
names(Toluca)=c("Lot.Size","Hours")

#Plot the data
with(Toluca,plot(Lot.Size,Hours,xlab="Lot Size (parts/lot)",ylab="Work Hours"))

#Fit a simple linear regression model
Toluca.lm <- lm(Hours ~ Lot.Size,data=Toluca)

#summaries of linear models object
attributes(Toluca.lm)
str(Toluca.lm)
summary(Toluca.lm)

#Add regression line using linear models object
abline(Toluca.lm,col="red")

#Page through diagnostic plots
plot(Toluca.lm)

#Prediction and confidence intervals for new data
newdata = data.frame(Lot.Size=c(65,100))
predict(Toluca.lm, newdata, interval="predict",level=0.95) 
predict(Toluca.lm, newdata, interval="confidence") # .95 is the default 
newdata=data.frame(Lot.Size=seq(min(Toluca$Lot.Size),max(Toluca$Lot.Size)))
predict(Toluca.lm,newdata)
Toluca.conf <- predict(Toluca.lm, newdata, interval="confidence",level=0.90,type="response")
Toluca.predict <- predict(Toluca.lm, newdata, interval="predict",level=0.90,type="response")
with(Toluca,plot(Lot.Size,Hours,xlab="Lot Size (parts/lot)",ylab="Work Hours"))
abline(Toluca.lm,col="black")
lines(newdata[,1],Toluca.conf[,2],col="red",lty=2)
lines(newdata[,1],Toluca.conf[,3],col="red",lty=2)
lines(newdata[,1],Toluca.predict[,2],col="blue",lty=2)
lines(newdata[,1],Toluca.predict[,3],col="blue",lty=2)

#Confidence intervals for intercept and slope
confint(Toluca.lm,level=0.90)

#Pearson and Spearman correlations and confidence intervals
#cor() lacks functionality
cor(Toluca)
with(Toluca,cor(Lot.Size,Hours))
cor(Toluca,method="spearman")
with(Toluca,cor.test(Lot.Size,Hours))
#No CI for Spearman--use alternate package
with(Toluca,cor.test(Lot.Size,Hours,method="spearman"))