oxide_read.table("oxide.dat",skip=18)
names(oxide)_c("day","wind","temp","humid","insol","ox")
attach(oxide)
motif()
pairs(oxide)

#multiple regression
ox.lm.1_lm(ox ~ temp)
ox.lm.2_lm(ox ~ temp + wind)
summary(ox.lm.1,cor=F)
summary(ox.lm.2,cor=F)

#the design matrix
model.matrix(ox.lm.2)

#examine the parts of the output
summary(ox.lm.2,cor=F)

#analysis of residuals
par(mfrow=c(2,2))
plot(temp,ox.lm.2$resid)
plot(wind,ox.lm.2$resid)
plot(ox,ox.lm.2$resid)
plot(ox.lm.2$fitted,ox.lm.2$resid)
par(mfrow=c(1,1))
qqnorm(ox.lm.2$resid)

#visualize in three dimensions
persp(interp(temp,wind,ox))

summary(oxide)
persp(interp(temp,wind,ox),eye=c(-6*(92-67),8*(65-35),5*(25-4)))
persp(interp(temp,wind,ox),eye=c(-6*(92-67),4*(65-35),3*(25-4)))

par(mfrow=c(2,2))
persp(interp(temp,wind,ox),eye=c(-6*(92-67),4*(65-35),3*(25-4)))
title("Data")
persp(interp(temp,wind,ox.lm.2$fitted),eye=c(-6*(92-67),4*(65-35),3*(25-4)))
title("Fitted")
persp(interp(temp,wind,ox.lm.2$resid),eye=c(-6*(92-67),4*(65-35),3*(25-4)))
title("Resid")
par(mfrow=c(1,1))

spin( matrix(c(temp,wind,ox),30,3), collab=c("temp","wind","ox"),highlight=rep(T,30))

#examining predictions
plot(temp,ox)
lines(temp[order(temp)],fitted(ox.lm.2)[order(temp)])

coef(ox.lm.2)
lines(temp[order(temp)],coef(ox.lm.2)[2]*temp[order(temp)]+coef(ox.lm.2)[1]+coef(ox.lm.2)[3]*mean(wind),lty=2)

lines(temp[order(temp)],fitted(ox.lm.1)[order(temp)],lty=4)


#finding important variables
#first look at t tests
ox.lm.3_lm(ox ~ .,data=oxide)
summary(ox.lm.3)

ox.lm.4_lm(ox ~ .-day,data=oxide)
summary(ox.lm.4,cor=F)

ox.lm.5_lm(ox ~ .-day-insol,data=oxide)
summary(ox.lm.5,cor=F)

#stepwise algorithms
step(lm(ox~.,data=oxide))

stepwise(oxide[,-6],ox)

leaps(oxide[,-6],ox)

#F tests
ox.lm.3_lm(ox ~ .,data=oxide)
anova(ox.lm.3)

ox.lm.6_lm(ox ~ day + insol + humid + temp + wind)
anova(ox.lm.6)

ox.lm.7_lm(ox ~ wind + temp + humid + insol + day)
anova(ox.lm.7)

#examine residuals:  constant variance?  other variables?
ox.lm.8_lm(ox ~ day)
qqnorm(ox.lm.8$resid)
plot(day,ox.lm.8$resid)
plot(wind,ox.lm.8$resid)

#transformations
detach()
cars_read.table("mercedes.dat",skip=24,header=T)
attach(cars)
pairs(cars)

plot(Age,Price)
cars.lm.1_lm(Price~Age)
summary(cars.lm.1,cor=F)
plot(Age,resid(cars.lm.1))

cars.lm.2_lm(log(Price)~Age)
summary(cars.lm.2,cor=F)
plot(Age,resid(cars.lm.2))

#multicollinearity
pairs(cars)
cor(cars)
plot(Age,Mile)

cars.lm.3_lm(log(Price)~Age+Mile)
summary(cars.lm.3,cor=F)
summary(cars.lm.2,cor=F)
summary(lm(log(Price)~Mile),cor=F)


#polynomial regression
cars.lm.4_lm(log(Price)~Age^2+Age+Mile)
summary(cars.lm.4)

#interactions
ox.lm.9_lm(ox~wind*temp)
summary(ox.lm.9)

step(lm(ox~.^2,data=oxide))




#factor models
cars$Mod_as.factor(cars$Mod)
detach()
attach(cars)
cars.lm.5_lm(log(Price)~Age+Mod)
summary(cars.lm.5,cor=F)
model.matrix(cars.lm.5)
contrasts(Mod)

contrasts(Mod)_contr.treatment(6)
contrasts(Mod)
cars.lm.6_lm(log(Price)~Age+Mod)
model.matrix(cars.lm.6)
summary(cars.lm.5,cor=F)
summary(cars.lm.6,cor=F)

anova(cars.lm.6)

#factor model 2
cars.lm.7_lm(log(Price)~Age*Mod)
model.matrix(cars.lm.7)
summary(cars.lm.7,cor=F)
anova(cars.lm.7)

#autoregression
acf(ox)
acf(ox,type="partial")

ox
lag(ox)
lag(ox,-1)

ox.lm.10_lm(ox[2:30]~ox[1:29])
summary(ox.lm.10,cor=F)

plot(ox.lm.2$resid)
acf(ox.lm.2$resid)