attach(airquality)
head(airquality)
tail(airquality)


modelS = lm( Ozone ~ Solar.R )
summary(modelS)

modelW = lm( Ozone ~ Wind )
summary(modelW)

modelT = lm( Ozone ~ Temp )
summary(modelT)


modelSTW = lm( Ozone ~ Solar.R  + Temp + Wind )
summary(modelSTW)
AIC(modelSTW)


# greated radiation, temperature increases? 

modelSstarTW = lm( Ozone ~ Solar.R * Temp + Wind )
summary(modelSstarTW)
AIC(modelSstarTW)

# does Ozone grow **proportionally with temperature?

modelT2 = lm( Ozone ~ Temp + I(Temp^2))
summary(modelT2)
AIC(modelT2)

# which minimal adequate model ?

modelSstarT2W = lm( Ozone ~ Solar.R * Temp + I(Temp^2) + Wind )
summary(modelSstarT2W)
AIC(modelSstarT2W)

modelSstarT2W2 = lm( Ozone ~ Solar.R * Temp + I(Temp^2) + Wind + I(Wind^2) )
summary(modelSstarT2W2)
AIC(modelSstarT2W2)

par(mfrow = c(2,2))
plot(modelSstarT2W2)