newfood = read.csv("http://faculty.chicagobooth.edu/nicholas.polson/teaching/41000/newfood.csv",header=T)
attach(newfood)
names(newfood)

# correlation matrix
cor(cbind(sales,price,adv,locat,income,svol))

# Sales on Price, Adv, Locat

model1 = lm(sales~price+adv+locat)
summary(model1)

# Build kitchen-sink model 

model = lm(sales~price+adv+locat+income+svol)
summary(model)

# check diagnostics

plot(model,pch=20,col="blue")

# log-log model
# can't transform dummy variables: adv, locat

log_sales = log(sales)
log_price = log(price)
log_income = log(income)
log_svol = log(svol)


# Build model

modelnew = lm(log_sales~log_price+adv+log_income+log_svol)
summary(modelnew)

# check diagnostics

plot(modelnew,pch=20,col="blue")

plot(cooks.distance(modelnew),pch=20,col="maroon")



# statistical significance

 

summary(modelnew)


# Prediction

newdata1 = data.frame(log_price=log(30),adv=1,log_income=log(8),log_svol=log(34))
predict.lm(modelnew,newdata1,se.fit=T,interval="confidence",level=0.95)

# predict.lm at median(log_price), adv=1, median(log_income), median(log_svol)

newdata2 = data.frame(log_price=median(log_price),adv=1,
                      log_income=median(log_income),log_svol=median(log_svol))

predict.lm(modelnew,newdata2,se.fit=T,interval="prediction")

# prediction line for log-log
layout(matrix(c(1,2,3,4),2,2))
termplot(modelnew,ylabs="log_sales",terms="log_price",se=T)  
termplot(modelnew,ylabs="log_sales",terms="adv",se=T)  
termplot(modelnew,ylabs="log_sales",terms="log_income",se=T)  
termplot(modelnew,ylabs="log_sales",terms="log_svol",se=T)