###----------------------------------------------------------------------------
### 8.26 Multiple Regression
###----------------------------------------------------------------------------

## Read the data
CableData <- read.table("Table_8_10.csv", header = TRUE)

## Make a linear regression
CableLM <- lm(Y~X2+X3+X4+X5+X6, data = CableData) # With intercept
CableLMNoInt <- lm(Y~0+X2+X3+X4+X5+X6, data = CableData) # Without intercept

## Summarize the models
summary(CableLM)
summary(CableLMNoInt)

## See what are available in the regression object
names(CableLM)
CableLM$fitted.values # Y Hat
CableLM$residuals # Residuals

## Predictions
predict(CableLM, se.fit = TRUE) #same as CableLM$fitted.values but also show
                                #the standard error for the predictions

## The coefficients
coef(CableLM)

## Variance covariance matrix for coefficients
vcov(CableLM)

## Prediction with new values
predict(CableLM, newdata = CableData[1:6, ], se.fit = TRUE)

## Plot the model
plot(CableLM)

## Histogram of the residuals
hist(CableLM$residuals)





###----------------------------------------------------------------------------
### 9.22 Regression with dummies
###----------------------------------------------------------------------------

## Read the data
SalesData <- read.table("Table_9_3.csv", header = TRUE)

## Create dummies,
## Seasonal data,
n <- nrow(SalesData)
D2 <- as.numeric(((1:n)%%4) == 2) # Check if from quarter II
D3 <- as.numeric(((1:n)%%4) == 3) # Check if from quarter III
D4 <- as.numeric(((1:n)%%4) == 0) # Check if from quarter IV
SalesDataWithDummies <- cbind(SalesData, D2, D3, D4)

DISHLM <- lm(DISH~D2+D3+D4, data = SalesDataWithDummies)
FRIGLM <- lm(FRIG~D2+D3+D4, data = SalesDataWithDummies)
summary(DISHLM)
summary(FRIGLM)

## Regression with dummies is exactly the same as the usual regression