#####  Linear Regression Model  ######

weight<-c(3.4,3.8,4.1,2.2,2.6,2.9,2.0,2.7,1.9,3.4)      

consum<-c(5.5,5.9,6.5,3.3,3.6,4.6,2.9,3.6,3.1,4.9)

n<-length(weight)

obsno<-1:n     

seq1<-seq(0, 4, 0.5)                       # sequence command (equally-spaced)
seq1 

re0<-rep(2:4, 2)                           #  replicate command
rep0

re1<-rep(2:4, 1:3)                 
rep1

car<-cbind(obsno, weight, consum)          ## combine vectors by columns
car

car2<-rbind(weight, consum)                ## combine vectors by rows
car2


# first row (observation) in car data
car[1,]

# second column in the car data
car[,2]

# linear model fit lm(y ~ x) 
lm(consum ~ weight )                         # model  y=a+b*x 

lm(consum ~ weight -1)                       # model y=b*x, no intercept

beta<-c(-0.363,1.639)                       # input coefficients as a vector
beta
                                 # transpose of a vector           

M<-matrix(1:4, ncol=2, byrow=T)            # create a matrix
solve(M)                                   # inverse matrix of M

X <- cbind(rep(1,n),car[,2])
X
fitted.values <- X %*% beta                   #  '%*%' matrix multiplication
fitted.values

residuals <- consum - fitted.values
residuals
sum(residuals)

sum(t(residuals)%*%weight)

### Descriptive Statistics ###

summary(lm(consum ~ weight ) )

### One-Way ANOVA Table for Simple Linear Regression###

anova(lm(consum~weight))