HW-Linear Model_1

data(mtcars)

mtcars$cyl <- factor(mtcars$cyl)
mtcars$am  <- factor(mtcars$am)
Intercept <- rep(1, nrow(mtcars)) #Intercept column would be 1
cyl6 <- ifelse(mtcars$cyl == "6", 1, 0)   #Main effects of cyl
cyl8 <- ifelse(mtcars$cyl == "8", 1, 0)
am1 <- ifelse(mtcars$am == "1", 1, 0)   #Main effects of transmission
cyl6_am1 <- cyl6 * am1  #interaction effect
cyl8_am1 <- cyl8 * am1
X_manual <- cbind(  Intercept, cyl6, cyl8, am1, cyl6_am1, cyl8_am1)

colnames(X_manual) <- c( "(Intercept)","cyl6","cyl8", "am1", "cyl6:am1",
  "cyl8:am1"
)
dim(X_manual)

## [1] 32  6

X_manual[1:10, ]   #subset of the design matrix

##       (Intercept) cyl6 cyl8 am1 cyl6:am1 cyl8:am1
##  [1,]           1    1    0   1        1        0
##  [2,]           1    1    0   1        1        0
##  [3,]           1    0    0   1        0        0
##  [4,]           1    1    0   0        0        0
##  [5,]           1    0    1   0        0        0
##  [6,]           1    1    0   0        0        0
##  [7,]           1    0    1   0        0        0
##  [8,]           1    0    0   0        0        0
##  [9,]           1    0    0   0        0        0
## [10,]           1    1    0   0        0        0

X_auto <- model.matrix(mpg ~ cyl * am, data = mtcars) 
#comparing it with model.matrix to check if my manual X is correct
all(X_manual == X_auto)

## [1] TRUE