x <- cbind(1, mtcars$wt)
y <- mtcars$mpg

head(x)

head(y)

dim(x)

length(y)

x <- model.matrix(mpg ~ wt, data = mtcars)
y <- model.response(model.frame(mpg ~ wt, data = mtcars))

solve(t(x) %*% x) %*% t(x) %*% y

lm(mpg ~ wt, data = mtcars)$coefficients

x <- model.matrix(mpg ~ wt, data = mtcars)
y <- log(mtcars$mpg)

glm(mpg ~ wt, data = mtcars, family = poisson(link = "log"))$coefficients