Module-4-Example-11.R

# Reference 
# https://datascienceplus.com/linear-regression-from-scratch-in-r/
# Use MASS library for Boston data set
library(MASS)

# Create response vector y
y <- Boston$medv

# Matrix of feature variables from Boston
X <- as.matrix(Boston[-ncol(Boston)])

# vector of ones with same length as rows in Boston
int <- rep(1, length(y))

# Add intercept column to X
X <- cbind(int, X)

# Implement closed-form solution
betas <- solve(t(X) %*% X) %*% t(X) %*% y

# Round for easier viewing
betas <- round(betas, 2)

# Linear regression model
lm.mod <- lm(medv ~ ., data=Boston)

# Round for easier viewing
lm.betas <- round(lm.mod$coefficients, 2)


# Create data.frame of results
results <- data.frame(our.results=betas, lm.results=lm.betas)

print(results)