I am enrolled in a machine learning course for machine learning where we have a lab to implement linear regression I am attempting to do it in R to get a better understanding of the material and of R for myself (i don't intend to submit this as a lab as the course doesn't use R) but am coming up against a wall

My understanding of the process is as follows

• User Generates a model based on the hypothesis $hθ(x) = θx= θ0 +θ1x1$

• Take error rate of your model by using squared error cost function, then iterate, create a new hypothesis and get the error rate of this. Continue through n amounts of iterations based on the formula $J(θ0,θ1)=1/2m∑i=1m(hθ(x(i))−y(i))^2$. Assume the cost function in the code is based on this formula

• Take all the error rates you have recorded based on the cost history and use gradient descent to find automatically find the optimal values of your hypothesis

Using the code on R-Bloggers where the gradient descent is implement below based on vectors x and y

# add a column of 1's for the intercept coefficient
X <- cbind(1, matrix(x))

# gradient descent
for (i in 1:num_iters) {
 error <- (X %*% theta - y)
 delta <- (t(X) %*% error) / length(y)
 theta <- theta - alpha * delta
 cost_history[i] <- cost(X, y, theta)
 theta_history[[i]] <- theta
}

I was wondering if people could help me tease out the logic

1. Why is the number 1 applied to the matrix X. Is this so that X has 2 columns so that it can be multiplied by theta - y?

2. What is the formula delta actually calculating and why is the Transpose of X being used

Conceptually i think i understand the overall process but i just need to relate this back to the R code as i want to grasp the concept before proceeding to Multiple linear regression

I am enrolled in a machine learning course for machine learning where we have a lab to implement linear regression I am attempting to do it in R to get a better understanding of the material and of R for myself (i don't intend to submit this as a lab as the course doesn't use R) but am coming up against a wall

My understanding of the process is as follows

• User Generates a model based on the hypothesis $h_\theta(x) = \theta^TX= \theta_0x_0 +\theta_1x_1+\dots$

• Take error rate of your model by using squared error cost function, then iterate, create a new hypothesis and get the error rate of this. Continue through $n$ iterations based on the formula $J(\theta_0,\theta_1)=\frac{1}{2m}\displaystyle\sum_1^m(h_\theta(x^{(i)})−y^{(i)})^2$.

• Take all the error rates you have recorded based on the cost history and use gradient descent to find automatically the optimal values of your hypothesis.

Using the code on R-Bloggers where the gradient descent is implement below based on vectors x and y

# add a column of 1's for the intercept coefficient
X <- cbind(1, matrix(x))

# gradient descent
for (i in 1:num_iters) {
 error <- (X %*% theta - y)
 delta <- (t(X) %*% error) / length(y)
 theta <- theta - alpha * delta
 cost_history[i] <- cost(X, y, theta)
 theta_history[[i]] <- theta
}

I was wondering if people could help me tease out the logic

1. Why is the number 1 applied to the matrix X. Is this so that X has 2 columns so that it can be multiplied by theta - y?

2. What is the formula delta actually calculating and why is the Transpose of X being used

Conceptually I think i understand the overall process but i just need to relate this back to the R code as i want to grasp the concept before proceeding to Multiple linear regression