Instruction: Write all answers in the booklet. Please keep the question sheet and s booklet only. Each question is worth 8 points (112 points total) 1. Linear Regression with One Variable Suppose that we variable x. The training dataset is as follows. want to build a linear regression model to predict the value of variable y given Index x (input variable) The hypothesis of a penalize the model by the square error-y) linear regression model is that the relationship between x and y can be described as mathematical expression of the model ismx+ b, where m and b are model y (output variable)I is different from y, we each training example (x. y). if the predicted output value Question 1: Describe the eometric meaning of the square error. 2 For a liner model with parameter m- 1 and b-1, what is the average square error over all data examples? Question 3: Draw a coordinate plain in your booklet, plot the data points, the above linear model, and indicate the square errors. 6 5 4 3 1 2 3 4 5 6x The mean-square-error cost function J(m, b) is defined as follows: /(m, b) = n2(mx(i) + b-y(i))2 Question 4: Write the explicit expression for J(m.b) over the given dataset. Find its partial derivatives am ab Question 5: One method that finds the regression line that minimizes the cost function is the gradient descent algorithm. Explain how gradient descent algorithm works. Question 6: lim andbel at the beginning ofa gradient descent teration with learning rate equal to 0.1, how will the algorithm update m and b? Question I: What will happen if the learning rate is too large? What will happen if the learning rate is oo small