h(x)=Tx, for ,xRd, and we choose that minimizes the following "average square loss" objective function: J()=m1i=1m(h(xi)yi)2, where (x1,y1),,(xm,ym)RdR is our training data. While this formulation of linear regression is very convenient, it's more standard to use a hypothesis space of affine functions: h,b(x)=Tx+b, which allows a nonzero intercept term b - sometimes called a "bias" term. The standard way to achieve this, while still maintaining the convenience of the first representation, is to add an extra dimension to x that is always a fixed value, such as 1 , and use ,xRd+1. Convince yourself that this is equivalent. We will assume this representation. 5. Let XRm(d+1) be the design matrix, where the i 'th row of X is xi. Let y= (y1,,ym)TRm1 be the response. Write the objective function J() as a matrix/vector expression, without using an explicit summation sign. 1 6. Write down an expression for the gradient of J without using an explicit summation sign. 7. Write down the expression for updating in the gradient descent algorithm for a step size