Show that in the simple linear model the least squares estimates for Bo, B are given by: = 1 = - (xi x) (yi ) (*, - *)2 where each sum is from i = 1 to N, the sample size. Hints: This is essentially an exercise in algebra. The following walks you through the moves. (i) Simplify the system of equations given in the notes that resulted from taking the partial derivatives of RSS (B) (i.e., divide out any constants) and separate the sums for each term (e.g., (Yi o xi) = Yi - No - xi). (ii) Solve the first equation in the simplified system for Bo. Note that = #xandy = \ yi. (iii) Substitute the expression for o into the second equation in the system and solve for 1. This will result in the following fraction: = xiyi ? - xi (iv) To show the expression derived in the previous step is equal to the desired expression given in the problem statement, focus on the numerators and denominators separately. - For the numerator, starting with xiyi - xi, add and subtract the term Xi - For the denominator, starting with x i, add and subtract the term - y. xi. You may find it helpful to work backwards from the desired expressions, expanding the products, to see how to simplify the expressions going forwards.