8.3 Consider the following Gaussian dataset in which the dependent variables are assumed to have the same unknown standard deviation , xi yi 0:0 0:0 1:0 1:5 2:0 1:5 3:0 2:5 4:0 4:5 5:0 5:0 The data are to be fit to a linear model.

(a) Using the maximum likelihood method, find the analytic relationships between Pxi,Pyi,Pxiyi,Px2i , and the model parameters a and b.

(b) Show that the best-fit values of the model parameters are a D 0 and b D 1.