For the data set given below we consider to fit a regression model y_i = x_i + for i = 1, 2. Assume that Var() = ² .

i	yi	xi
1	5	4
2	3	1

(a) Find the LSE of and ² using S().

(b) We can write the model using matrix notation as y = X + . Give y, X, then draw y, X, L(X) and the residual e in two-dimensional space. Give the normal equation and find the LSE of geometrically.

(c) Find and e = y , then compute SSE = .

(d) Draw the pairs of the observed data (y_i, x_i) for i = 1, 2 and the fitted line _i = x_i.

2 8 2 8