LINEAR MODEL (STATISTICS)

LINEAR MODEL (STATISTICS)

I ONLY NEED HELP WITH QUESTION 2.4 BECAUSE THE REST OF THE QUESTIONS HAVE SOLUTIONS

Consider a linear model coirth 5 1 33 BE O 6 4 4 2 2 O 36 2 2A 1 O O 0 1 26 2 .1 The normal equations x14 = (x / x ) B 1 1 1 1 0 O 33 XX OO 2 2 O O 0 3 6 38 26 208 14 4 4 4 0 0 38 O 26 The above system reprents normal equations 2 2 Since XX ) = 0 and Tank of the 3 Now Two find generalized inverses , and G2 ofWe have obtain a non. singular minor of ". Frank 3. let His 4 6 0 O O O NOW MT. = ly 0 1 1 O O Hence 67 = O O O 10 O O O 0 1 Now again obtain a. non- singular minor of rank ? Jel M 2 = y 0 1 14 O 4 0 0 O -171 -1 Heng Gaze -1 - 1 0 0 0 - Hence G, and Giz all two generalized inverses of x.X. 2. 3 Now first estimate of B. BS GixlyO O 208 O 1/ 4 quy 36 O O O 38 38 O O O 1 2 6 26 36 38 26 Noco Ind estimate of Bi- BZ = Gzxly 0 Y4 0 208 9.5 O O 14 4 2 6 O - / 38 80 2 3 O O 26 O Hence Bland BZ are estimates of B corresponding to G7 , and 6212QUESTION 2 [22 Marks] Consider a linear model with 1 1 0 0 31 1 1 0 0 33 ,u _ 1 1 0 0 _ 44 _ a1 X_1100'y_36\"8_ a2 1 0 1 0 38 a3 1 O 0 1 26 2.1 Write the normal equations. (6) 2.2 Find two generalized inverses G1 and Gg of XX. (6) 2.3 Use your result in part (2.2) considering E = Gx'y in general, to nd two estimates 3 of ,6 . (5) 2.4 Find two linear combinations of the elements 25 that are the same for both estimates and two that are different