Question: 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

LINEAR MODEL (STATISTICS)

LINEAR MODEL (STATISTICS)

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

LINEAR MODEL (STATISTICS) LINEAR MODELLINEAR MODEL (STATISTICS) LINEAR MODELLINEAR MODEL (STATISTICS) LINEAR MODELLINEAR MODEL (STATISTICS) LINEAR MODEL
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

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