Question

linear algebra

Question 2: Consider the data (-2,-2), (-14), (0,0), (1,5), (2,8). Find the matrix A that would solve the least squares line, and the matrix B that would solve the least squares quadratic. Answer Question 3: Find the least squares line and residual vector for the data found in Question 2 Answer:

Answer 1

Residual vector is difference of actual y(given y value as data) value and estimated y value(estimated from equation obtained) by mode

data. we ave gn he data linera a ineav model bave Standoyd eauwhon I oc Yi 2. x8 ;Transpose given deta i 2,1)) (2,%) GI 2 21 2

2 -2 O 2 So AI12 2 6 5 This is the mctvix e ine We can solve mis, insl multipla T. Nouj de neesd to hnd omspose inverse a x x d b 2 0

5 5 3 .2 Ο 2-I O ME 2.1 oC d2

1-a 4 2. 5 2 ー2-101 2 1 2 4 1o o 3 4

-1 1 91 5 0 10 o 10 o l-5 340 +10 (0-100) 10 0 391-700 or co (a cloγ A d j A-Transpose matrix lt fox aij term Cofactor aij t by delet th Yod 3t coloxwnms. 340 03 +2 0 34 lo O 92/ =。 o 34

lo 34 0 to o D100 10 Colact q31ご 5 to Colg다 aq33= -1 O 10 -100 0 50 10 L 1000 So -1 340 000 -100 | -1000

2. 1 5 2. -t ot 4 5 1 3 40 0 -10 0 15 o O 1470 t 15o 100 2 .214

velea nregresion model. actual g 2actual y valo estimated valua eshrated 2-14-2 +3=-1.21-0.8 2 2, 2-1木0+3-3 /.-3 2. 0.689 .51 4 884 1.6 3 3.3 2 -a-51 CD 116 O.31 4+ 5 厂一1.23 3.32 - 3.57 Residust Vector 37