Given the following models determine each models type ie if

Given the following models, determine each model\'s type (i.e., if it is a first order model, a first order model with interaction terms or a second order model). Then use a computer (DO NOT draw by hand) to draw the response surface Let x_1 and x_2 vary in the range [-2, +2]. Please choose a fine enough grid to draw the graph, indicate x_1, x_2, and y on the graph. (a) y = 10+5x_1+3x_2+10x_1x_2 (b) y = 80 + 4x_1 + 8x_2 - 8x_1^2 - 12x_2^2 - 12x_1 x_2 (c) y = 15 + 5x_1 -6x_2 MATLAB coding exercise (a) In Question 2 above, regardless how you did the calculation in 2(a), re-do it using MATLAB, and write down the MATLAB codes you used. (b) Use MATLAB to calculate epsilon = y - X(X\'X)^-1 X\'y and epsilon\' epsilon, where

Solution

Create a matrix of real numbers and compute its transpose. B has the same elements as A, but the rows of B are the columns of A and the columns of B are the rows of A.

A = magic(4)
A = 16 2 3 13 5 11 10 8 9 7 6 12 4 14 15 1
B = A.\'
B = 16 5 9 4 2 11 7 14 3 10 6 15 13 8 12 1

Complex Matrix

Open Script

Create a matrix containing complex elements and compute its nonconjugate transpose. B contains the same elements as A, except the rows and columns are interchanged. The signs of the imaginary parts are unchanged.

A = [1 3 4-1i 2+2i; 0+1i 1-1i 5 6-1i]
A = 1.0000 + 0.0000i 3.0000 + 0.0000i 4.0000 - 1.0000i 2.0000 + 2.0000i 0.0000 + 1.0000i 1.0000 - 1.0000i 5.0000 + 0.0000i 6.0000 - 1.0000i
B = A.\'
B = 1.0000 + 0.0000i 0.0000 + 1.0000i 3.0000 + 0.0000i 1.0000 - 1.0000i 4.0000 - 1.0000i 5.0000 + 0.0000i 2.0000 + 2.0000i 6.0000 - 1.000