Question

d. We will use pinv function to find a linear regression model to map the measurement data to truth data. Our model will be Y-AX. Y is the truth data matrix Y [ yı; y2i yai ya; ysi yg: y7 ]. A is the tmeasurement data matrix A=[ 1 mh; 1 m2. 1 mai 1 m4; 1 ms: 1 mt 6:1 m7 I . and X-[Xo: x1] is the coefficient of your regression model. Truth Data yn -1 0 Measurement Data 10.03 7.97 63.9 2.1 0.05 -2.05 mn *n is the number of data point, we have seven points. d.1 (5pts) Generate your matrix Y-AX in Matlab. What is Y and A ? (show the matrix Y and A.) d.2 (10pts) Use pseudoinverse pinv function to find your coefficient X. (show the mtrix X) and give me your equation, it should look like yn-x0% * mn. Put certain value in xo and x1. Example model(your result will be different with the example model): уп--6, 1978 + 1.0137-m, d.3 (10pts) Plot your result. Plot the train data (You will need to plot measurement ata in x-asix and truth data in y-axis) and the predict line Example Figure (Your result will be different with it) 10 O Train Data yr6.1978 +1.0137 9 i Predict Line 12 13 14 Measure Data m

Answer 1

clc;
clear all;close all;

y=[-1;0;1;2;4;5;6];
A=[1 10.03;1 7.97;1 6,;1 .9;1 2.1;1 0.05;1 -2.05];
x=pinv(A)*y
m=[10.03 7.97 6 3.9 2.1 0.05 -2.05];

y_n=x(1)+(x(2)*m);

plot(m,y,'o',m,y_n);
grid on;
legend('True Data','Predic Line')

6 O True Data 5 Predic Line 4 3 2 0 -4 0 2 4 10 12