Lecture 13
●
MEEN 357 Homework Solution
1
Lecture-13-Homework-Solution-2009.doc
RMB
1.
Problem 14.8 of the textbook.
Solution
:
You are asked to apply multiple liner regression to the data
1
x
0
1
1
2
2
3
3
4
4
2
x
0
1
2
1
2
1
2
1
2
y
15.1
17.9
12.7
25.6
20.5
35.1
29.7
45.4
40.2
This problem is virtually identically to the example worked in class during Lecture 13.
The script for that example modified is
clc
clear
all
x1=[0,1,1,2,2,3,3,4,4]'
x2=[0,1,2,1,2,1,2,1,2]'
y=[15.1,17.9,12.7,25.6,20.5,35.1,29.7,45.4,40.2]'
A=[ones(9,1),x1,x2]
%The direct solution of A'*A*c=A'*y is
c=inv(A'*A)*A'*y
%Or capitalizing on the special properties of the left division
c=A\y
%Plot of above results by the script
plot3(x1,x2,y,
'o'
,
'MarkerFaceColor'
,
'k'
,
'MarkerSize'
,11)
xlabel(
'x_1'
),ylabel(
'x_2'
),zlabel(
'y'
)
grid
on
hold
x1values=[0:.1:4];x2values=[0:.1:2]
[X1,X2]=meshgrid(x1values,x2values);
yvalues=c(1)+c(2)*X1+c(3)*X2
mesh(X1,X2,yvalues)
title(
'Exercise 14.8'
)
The output is
c =
14.4609
9.0252
-5.7043
or, equivalently,
12
14.409
9.0252
5.7042
y
xx
=+
−
(13.1)
The above script also generates the following plot