Filter
Top Products
Page 18-57
Multiple linear fitting
Consider a data set of the form
Suppose that we search for a data fitting of the form y = b
0
+ b
1
⋅x
1
+ b
2
⋅x
2
+
b
3
⋅x
3
+ … + b
n
⋅x
n
. You can obtain the least-square approximation to the
values of the coefficients b = [b
0
b
1
b
2
b
3
… b
n
], by putting together the
matrix X:
__
__
Then, the vector of coefficients is obtained from b = (X
T
⋅X)
-1
⋅X
T
⋅y, where y is
the vector y = [y
1
y
2
… y
m
]
T
.
For example
, use the following data to obtain the multiple linear fitting
y = b
0
+ b
1
⋅x
1
+ b
2
⋅x
2
+ b
3
⋅x
3,
x
1
x
2
x
3
…x
n
y
x
11
x
21
x
31
…x
n1
y
1
x
12
x
22
x
32
…x
n2
y
2
x
13
x
32
x
33
…x
n3
y
3
... ..
......
x
1,m-1
x
2,m-1
x
3,m-1
…x
n,m-1
y
m-1
x
1,m
x
2,m
x
3,m
…x
n,m
y
m
1x
11
x
21
x
31
…x
n1
1x
12
x
22
x
32
…x
n2
1x
13
x
32
x
33
…x
n3
.... .
......
1x
1,m
x
2,m
x
3,m
…x
n,m