Page 18-57
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
y
1.20 3.10 2.00 5.70
2.50 3.10 2.50 8.20
3.50 4.50 2.50 5.00
4.00 4.50 3.00 8.20
6.00 5.00 3.50 9.50
With the calculator, in RPN mode, you can proceed as follows:
First, within your HOME directory, create a sub-directory to be called MPFIT
(Multiple linear and Polynomial data FITting) , and enter the MPFIT sub-
directory. Within the sub-directory, type this program:
«
X y
«
X TRAN X * INV X TRAN * y *
»
»
and store it in a variable called MTREG (MulTiple REGression).
Next, enter the matrices
X
and
b
into the stack:
[[1,1.2,3.1,2][1,2.5,3.1,2.5 ][1,3.5,4.5,2.5][1,4,4.5,3][1,6,5,3.5]]
``
(keep an extra copy)
[5.7,8.2,5.0,8.2,9.5]
`
Press
J
@MTREG
. The result is: [-2.1649…,–0.7144…,-1.7850…,7.0941…],
i.e.,
y = -2.1649–0.7144
⋅
x
1
-1.7850
×
10
-2
⋅
x
2
+ 7.0941
⋅
x
3
.
