HP 48gII - Manual (Page 628)

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
.