# Multiple Linear Fitting, - HP 49g+ User Manual

Graphing calculator.

Example 3 – Test of significance for the linear regression.
hypothesis for the slope H
0, at the level of significance α = 0.05, for the linear fitting of Example 1.
The test statistic is t
= (b -Β
0
The critical value of t, for ν = n – 2 = 3, and α/2 = 0.025, was
18.95.
obtained in Example 2, as t
t
, we must reject the null hypothesis H
α
/2
= 0.05, for the linear fitting of Example 1.
Multiple linear fitting
Consider a data set of the form
x
1
x
11
x
12
x
13
.
.
x
x
1,m-1
x
1,m
Suppose that we search for a data fitting of the form y = b
⋅x
⋅x
b
+ ... + b
. You can obtain the least-square approximation to the
3
3
n
n
values of the coefficients b = [b
matrix X:
_
1
x
11
1
x
12
1
x
13
.
.
.
.
1
x
1,m
_
: Β = 0, against the alternative hypothesis, H
0
)/(s
/√S
) = (3.24-0)/(√0.18266666667/2.5) =
0
e
xx
= t
= 3.18244630528. Because, t
α
n-2,
/2
3,0.025
: Β ≠ 0, at the level of significance α
1
x
x
...
2
3
x
x
...
21
31
x
x
...
22
32
x
x
...
32
33
.
.
.
.
.
x
...
2,m-1
3,m-1
x
x
...
2,m
3,m
b
b
b
... b
0
1
2
3
x
x
21
31
x
x
22
32
x
x
32
33
.
.
.
.
x
x
2,m
3,m
Test the null
x
y
n
x
y
n1
1
x
y
n2
2
x
y
n3
3
.
.
.
.
x
y
n,m-1
m-1
x
y
n,m
m
⋅x
+ b
+ b
0
1
1
2
], by putting together the
n
_
...
x
n1
...
x
n2
...
x
n3
.
.
.
...
x
n,m
_
Page 18-56
: Β ≠
1
>
0
⋅x
+
2