HP 49g+, User Manual, Page: 620 / 862

Page 18-53
•
Hypothesis testing on the intercept ,
Α:
Null hypothesis, H
0
:
Α
=
Α
0
, tested against the alternative hypothesis, H
1
:
Α ≠ Α
0
. The test statistic is t
0
= (a-
Α
0
)/[(1/n)+

x
2
/S
xx
]
1/2
, where t follows
the Student’s t distribution with
ν
= n – 2, degrees of freedom, and n
represents the number of points in the sample. The test is carried out as
that of a mean value hypothesis testing, i.e., given the level of
significance,
α
, determine the critical value of t, t
α
/2
, then, reject H
0
if t
0
>
t
α
/2
or if t
0
< - t
α
/2
.
•
Confidence interval for the mean value of Y at x = x
0
, i.e.,
α
+
β
x
0
:
a+b
⋅
x
−
(t
n-2,
α
/2
)
⋅
s
e
⋅
[(1/n)+(x
0
-

x)
2
/S
xx
]
1/2
<
α
+
β
x
0
<
a+b
⋅
x+(t
n-2,
α
/2
)
⋅
s
e
⋅
[(1/n)+(x
0
-

x)
2
/S
xx
]
1/2
.
•
Limits of prediction: confidence interval for the predicted value Y
0
=Y(x
0
):
a+b
⋅
x
−
(t
n-2,
α
/2
)
⋅
s
e
⋅
[1+(1/n)+(x
0
-

x)
2
/S
xx
]
1/2
< Y
0
<
a+b
⋅
x+(t
n-2,
α
/2
)
⋅
s
e
⋅
[1+(1/n)+(x
0
-

x)
2
/S
xx
]
1/2
.
Procedure for inference statistics for linear regression using the
calculator
1) Enter (x,y) as columns of data in the statistical matrix
Σ
DAT.
2) Produce a scatterplot for the appropriate columns of
Σ
DAT, and use
appropriate H- and V-VIEWS to check linear trend.
3) Use
‚Ù˜˜ @@@OK@@@
, to fit straight line, and get a, b, s
xy
(Covariance), and r
xy
(Correlation).
4) Use
‚Ù˜ @@@OK@@@
, to obtain

x,

y, s
x
, s
y
. Column 1 will show the
statistics for x while column 2 will show the statistics for y.
5) Calculate
2
) 1 (
x xx
s n S ⋅ − =
,
) 1 (
2
1
2 2 2
xy y e
r s
n
n
s − ⋅ ⋅
−
−
=
6) For either confidence intervals or two-tailed tests, obtain t
α
/2
, with (1-
α
)100% confidence, from t-distribution with
ν
= n -2.
7) For one- or two-tailed tests, find the value of t using the appropriate
equation for either
Α
or
Β
. Reject the null hypothesis if P-value <
α
.
8) For confidence intervals use the appropriate formulas as shown above.