HP 50g User Manual page 620
Graphing calculator
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Confidence limits for regression coefficients:
For the slope ( ): b
For the intercept ( ):
a
(t
) s
n-2, /2
e
1/2
S
]
, where t follows the Student's t distribution with
xx
of freedom, and n represents the number of points in the sample.
Hypothesis testing on the slope,
Null hypothesis, H
. The test statistic is t
0
Student's t distribution with
the number of points in the sample.
mean value hypothesis testing, i.e., given the level of significance,
determine the critical value of t, t
t
.
/2
If you test for the value
do not reject the null hypothesis, H
regression is in doubt.
the assertion that
regression model.
Hypothesis testing on the intercept ,
Null hypothesis, H
. The test statistic is t
0
the Student's t distribution with
represents the number of points in the sample.
that of a mean value hypothesis testing, i.e., given the level of significance,
, determine the critical value of t, t
- t
.
/2
Confidence interval for the mean value of Y at x = x
a+b x (t
) s
n-2, /2
Limits of prediction: confidence interval for the predicted value Y
a+b x (t
n-2, /2
(t
) s
n-2, /2
2
[(1/n)+ x
/S
]
xx
:
=
, tested against the alternative hypothesis, H
0
0
0
= n – 2, degrees of freedom, and n represents
= 0, and it turns out that the test suggests that you
0
In other words, the sample data does not support
0. Therefore, this is a test of the significance of the
:
=
, tested against the alternative hypothesis, H
0
0
= (a-
0
[(1/n)+(x
- x)
e
0
a+b x+(t
) s
[1+(1/n)+(x
e
/ S
<
e
xx
1/2
<
< a
= (b -
)/(s
/ S
0
e
The test is carried out as that of a
, then, reject H
/2
:
= 0, then, the validity of a linear
0
)/[(1/n)+ x
0
= n – 2, degrees of freedom, and n
, then, reject H
/2
2
1/2
/S
]
< + x
xx
) s
n-2,
/2
2
1/2
- x)
/S
]
0
xx
b
(t
) s
n-2, /2
(t
) s
[(1/n)+ x
n-2, /2
e
= n – 2, degrees
), where t follows the
xx
if t
> t
0
0
/2
2
1/2
/S
]
, where t follows
xx
The test is carried out as
if t
> t
0
0
/2
, i.e., + x
0
<
0
2
[(1/n)+(x
- x)
e
0
< Y
<
0
/ S
,
e
xx
2
/
:
1
,
or if t
< -
0
:
1
or if t
<
0
:
0
1/2
/S
]
.
xx
=Y(x
):
0
0
Page 18-53
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