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