–
Equivalently it is called a 100(1-
α
)%
confidence interval.
–
Usually
α
= 0.01 or
α
= 0.05, so that we obtain
a 99% confidence interval or a 95% confidence
interval.
3.1
Interval Estimation
3.1.2
Obtaining Interval
Estimates

Principles of Econometrics, 4t
h
Edition
Page 49
Chapter 1: An Introduction to Econometrics
The interpretation of confidence intervals requires a
great deal of care
–
The properties of the interval estimation procedure
are based on the notion of repeated sampling
–
Any one interval estimate, based on one sample of
data, may or may not contain the true parameter
β
k
,
and because
β
k
is unknown, we will never know
whether it does or does not
–
When ‘‘confidence intervals’’ are discussed,
remember that our confidence is in the procedure
used to construct the interval estimate; it is not in
any one interval estimate calculated from a sample
of data
3.1
Interval Estimation
3.1.2
Obtaining Interval
Estimates

Principles of Econometrics, 4t
h
Edition
Page 50
Chapter 1: An Introduction to Econometrics
For the food expenditure data
–
The critical value
t
c
= 2.024, which is
appropriate for
= .05 and 38 degrees of
freedom
–
To construct an interval estimate for
2
we use
the least squares estimate
b
2
= 10.21 and its
standard error
3.1.3
An Illustration
95
.
0
024
.
2
024
.
2
2
2
2
2
2
b
se
b
b
se
b
P
Eq. 3.6
09
.
2
38
.
4
r
a
ˆ
v
2
2
b
b
se
3.1
Interval Estimation