71
Hypothesis Tests and Confidence Intervals
in Multiple Regression
(SW Chapter 7)
Outline
1.
Hypothesis tests and confidence intervals for a single
coefficient
2.
Joint hypothesis tests on multiple coefficients
3.
Other types of hypotheses involving multiple coefficients
4.
How to decide what variables to include in a regression
model?
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Hypothesis Tests and Confidence Intervals for a Single
Coefficient in Multiple Regression
(SW Section 7.1)
•
1
1
1
ˆ
ˆ
(
)
ˆ
var(
)
E
β
β
β
−
is approximately distributed
N
(0,1) (CLT).
•
Thus hypotheses on
β
1
can be tested using the usual
t

statistic, and confidence intervals are constructed as {
1
ˆ
β
±
1.96
×
SE
(
1
ˆ
β
)}.
•
So too for
β
2
,…,
β
k
.
•
1
ˆ
β
and
2
ˆ
β
are generally not independently distributed – so
neither are their
t
statistics (more on this later).
72