The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

FIGURE 8.1
The 95% confidence
interval for 
t
(60 df).
0
t
+2.0
–2.0
f
(
t
)
Density
Critical
region,
2.5%
t
= –2.82
Critical region,
2.5%
95%
Region of acceptance
guj75772_ch08.qxd 12/08/2008 10:03 AM Page 236

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Chapter 8
Multiple Regression Analysis: The Problem of Inference
237
u
i
, we can observe their proxy, the 
ˆ
u
i
, that is, the residuals. For our mortality regression,
the histogram of the residuals is as shown in Figure 8.2.
From the histogram it seems that the residuals are normally distributed. We can also
compute the 
Jarque–Bera
(JB) test of normality, as shown in Eq. (5.12.1). In our case the
JB value is 0.5594 with a 
p
value 0.76.
3
Therefore, it seems that the error term in our
example follows the normal distribution. Of course, keep in mind that the JB test is a large-
sample test and our sample of 64 observations may not be necessarily large.
8.4
Testing the Overall Significance of the Sample Regression
Throughout the previous section we were concerned with testing the significance of the
estimated partial regression coefficients individually, that is, under the separate hypothesis
that each true population partial regression coefficient was zero. But now consider the
following hypothesis:
H
0
:
β
2
=
β
3
=
0
(8.4.1)
This null hypothesis is a joint hypothesis that 
β
2
and 
β
3
are jointly or simultaneously equal
to zero. A test of such a hypothesis is called a test of the