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

(10.6.2)
This 
F
value is obviously highly significant.
It is interesting to look at this result geometrically. (See Figure 10.3.) Based on the re-
gression (10.6.1), we have established the individual 95 percent confidence intervals for
β
2
and 
β
3
following the usual procedure discussed in Chapter 8. As these intervals show,
individually each of them includes the value of zero. Therefore, 
individually
we can accept
the hypothesis that the two partial slopes are zero. But, when we establish the joint confi-
dence interval to test the hypothesis that 
β
2
=
β
3
=
0, that hypothesis cannot be accepted
since the joint confidence interval, actually an ellipse, does not include the origin.
16
As already pointed out, when collinearity is high, tests on individual regressors are not re-
liable; in such cases it is the overall 
F
test that will show if 
Y
is related to the various
regressors.
Our example shows dramatically what multicollinearity does. The fact that the 
F
test is
significant but the 
t
values of 
X
2
and 
X
3
are individually insignificant means that the two
variables are so highly correlated that it is impossible to isolate the individual impact of
Y,
$
X
2
, $
X
3
, $
70
80
810
65
100
1009
90
120
1273
95
140
1425
110
160
1633
115
180
1876
120
200
2052
140
220
2201
155
240
2435
150
260
2686