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

recursive residual
test.
We will take this topic up in Chapter 13, the chapter on model specification analysis.
8.8
Prediction with Multiple Regression
In Section 5.10 we showed how the estimated two-variable regression model can be used
for (1) 
mean prediction,
that is, predicting the point on the population regression function
(PRF), as well as for (2) 
individual prediction,
that is, predicting an individual value of 
Y
given the value of the regressor 
X
=
X
0
, where 
X
0
is the specified numerical value of 
X
.
The estimated multiple regression too can be used for similar purposes, and the proce-
dure for doing that is a straightforward extension of the two-variable case, except the for-
mulas for estimating the variances and standard errors of the forecast value (comparable to
Eqs. [5.10.2] and [5.10.6] of the two-variable model) are rather involved and are better han-
dled by the matrix methods discussed in 
Appendix C.
Of course, most standard regression
packages can do this routinely, so there is no need to look up the matrix formulation. It is
given in 
Appendix C
for the benefit of the mathematically inclined students. This appen-
dix also gives a fully worked out example.
*8.9
The Troika of Hypothesis Tests: The Likelihood Ratio (LR),
Wald (W), and Lagrange Multiplier (LM) Tests
18
In this and the previous chapters we have, by and large, used the 
t
, 
F
, and chi-square tests
to test a variety of hypotheses in the context of linear (in-parameter) regression models. But
once we go beyond the somewhat comfortable world of linear regression models, we need
a method(s) to test hypotheses that can handle regression models, linear or not.
The well-known trinity of