Suppose that we have two independent samples, say Two models can be fit to these samples, [begin{gathered}y_{i}=beta_{0}+beta_{1}
Question:
Suppose that we have two independent samples, say
Two models can be fit to these samples,
\[\begin{gathered}y_{i}=\beta_{0}+\beta_{1} x_{i}+\varepsilon_{i}, \quad i=1,2, \ldots, n_{2} \\y_{i}=\gamma_{0}+\gamma_{1} x_{i}+\varepsilon_{i}, \quad i=n_{1}+1, n_{1}+2, \ldots, n_{1}+n_{2}\end{gathered}\]
a. Show how these two separate models can be written as a single model.
b. Using the result in part a, show how the general linear hypothesis can be used to test the equality of slopes $\beta_{1}$ and $\gamma_{1}$.
c. Using the result in part a, show how the general linear hypothesis can be used to test the equality of the two regression lines.
d. Using the result in part a, show how the general linear hypothesis can be used to test that both slopes are equal to a constant $c$.
Step by Step Answer:
Introduction To Linear Regression Analysis
ISBN: 9781119578727
6th Edition
Authors: Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining