Imagine that we intend x2i to be a dummy variable in the population relationship of equation (11.1).
Question:
Imagine that we intend x2i to be a dummy variable in the population
�relationship of equation (11.1).
(a) Unfortunately, we make a mistake. We assign the value x2i = 2 to observations that have the characteristic of interest and the value x2i = 1 to observations that do not. Modify the analysis of equations (13.1) through
(13.9) to derive the appropriate interpretation of β2 in this case.
(b) Based on the answer to part
a, what would be the consequence if we assigned the value x2i = 3 to observations that have the characteristic of interest and the value x2i = 2 to observations that do not? What about the values 5 and 4? What about any two values that differ only by one?
(c) Based on the answers to parts a and
b, what would be the consequence if we assigned the value x2i = 3 to observations that have the characteristic of interest and the value x2i = 1 to observations that do not? What about any two values that differ by two? What about any two values that differ by any amount?
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