Dummy variable prob

Learning Goal: I’m working on a statistics question and need the explanation and answer to help me learn.

Consider the two variable regression problem with a dummy variable in the design matrix: y
=
β0+β1x
+
γd
+
ϵ
,
where d
is a dummy-variable that is coded 1 if the observation satisfies a certain condition, and is 0 otherwise. Consider replacing the 0 and 1 values in d
with −0.5 and 0.5, respectively. What is the resulting regression equation? In particular, how does the dummy variable parameter in the recoded model relate to γ ? Describe how to interpret the parameters of the recoded model. Is there a reason to prefer one coding over the other?

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