2-dimensional represent of a multiple regression function Y_i=beta_1+beta_2X_(2i)+beta_3X_(3i)+u_(i)

Hunter Shah 2022-10-13 Answered
2-dimensional representation of a multiple regression function
Supposing I have a multiple regression population function of the form:
Y i = β 1 + β 2 X 2 i + β 3 X 3 i + u i
with X 3 i a dummy variable (only takes values 0 and 1).
I am given a sample of points. Although the latter takes place in 3 dimensional space, the question states "its results can be represented in Y vs X 2 space". I don't understand how graphing Y vs X 2 will give us a 2 dimensional representation of our population regression function. Isn't X 3 i being completely omitted?
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Answers (1)

scranna0o
Answered 2022-10-14 Author has 16 answers
Assuming that I properly understand your problem, you have
Y = β 1 + β 2 X 2 + β 3 X 3
where X 3 is a binary variable.
This means
X 3 = 0 Y = β 1 + β 2 X 2
X 3 = 1 Y = ( β 1 + β 3 ) + β 2 X 2
and then, the two dimensional representation of the function (two parallel lines).
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