Dummy Variables  I
•
We next consider the case when
X
i
is a
dummy variable
, or
binary variable.
•
A dummy variable is a variable that takes on
only the values 0 or 1.
Often categorical
variables are “quantified” in this way, e.g.
–
X
i
= 1 if female,
X
i
= 0 if male,
–
X
i
= 1 if use advertising campaign A,
X
i
= 0 if use
advertising campaign B.
Dummy Variables  II
•
Nothing major changes when
X
i
is a dummy variable.
However, the interpretation of the estimated coefficients
β
0
and
β
1
is a bit different.
•
Example:
Sales
i
=
β
0
+
β
1
AdCampaign
i
+ u
i
– AdCampaign
i
=1 if use advertising campaign A in region
i
– AdCampaign
i
=0 if use advertising campaign B in region
i
– Sales
i
= unit sales in region
i
•
Suppose we regress Sales
i
on AdCampaign
i
and get estimated
coefficients
β
0
and
β
1
.
What do these coefficients tell us?
•
Recall predicted value formula……
Dummy Variables  III
•
The predicted value formula says that when advertising
campaign A is used, (i.e. when AdCampaign
i
=1) predicted
sales are:
•
When advertising campaign B is used (i.e. AdCampaign
i
=0),
predicted sales are:
•
So the estimated coefficient
β
1
measures the
difference
in
predicted sales between the two campaigns.
n
0
1
ˆ
ˆ
Sales
AdCampaign
i
i
β
β
=
+
n
0
1
ˆ
ˆ
Sales
i
β
β
=
+
n
0
ˆ
Sales
i
β
=
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Dummy Variables  IV
•
Therefore, if we want to test whether the two ad campaigns
generate the same amount of sales, we should test the null
hypothesis that the slope coefficient
β
1
=0.
•
Suppose regression results are:
•
The
t
STAT
for the hypothesis test that
β
1
=0 is 1.46.
Hence we
cannot reject the null hypothesis that the campaigns generate
equivalent amounts of sales.
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 Spring '07
 SandraBlack
 Econometrics, Regression Analysis, advertising campaign

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