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1. Which of these equations is it possible to estimate using regression techniques?
a.)
Y
i
=
β
0
+
β
1
X
1i
+
β
2
X
2i
+
ε
This equation is already in a form interpreted to be capable of estimating through standard
regression techniques. See equation (1.12) in the Studenmund book – this is the definition of a
multivariate regression model with two explanatory variables.
b.)
Y
i
= e
β
0+
β
1X1i+
ε
i
This equation is capable of being transformed into a something a little more familiar:
First, take the log of both sides:
ln Y
i
= ln e
β
0+
β
1X1i+
ε
I
Using the properties of logs given in Chapter 7 of Studenmund:
ln Y
i
= (
β
0
+
β
1
X
1i
+
ε
i
)*ln e
Since the ln e = 1, we then have:
ln Y
i
=
β
0
+
β
1
X
1i
+
ε
I,
which is just the standard semilog equation from Chapter 7.
c.)
Y
i
=
β
0
X
1i
β1
X
2i
β2
e
ε
I
Again, this equation can be transformed into something more useful by taking the log of both
sides:
ln Y
i
= ln (
β
0
X
1i
β1
X
2i
β2
e
ε
I
)
Using the properties of logs given on the bottom of page 205, we can rewrite the rightside as:
ln Y
i
= ln
β
0
+ ln X
1i
β1
+
ln X
2i
β2
+ ln e
ε
I
Using the exponent rule of logs also listed on page 205, we can rewrite it as:
ln Y
i
= ln
β
0
+
β
1
ln X
1i
+
β
2
ln X
2i
+
ε
i
ln e
And since ln e = 1, we have:
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View Full Document ln Y
i
= ln
β
0
+
β
1
ln X
1i
+
β
2
ln X
2i
+
ε
I
,
which is just the doublelog form listed in Chapter 7 (ln
β
0
is still just a constant).
d.)
Y
i
=
β
0
+ X
1i
β1
+ X
2i
β2
+ e
ε
I
This model is
not
able to be estimated by any regression techniques, as the coefficients in the
exponent of addition terms prohibit it from being estimated. Even if one tries to take the log of
both sides of the model, it would get them no where in advancing this model as something
capable of being estimated.
e.) Y
i
=
β
0
+
β
1
(1/X
1i
) +
β
2
X
2i
+
ε
i
If you look at equation (7.13) from Studenmund, this model is the standard Inverse Form
equation given. It is quite capable of being estimated, with the values of the coefficients
described in pages 211212.
2) We are interested in the effect of the presence of various benefit programs on employee views
of their boss….
A) Interpret the impact of each factor on job satisfaction and test the null.
Critical tvalues:
Two tailed
one tailed
10%  1.645
1.282
5% 
1.960
1.645
1% 
2.576
2.32
Note that all the hypothesis tests except the test for the coefficient on female have a positive
alternative hypothesis and a null of less than or equal to zero.
The test for female is two tailed.
Education
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This note was uploaded on 07/25/2008 for the course LIR 832 taught by Professor Belman during the Spring '07 term at Michigan State University.
 Spring '07
 BELMAN

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