The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

Empirical Results.
When the third-degree polynomial regression was fitted to the data
of Table 7.4, we obtained the following results:
ˆ
Y
i
=
141.7667
+
63.4776
X
i
−
12
.
9615
X
2
i
+
0
.
9396
X
3
i
(6.3753) (4.7786) (0.9857)
(0.0591)
R
2
=
0.9983
(7.10.6)
(Note:
The figures in parentheses are the estimated standard errors.) Although we will examine
the statistical significance of these results in the next chapter, the reader can verify that they
are in conformity with the theoretical expectations listed in Eq. (7.10.5). We leave it as an
exercise for the reader to interpret the regression (7.10.6).
18
See Alpha C. Chiang, 
Fundamental Methods of Mathematical Economics,
3d ed., McGraw-Hill, New
York, 1984, pp. 250–252.
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Chapter 7
Multiple Regression Analysis: The Problem of Estimation
213
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7.11
Partial Correlation Coefficients
Explanation of Simple and Partial Correlation Coefficients
In Chapter 3 we introduced the coefficient of correlation 
r
as a measure of the degree of
linear association between two variables. For the three-variable regression model we can
compute three correlation coefficients: 
r
1 2
(correlation between 
Y
and 
X
2
), 
r
1 3
(correlation
coefficient between 
Y
and 
X
3
), and 
r
2 3
(correlation coefficient between 
X
2
and 
X
3
); notice
that we are letting the subscript 1 represent 
Y
for notational convenience. These correlation
coefficients are called