Transcript Chapter 1 exercise 1.5 (EC220)

Christopher Dougherty
EC220 - Introduction to econometrics
(chapter 1)
Slideshow: exercise 1.5
Original citation:
Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 1). [Teaching Resource]
© 2012 The Author
This version available at: http://learningresources.lse.ac.uk/127/
Available in LSE Learning Resources Online: May 2012
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EXERCISE 1.5
1.5
The output below shows the result of regressing the weight
of the respondent in 1985, measured in pounds, on his or
her height, measured in inches. Provide an interpretation
of the coefficients.
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
1
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
The regression output above gives the result of regressing weight, measured in pounds, in
1985 on height, measured in inches, using EAEF data set 21.
2
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
The coefficient of height is 5.19. This implies that a one-unit increase in height increases
weight by 5.19 units.
3
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
The units of height are inches and those of weight are pounds. So the coefficient implies
that weight increases by 5.19 pounds for each additional inch of height.
4
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
The intercept is –194.7. Literally it implies that a person with zero height weighs minus 195
pounds.
5
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
How can we explain this nonsense result? (Try to work it out yourself, before proceeding.)
6
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
One perfectly good explanation is that a height of zero makes no sense at all and the
regression relationship has no meaning for such a value.
7
EXERCISE 1.5
. reg WEIGHT85 HEIGHT
Source |
SS
df
MS
-------------+-----------------------------Model | 261111.383
1 261111.383
Residual | 394632.365
538 733.517407
-------------+-----------------------------Total | 655743.748
539 1216.59322
Number of obs
F( 1,
538)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
355.97
0.0000
0.3982
0.3971
27.084
-----------------------------------------------------------------------------WEIGHT85 |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------HEIGHT |
5.192973
.275238
18.87
0.000
4.6523
5.733646
_cons | -194.6815
18.6629
-10.43
0.000
-231.3426
-158.0204
------------------------------------------------------------------------------
Another explanation is that the true relationship is nonlinear, and the reason that we get a
negative intercept is that the mathematical from of the relationship has been misspecified.
8
Copyright Christopher Dougherty 1999-2006. This slideshow may be freely copied for
personal use.
18.06.06