[Stata Program]
use http://www.gseis.ucla.edu/courses/data/curve
generate x2 = x^2
generate x3 = x^3
summarize
regress y x
predict p1
predict r1, residual
plot y x
plot r1 x
plot r1 p1
regress y x x2 x3
predict p2
predict r2, residual
plot r2 x
plot r2 p2
regress y x x2
predict p3
predict r3, residual
plot r3 x
plot r3 p3
[Stata Output]
generate x2 = x^2
generate x3 = x^3
summarize
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
y | 43 17.69767 5.841293 3 24
x | 43 14.69767 8.302423 2 28
x2 | 43 283.3488 252.4485 4 784
x3 | 43 6153.674 6964.894 8 21952
regress y x
Source | SS df MS Number of obs = 43
---------+------------------------------ F( 1, 41) = 28.11
Model | 582.915921 1 582.915921 Prob > F = 0.0000
Residual | 850.153846 41 20.7354597 R-squared = 0.4068
---------+------------------------------ Adj R-squared = 0.3923
Total | 1433.06977 42 34.1207087 Root MSE = 4.5536
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | .4487179 .0846306 5.302 0.000 .277803 .6196329
_cons | 11.10256 1.424584 7.794 0.000 8.225559 13.97957
------------------------------------------------------------------------------
predict p1
(option xb assumed; fitted values)
predict r1, residual
plot y x
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2 x 28
plot r1 x
6.30769 +
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2 x 28
plot r1 p1
6.30769 +
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+----------------------------------------------------------------+
12 Fitted values 23.6667
regress y x x2 x3
Source | SS df MS Number of obs = 43
---------+------------------------------ F( 3, 39) = 245.95
Model | 1361.12452 3 453.708175 Prob > F = 0.0000
Residual | 71.9452429 39 1.84474982 R-squared = 0.9498
---------+------------------------------ Adj R-squared = 0.9459
Total | 1433.06977 42 34.1207087 Root MSE = 1.3582
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 2.829993 .2960827 9.558 0.000 2.23111 3.428877
x2 | -.0928338 .0229421 -4.046 0.000 -.1392386 -.046429
x3 | .0004671 .0005088 0.918 0.364 -.000562 .0014962
_cons | -.4667211 1.023599 -0.456 0.651 -2.537145 1.603703
------------------------------------------------------------------------------
predict p2
(option xb assumed; fitted values)
predict r2, residual
plot r2 x
4.52898 +
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+----------------------------------------------------------------+
2 x 28
plot r2 p2
4.52898 +
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+----------------------------------------------------------------+
4.82567 Fitted values 23.1192
regress y x x2
Source | SS df MS Number of obs = 43
---------+------------------------------ F( 2, 40) = 369.95
Model | 1359.56964 2 679.784819 Prob > F = 0.0000
Residual | 73.5001293 40 1.83750323 R-squared = 0.9487
---------+------------------------------ Adj R-squared = 0.9461
Total | 1433.06977 42 34.1207087 Root MSE = 1.3555
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x | 2.576439 .1065162 24.188 0.000 2.361162 2.791717
x2 | -.0720191 .0035031 -20.559 0.000 -.079099 -.0649391
_cons | .2365281 .6776342 0.349 0.729 -1.133022 1.606078
------------------------------------------------------------------------------
predict p3
(option xb assumed; fitted values)
predict r3, residual
plot r3 x
4.76118 +
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+----------------------------------------------------------------+
2 x 28
plot r3 p3
4.76118 +
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+----------------------------------------------------------------+
5.10133 Fitted values 23.2783