[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

      24 +  
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       3 + *
          +----------------------------------------------------------------+
                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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-2.39781 +     *                        *
          +----------------------------------------------------------------+
                2                        x                              28


plot r2 p2

 4.52898 +  
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-2.39781 +                *                                            *
          +----------------------------------------------------------------+
          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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-2.38998 + *   *                        *    *
          +----------------------------------------------------------------+
                2                        x                              28


plot r3 p3

 4.76118 +  
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-2.38998 + *              *                                            *  *
          +----------------------------------------------------------------+
          5.10133                  Fitted values                   23.2783