--------------------------------------------------------------------------------
      name:  <unnamed>
       log:  H:\Documents and Settings\Lee\My Documents\Document\Stata\E5.3.log
  log type:  text
 opened on:  26 Oct 2009, 11:05:43

Part a.
. 
. reg ed dist, vce(hc3)

Linear regression                                      Number of obs =    3796
                                                       F(  1,  3794) =   29.58
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.0074
                                                       Root MSE      =  1.8074

------------------------------------------------------------------------------
             |             Robust HC3
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dist |  -.0733727   .0134906    -5.44   0.000    -.0998222   -.0469232
       _cons |   13.95586   .0378502   368.71   0.000     13.88165    14.03006
------------------------------------------------------------------------------

Ho:  b2=0
Ha:  b2 not= 0

t= -5.44<-1.96 therefore reject Ho in favor of Ha: at the 5% level.
The pvalue is < .000 <.05 therefore we are in the rejection region of this test.

Part b.
. 
. /* Check the confidence interval computed by Stata */
. scalar lu = _b[dist]+1.96*_se[dist]

. scalar ll = _b[dist]-1.96*_se[dist]

. scalar list lu ll
        lu = -.04693118
        ll = -.09981423

The 95% CI is (-.00998,-.0469) which matches the ones automatically produced by Stata.
No need to recompute these for parts (c) and (d).
. 
. /* CI results match, so no need to do this manually again */
. 
Part c.
. reg ed dist if female ==1, vce(hc3)

Linear regression                                      Number of obs =    2070
                                                       F(  1,  2068) =   11.92
                                                       Prob > F      =  0.0006
                                                       R-squared     =  0.0056
                                                       Root MSE      =  1.8024

------------------------------------------------------------------------------
             |             Robust HC3
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dist |  -.0641676   .0185887    -3.45   0.001    -.1006221    -.027713
       _cons |   13.93587   .0514246   271.00   0.000     13.83502    14.03672
------------------------------------------------------------------------------

. scalar fd = _b[dist]

. scalar fd_se= _se[dist]

The pvalue associated with the two sided test of b2=0 is .001<.05, therefore we reject
the hypothesis that distance has no effect at the 5% level.  The 95% CI excludes zero,
which confirms this.

Part d. 

. reg ed dist if female ==0, vce(hc3)

Linear regression                                      Number of obs =    1726
                                                       F(  1,  1724) =   18.01
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.0099
                                                       Root MSE      =  1.8142

------------------------------------------------------------------------------
             |             Robust HC3
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dist |   -.083837   .0197567    -4.24   0.000    -.1225866   -.0450875
       _cons |   13.97899   .0560429   249.43   0.000     13.86907    14.08891
------------------------------------------------------------------------------

. scalar md = _b[dist]

. scalar md_se= _se[dist]

The pvalue associated with the two sided test of b2=0 is .001<.05, therefore we reject
the hypothesis that distance has no effect at the 5% level.  The 95% CI excludes zero,
which confirms this.
. 
Part e.

. scalar diff = fd - md

. scalar sd_diff = sqrt(fd_se^2+md_se^2)

. scalar tstat = diff/sd_diff

. scalar pval = 2*(1-normal(tstat))

. scalar list diff sd_diff tstat pval
      diff =  .01966948
   sd_diff =  .02712686
     tstat =  .72509248
      pval =   .4683953

The p-value for the test of the null hypothesis that b2_m=b2_f against the alternative that they are not equal is .468>.05.
We cannot reject the null at the 5% level.

. 
. /* Using multiple regression to do the test */
. gen f_dist=female*dist

. reg ed dist female f_dist, vce(hc3)

Linear regression                                      Number of obs =    3796
                                                       F(  3,  3792) =    9.98
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.0076
                                                       Root MSE      =  1.8078

------------------------------------------------------------------------------
             |             Robust HC3
          ed |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dist |   -.083837   .0197567    -4.24   0.000    -.1225717   -.0451024
      female |  -.0431251   .0760612    -0.57   0.571    -.1922499    .1059997
      f_dist |   .0196695   .0271269     0.73   0.468    -.0335152    .0728541
       _cons |   13.97899   .0560429   249.43   0.000     13.86911    14.08887
------------------------------------------------------------------------------

Notice that the distance coefficient is the same and that the f_dist coefficient
is now directly measuring the difference in slopes. The se is the same as is the 
t-ratio.  
. 
. log close
      name:  <unnamed>
       log:  H:\Documents and Settings\Lee\My Documents\Document\Stata\E5.3.log
  log type:  text
 closed on:  26 Oct 2009, 11:05:43
--------------------------------------------------------------------------------