[Stata Program]              
  
input p s be ba new
 48.5   1.10   3   1   0
 55.0   1.01   3   2   0
 68.0   1.45   3   2   0
137.0   2.40   3   3   0
309.4   3.30   4   3   1
 17.5    .40   1   1   0
 19.6   1.28   3   1   0
 24.5    .74   3   1   0
 34.8    .78   2   1   0
 32.0    .97   3   1   0
 28.0    .84   3   1   0
 49.9   1.08   2   2   0
 59.9    .99   2   1   0
 61.5   1.01   3   2   0
 60.0   1.34   3   2   0
 65.9   1.22   3   1   0
 67.9   1.28   3   2   0
 68.9   1.29   3   2   0
 69.9   1.52   3   2   0
 70.5   1.25   3   2   0
 72.9   1.28   3   2   0
 72.5   1.28   3   1   0
 72.0   1.36   3   2   0
 71.0   1.20   3   2   0
 76.0   1.46   3   2   0
 72.9   1.56   4   2   0
 73.0   1.22   3   2   0
 70.0   1.40   2   2   0
 76.0   1.15   2   2   0
 69.0   1.74   3   2   0
 75.5   1.62   3   2   0
 76.0   1.66   3   2   0
 81.8   1.33   3   2   0
 84.5   1.34   3   2   0
 83.5   1.40   3   2   0
 86.0   1.15   2   2   1
 86.9   1.58   3   2   1
 86.9   1.58   3   2   1
 86.9   1.58   3   2   1
 87.9   1.71   3   2   0
 88.1   2.10   3   2   0
 85.9   1.27   3   2   0
 89.5   1.34   3   2   0
 87.4   1.25   3   2   0
 87.9   1.68   3   2   0
 88.0   1.55   3   2   0
 90.0   1.55   3   2   0
 96.0   1.36   3   2   1
 99.9   1.51   3   2   1
 95.5   1.54   3   2   1
 98.5   1.51   3   2   0
100.1   1.85   3   2   0
 99.9   1.62   4   2   1
101.9   1.40   3   2   1
101.9   1.92   4   2   0
102.3   1.42   3   2   1
110.8   1.56   3   2   1
105.0   1.43   3   2   1
 97.9   2.00   3   2   0
106.3   1.45   3   2   1
106.5   1.65   3   2   0
116.0   1.72   4   2   1
108.0   1.79   4   2   1
107.5   1.85   3   2   0
109.9   2.06   4   2   1
110.0   1.76   4   2   0
120.0   1.62   3   2   1
115.0   1.80   4   2   1
113.4   1.98   3   2   0
114.9   1.57   3   2   0
115.0   2.19   3   2   0
115.0   2.07   4   2   0
117.9   1.99   4   2   0
110.0   1.55   3   2   0
115.0   1.67   3   2   0
124.0   2.40   4   2   0
129.9   1.79   4   2   1
124.0   1.89   3   2   0
128.0   1.88   3   2   1
132.4   2.00   4   2   1
139.3   2.05   4   2   1
139.3   2.00   4   2   1
139.7   2.03   3   2   1
142.0   2.12   3   3   0
141.3   2.08   4   2   1
147.5   2.19   4   2   0
142.5   2.40   4   2   0
148.0   2.40   5   2   0
149.0   3.05   4   2   0
150.0   2.04   3   3   0
172.9   2.25   4   2   1
190.0   2.57   4   3   1
280.0   3.85   4   3   0
end
 
label variable p  "selling price in thousands" 
label variable s "size in thousands"
label variable be "number bedrooms" 
label variable ba "number bathrooms" 
label variable new "new-1 or old-0"
 
summarize s ba p
corr s ba p
stem s 
stem ba 
stem p
graph p s ba, matrix half
  
regress p s ba, beta
pcorr p ba s
rvfplot
rvpplot s
rvpplot ba
vif
collin p s ba  /* user written program: findit collin */
predict sresid, rstandard
sort sresid
list p s ba sresid in 1/10
list p s ba sresid in -10/l
 
summarize sresid, detail
stem sresid
pnorm sresid
qnorm sresid
  
regress p s
regress p s ba
regress p ba
regress p s ba be
test be
sw regress p s ba be, pe(.05)
  
[Stata Output]
 
label variable p  "selling price in thousands"
label variable s "size in thousands"
label variable be "number bedrooms" 
label variable ba "number bathrooms" 
label variable new "new-1 or old-0"
 
summarize s ba p
 
Variable |     Obs        Mean   Std. Dev.       Min        Max
---------+-----------------------------------------------------
       s |      93    1.649677   .5252607         .4       3.85  
      ba |      93    1.956989   .4147807          1          3  
       p |      93    99.53333   44.18413       17.5      309.4  
 
corr s ba p
(obs=93)
 
         |        s       ba        p
---------+---------------------------
       s |   1.0000
      ba |   0.6625   1.0000
       p |   0.8988   0.7137   1.0000
 
stem s 
 
Stem-and-leaf plot for s (size in thousands)
 
s rounded to nearest multiple of .01
plot in units of .01

  0** | 40
  0** | 74,78
  0** | 84,97,99
  1** | 01,01,08,10,15,15
  1** | 20,22,22,25,25,27,28,28,28,28,29,33,34,34,34,36,36
  1** | 40,40,40,42,43,45,45,46,51,51,52,54,55,55,55,56,56,57,58,58,58
  1** | 62,62,62,65,66,67,68,71,72,74,76,79,79
  1** | 80,85,85,88,89,92,98,99
  2** | 00,00,00,03,04,05,06,07,08,10,12,19,19
  2** | 25
  2** | 40,40,40,40,57
  2** | 
  2** | 
  3** | 05
  3** | 30
  3** | 
  3** | 
  3** | 85
 
stem ba 
 
Stem-and-leaf plot for ba (number bathrooms)
 
  0* | 1111111111
  0* | 222222222222222222222222222222222222222222222222222222222222222 ... (77)
  0* | 333333
 
stem p
 
Stem-and-leaf plot for p (selling price in thousands)
 
p rounded to integers
 
  0** | 18
  0** | 20,25,28,32,35
  0** | 49,50,55
  0** | 60,60,62,66,68,68,69,69,70,70,71,71,72,73,73,73,73,76,76,76,76
  0** | 82,84,85,86,86,87,87,87,87,88,88,88,88,90,90,96,96,98,99
  1** | 00,00,00,02,02,02,05,06,07,08,08,10,10,10,11,13,15,15,15,15,15,16,18
  1** | 20,24,24,28,30,32,37,39,39
  1** | 40,41,42,43,48,48,49,50
  1** | 73
  1** | 90
  2** | 
  2** | 
  2** | 
  2** | 
  2** | 80
  3** | 09
 
graph p s ba,matrix half
 
   
 
regress p s ba, beta
  
  Source |       SS       df       MS                  Number of obs =      93
---------+------------------------------               F(  2,    90) =  224.11
   Model |  149573.054     2   74786.527               Prob > F      =  0.0000
Residual |  30032.8082    90  333.697869               R-squared     =  0.8328
---------+------------------------------               Adj R-squared =  0.8291
   Total |  179605.862    92  1952.23763               Root MSE      =  18.267
 
------------------------------------------------------------------------------
       p |      Coef.   Std. Err.       t     P>|t|                       Beta
---------+--------------------------------------------------------------------
       s |   63.86315   4.840401     13.194   0.000                   .7592047
      ba |   22.44845   6.129679      3.662   0.000                   .2107359
   _cons |  -49.75164   9.183284     -5.418   0.000                          .
------------------------------------------------------------------------------
  
pcorr p ba s
(obs=93)
 
Partial correlation of p with

    Variable |    Corr.     Sig.
-------------+------------------
          ba |   0.3601    0.000
           s |   0.8119    0.000
  
rvfplot, yline(0)
  

  
rvpplot s, yline(0)
  

  
rvpplot ba, yline(0)
  

  
vif
  
Variable |      VIF      1/VIF  
---------+----------------------
      ba |      1.78    0.561117
       s |      1.78    0.561117
---------+----------------------
Mean VIF |      1.78
   
collin p s ba
   
  Collinearity Diagnostics

                        SQRT                           Cond        R-
  Variable       VIF    VIF    Tolerance  Eigenval     Index    Squared
------------------------------------------------------------------------
         s      1.78    1.33    0.5611     1.6625     1.0000     0.4389
        ba      1.78    1.33    0.5611     0.3375     2.2194     0.4389
------------------------------------------------------------------------
  Mean VIF      1.78              Condition Number    2.2194
                 Determinant of correlation matrix    0.5611
 
predict sresid,rstandard
 
sort sresid
 
list p s ba sresid in 1/10
 
             p          s         ba     sresid 
  1.       149       3.05          2   -2.41815
  2.      88.1        2.1          2  -2.279348
  3.        69       1.74          2  -2.051483
  4.      19.6       1.28          1  -1.990447
  5.       137        2.4          3  -1.933392
  6.        76       1.66          2  -1.384791
  7.      97.9          2          2  -1.379334
  8.       124        2.4          2  -1.368973
  9.      75.5       1.62          2  -1.271868
 10.      69.9       1.52          2  -1.229592
  
list p s ba sresid in -10/l
  
             p          s         ba     sresid 
 84.       105       1.43          2   1.022334
 85.     106.3       1.45          2   1.023229
 86.      72.5       1.28          1   1.031645
 87.     114.9       1.57          2   1.073262
 88.      17.5         .4          1    1.10068
 89.     129.9       1.79          2   1.125482
 90.       120       1.62          2    1.17789
 91.      59.9        .99          1   1.361192
 92.     172.9       2.25          2   1.896437
 93.     309.4        3.3          3   4.734716 
  
summarize sresid, detail
  
                   Standardized residuals
-------------------------------------------------------------
      Percentiles      Smallest
 1%     -2.41815       -2.41815
 5%    -1.933392      -2.279348
10%    -1.229592      -2.051483       Obs                  93
25%    -.6306399      -1.990447       Sum of Wgt.          93

50%     .0940549                      Mean           .0024452
                        Largest       Std. Dev.      1.020772
75%     .7050466        1.17789
90%     1.022334       1.361192       Variance       1.041976
95%     1.125482       1.896437       Skewness       .6291919
99%     4.734716       4.734716       Kurtosis       6.807695
 
stem sresid
 
Stem-and-leaf plot for sresid (Studentized residuals)
 
sresid rounded to nearest multiple of .01
plot in units of .01
 
sresid rounded to nearest multiple of .01
plot in units of .01
 
 -2** | 42,28,05
 -1** | 99,93
 -1** | 38,38,37,27,23,20,15,11,09
 -0** | 93,91,87,80,80,79,73,68,68,63,55,50,50,50,50
 -0** | 48,45,34,33,32,26,25,24,23,22,15,08,06,04,02
  0** | 00,07,09,09,10,11,12,14,21,26,27,32,33,38,41,45,46,47,49
  0** | 53,53,61,69,69,70,71,73,73,74,77,82,87,87,88,91,91,96,97
  1** | 01,02,02,03,07,10,13,18,36
  1** | 90
  2** | 
  2** | 
  3** | 
  3** | 
  4** | 
  4** | 73
  
qnorm sresid
 

  
qnorm sresid
 

 
regress p s
 
  Source |       SS       df       MS                  Number of obs =      93
---------+------------------------------               F(  1,    91) =  382.63
   Model |  145097.459     1  145097.459               Prob > F      =  0.0000
Residual |  34508.4029    91  379.213218               R-squared     =  0.8079
---------+------------------------------               Adj R-squared =  0.8058
   Total |  179605.862    92  1952.23763               Root MSE      =  19.473

------------------------------------------------------------------------------
       p |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
       s |   75.60684   3.865208     19.561   0.000       67.92908     83.2846
   _cons |  -25.19356    6.68845     -3.767   0.000      -38.47935   -11.90778
------------------------------------------------------------------------------
 
regress p s ba
 
  Source |       SS       df       MS                  Number of obs =      93
---------+------------------------------               F(  2,    90) =  224.11
   Model |  149573.054     2   74786.527               Prob > F      =  0.0000
Residual |  30032.8082    90  333.697869               R-squared     =  0.8328
---------+------------------------------               Adj R-squared =  0.8291
   Total |  179605.862    92  1952.23763               Root MSE      =  18.267
 
------------------------------------------------------------------------------
       p |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
       s |   63.86315   4.840401     13.194   0.000       54.24685    73.47945
      ba |   22.44845   6.129679      3.662   0.000       10.27078    34.62613
   _cons |  -49.75164   9.183284     -5.418   0.000      -67.99584   -31.50744
------------------------------------------------------------------------------
 
regress p ba
 
  Source |       SS       df       MS                  Number of obs =      93
---------+------------------------------               F(  1,    91) =   94.47
   Model |  91484.3965     1  91484.3965               Prob > F      =  0.0000
Residual |  88121.4656    91  968.367754               R-squared     =  0.5094
---------+------------------------------               Adj R-squared =  0.5040
   Total |  179605.862    92  1952.23763               Root MSE      =  31.119
 
------------------------------------------------------------------------------
       p |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
      ba |   76.02581   7.821818      9.720   0.000       60.48873     91.5629
   _cons |  -49.24837   15.64364     -3.148   0.002      -80.32253   -18.17421
------------------------------------------------------------------------------
 
regress p s ba be
 
      Source |       SS       df       MS              Number of obs =      93
-------------+------------------------------           F(  3,    89) =  148.03
       Model |  149621.203     3  49873.7345           Prob > F      =  0.0000
    Residual |  29984.6586    89  336.906277           R-squared     =  0.8331
-------------+------------------------------           Adj R-squared =  0.8274
       Total |  179605.862    92  1952.23763           Root MSE      =  18.355
 
------------------------------------------------------------------------------
           p |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           s |   62.35406   6.292024     9.91   0.000     49.85194    74.85617
          ba |   22.91549   6.281753     3.65   0.000     10.43378     35.3972
          be |    1.63579   4.326989     0.38   0.706    -6.961846    10.23343
       _cons |  -53.38249   13.31866    -4.01   0.000    -79.84638   -26.91861
------------------------------------------------------------------------------
 
test be
 
 ( 1)  be = 0.0

       F(  1,    89) =    0.14
            Prob > F =    0.7063
  
sw regress p s ba be, pe(.05)
 
                      begin with empty model
p = 0.0000 <  0.0500  adding   s
p = 0.0004 <  0.0500  adding   ba
 
      Source |       SS       df       MS              Number of obs =      93
-------------+------------------------------           F(  2,    90) =  224.11
       Model |  149573.054     2   74786.527           Prob > F      =  0.0000
    Residual |  30032.8082    90  333.697869           R-squared     =  0.8328
-------------+------------------------------           Adj R-squared =  0.8291
       Total |  179605.862    92  1952.23763           Root MSE      =  18.267

------------------------------------------------------------------------------
           p |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           s |   63.86315   4.840401    13.19   0.000     54.24685    73.47945
          ba |   22.44845   6.129679     3.66   0.000     10.27078    34.62613
       _cons |  -49.75164   9.183284    -5.42   0.000    -67.99584   -31.50744
------------------------------------------------------------------------------