. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * VHm 812 - Winter 2015
. * 2al - Linear regression: predictors, confounding and interaction
.
. * change working directory and open a log file
. cd h:\vhm\vhm802\data_stata
h:\vhm\vhm802\data_stata

.
. * open the DAISY dataset
. use daisy2red.dta, clear

.
. *meaningless use of a nominal variable
. egen farm=group(herd)

. label var farm farm

. table farm, c(mean milk120)

----------+--------------
     farm | mean(milk120)
----------+--------------
        1 |        3357.8
        2 |        3279.3
        3 |        2778.6
        4 |        3032.5
        5 |        2838.2
        6 |        3730.6
        7 |        3435.8
----------+--------------

. twoway (scatter milk120 farm) (lfit milk120 farm) , name(pos, replace)

. regress milk120 farm

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =   33.10
       Model |  15802185.7     1  15802185.7           Prob > F      =  0.0000
    Residual |   732338007  1534  477404.177           R-squared     =  0.0211
-------------+------------------------------           Adj R-squared =  0.0205
       Total |   748140192  1535  487387.748           Root MSE      =  690.94

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
        farm |    50.90872    8.848643      5.75    0.000        33.552     68.26543
       _cons |    3026.143    37.27521     81.18    0.000      2953.028     3099.259
-------------+----------------------------------------------------------------

.
. gen farm1=abs(farm-7)+1

. preserve

. collapse milk120 farm, by(farm1)

. sort farm

. list farm milk120 farm1

     +------------------------+
     | farm   milk120   farm1 |
     +------------------------+
  1. |    1    3357.8       7 |
  2. |    2    3279.3       6 |
  3. |    3    2778.6       5 |
  4. |    4    3032.5       4 |
  5. |    5    2838.2       3 |
     +------------------------+
  6. |    6    3730.6       2 |
  7. |    7    3435.8       1 |
     +------------------------+

. restore

. twoway (scatter milk120 farm1) (lfit milk120 farm1) , name(pos, replace)

. regress milk120 farm1

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =   33.10
       Model |  15802185.7     1  15802185.7           Prob > F      =  0.0000
    Residual |   732338007  1534  477404.177           R-squared     =  0.0211
-------------+------------------------------           Adj R-squared =  0.0205
       Total |   748140192  1535  487387.748           Root MSE      =  690.94

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       farm1 |   -50.90872    8.848643     -5.75    0.000     -68.26543      -33.552
       _cons |    3433.413    41.84204     82.06    0.000      3351.339     3515.487
-------------+----------------------------------------------------------------

.
. * create a 4 level categorical variable for age
. egen parity_c4=cut(parity), at(1 2 3 4  99) icodes

. sort parity

. br parity parity_c4

. tab parity parity_c4

 Lactation |                  parity_c4
    number |         0          1          2          3 |     Total
-----------+--------------------------------------------+----------
         1 |       417          0          0          0 |       417
         2 |         0        374          0          0 |       374
         3 |         0          0        319          0 |       319
         4 |         0          0          0        222 |       222
         5 |         0          0          0        169 |       169
         6 |         0          0          0         69 |        69
         7 |         0          0          0          4 |         4
-----------+--------------------------------------------+----------
     Total |       417        374        319        464 |     1,574


.
. *INDICATOR VARIABLES
. * create indicator variables "manually"  (you never actually do this)
. gen parity_c4_0=(parity_c4==0) if !missing(parity)

. gen parity_c4_1=(parity_c4==1) if !missing(parity)

. gen parity_c4_2=(parity_c4==2) if !missing(parity)

. gen parity_c4_3=(parity_c4==3) if !missing(parity)

.
. br parity parity_c4 parity_c4_0 parity_c4_1 parity_c4_2 parity_c4_3

.
. * determine the average milk120 in each age group
. format milk120 %4.2f

. tab parity_c4, sum(milk120)

            | Summary of Milk volume (l) in first
            |        120 days of lactation
  parity_c4 |        Mean   Std. Dev.       Freq.
------------+------------------------------------
          0 |     2639.65      486.40         403
          1 |     3347.86      626.47         369
          2 |     3429.49      655.11         308
          3 |     3471.42      650.91         456
------------+------------------------------------
      Total |     3215.10      698.13        1536

.
. * regress -milk120- on the age groups
. reg milk120 parity_c4_1 parity_c4_2 parity_c4_3

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  3,  1532) =  166.65
       Model |   184071923     3  61357307.8           Prob > F      =  0.0000
    Residual |   564068269  1532  368190.776           R-squared     =  0.2460
-------------+------------------------------           Adj R-squared =  0.2446
       Total |   748140192  1535  487387.748           Root MSE      =  606.79

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
 parity_c4_1 |    708.2134    43.71992     16.20    0.000      622.4561     793.9706
 parity_c4_2 |    789.8435    45.92439     17.20    0.000      699.7622     879.9248
 parity_c4_3 |    831.7748    41.48567     20.05    0.000      750.4001     913.1495
       _cons |    2639.645    30.22623     87.33    0.000      2580.356     2698.934
-------------+----------------------------------------------------------------

. * or
. reg milk120 i.parity_c4

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  3,  1532) =  166.65
       Model |   184071923     3  61357307.8           Prob > F      =  0.0000
    Residual |   564068269  1532  368190.776           R-squared     =  0.2460
-------------+------------------------------           Adj R-squared =  0.2446
       Total |   748140192  1535  487387.748           Root MSE      =  606.79

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   parity_c4 |
          1  |    708.2134    43.71992     16.20    0.000      622.4561     793.9706
          2  |    789.8435    45.92439     17.20    0.000      699.7622     879.9248
          3  |    831.7748    41.48567     20.05    0.000      750.4001     913.1495
             |
       _cons |    2639.645    30.22623     87.33    0.000      2580.356     2698.934
-------------+----------------------------------------------------------------

. * testing a group of categorical predictors
. testparm i.parity_c4


 ( 1)  1.parity_c4 = 0


 ( 2)  2.parity_c4 = 0


 ( 3)  3.parity_c4 = 0


       F(  3,  1532) =  166.65
            Prob > F =    0.0000

.
. * HIERARCHICAL DUMMY VARIABLES
. * create hierarchical dummy variables "manually"
. gen parity_h0=1  if !missing(parity)

. gen parity_h1=(parity_c4>=1) if !missing(parity)

. gen parity_h2=(parity_c4>=2) if !missing(parity)

. gen parity_h3=(parity_c4>=3) if !missing(parity)

.
. br parity parity_c4 parity_h0 parity_h1 parity_h2 parity_h3

.
. * regress -milk120 on hierarchical dummy variables for parity
. reg milk120 parity_h1 parity_h2 parity_h3

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  3,  1532) =  166.65
       Model |   184071923     3  61357307.8           Prob > F      =  0.0000
    Residual |   564068269  1532  368190.776           R-squared     =  0.2460
-------------+------------------------------           Adj R-squared =  0.2446
       Total |   748140192  1535  487387.748           Root MSE      =  606.79

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   parity_h1 |    708.2134    43.71992     16.20    0.000      622.4561     793.9706
   parity_h2 |     81.6301    46.83195      1.74    0.082     -10.23141     173.4916
   parity_h3 |    41.93131    44.75333      0.94    0.349     -45.85295     129.7156
       _cons |    2639.645    30.22623     87.33    0.000      2580.356     2698.934
-------------+----------------------------------------------------------------

.
. * SCALING X VARIABLES
. * substract min value
. reg milk120 parity

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =  262.27
       Model |   109234227     1   109234227           Prob > F      =  0.0000
    Residual |   638905966  1534  416496.718           R-squared     =  0.1460
-------------+------------------------------           Adj R-squared =  0.1455
       Total |   748140192  1535  487387.748           Root MSE      =  645.37

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      parity |     178.347    11.01266     16.19    0.000      156.7455     199.9484
       _cons |     2727.08    34.33991     79.41    0.000      2659.722     2794.438
-------------+----------------------------------------------------------------

. gen parity_1=parity-1

. reg milk120 parity_1

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =  262.27
       Model |   109234227     1   109234227           Prob > F      =  0.0000
    Residual |   638905966  1534  416496.718           R-squared     =  0.1460
-------------+------------------------------           Adj R-squared =  0.1455
       Total |   748140192  1535  487387.748           Root MSE      =  645.37

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    parity_1 |     178.347    11.01266     16.19    0.000      156.7455     199.9484
       _cons |    2905.427    25.23474    115.14    0.000      2855.928     2954.925
-------------+----------------------------------------------------------------

.
. * centring
. reg milk120 c.herd_size##c.herd_size, vsquish

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  2,  1533) =  111.15
       Model |  94747175.1     2  47373587.5           Prob > F      =  0.0000
    Residual |   653393017  1533  426218.537           R-squared     =  0.1266
-------------+------------------------------           Adj R-squared =  0.1255
       Total |   748140192  1535  487387.748           Root MSE      =  652.85

------------------------+----------------------------------------------------------------
                 milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
------------------------+----------------------------------------------------------------
              herd_size |    28.73126    1.993023     14.42    0.000      24.82192      32.6406
c.herd_size#c.herd_size |   -.0608255    .0041101    -14.80    0.000     -.0688875    -.0527634
                  _cons |    66.06488    231.8877      0.28    0.776     -388.7858     520.9155
------------------------+----------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of regress model

   |    c.herd~e#
e(V)   | herd_s~e    c.herd~e    _cons
-------------+------------------------------
herd_size   |   1.0000
c.herd_size#  |
c.herd_size   |  -0.9907      1.0000
_cons   |  -0.9844      0.9535      1.0000

.
. summ herd_size

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
   herd_size |      1574    251.0076    62.01692        125        333

. gen hrdsz_ctr=herd_size - 251

. reg milk120 c.hrdsz_ctr##c.hrdsz_ctr, vsquish

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  2,  1533) =  111.15
       Model |  94747175.1     2  47373587.5           Prob > F      =  0.0000
    Residual |   653393017  1533  426218.537           R-squared     =  0.1266
-------------+------------------------------           Adj R-squared =  0.1255
       Total |   748140192  1535  487387.748           Root MSE      =  652.85

------------------------+----------------------------------------------------------------
                 milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
------------------------+----------------------------------------------------------------
              hrdsz_ctr |   -1.803116    .2847073     -6.33    0.000     -2.361573    -1.244659
c.hrdsz_ctr#c.hrdsz_ctr |   -.0608255    .0041101    -14.80    0.000     -.0688875    -.0527634
                  _cons |    3445.547    22.80494    151.09    0.000      3400.815     3490.279
------------------------+----------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of regress model

   |    c.hrds~r#
e(V)   | hrdsz_~r    c.hrds~r    _cons
-------------+------------------------------
hrdsz_ctr   |   1.0000
c.hrdsz_ctr#  |
c.hrdsz_ctr   |   0.3115      1.0000
_cons   |  -0.2118     -0.6830      1.0000

.
. * scale of measurement
. reg milk120 herd_size

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =    2.88
       Model |  1400932.73     1  1400932.73           Prob > F      =  0.0900
    Residual |   746739260  1534  486792.216           R-squared     =  0.0019
-------------+------------------------------           Adj R-squared =  0.0012
       Total |   748140192  1535  487387.748           Root MSE      =   697.7

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   herd_size |     -.49048    .2891242     -1.70    0.090     -1.057601     .0766405
       _cons |    3338.164    74.69789     44.69    0.000      3191.643     3484.685
-------------+----------------------------------------------------------------

. capture drop herdsz_100

. gen herdsz_100=herd_size/100 /*rescale herd_size so coef are larger*/

. reg milk120 herdsz_100

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  1,  1534) =    2.88
       Model |  1400930.12     1  1400930.12           Prob > F      =  0.0900
    Residual |   746739262  1534  486792.218           R-squared     =  0.0019
-------------+------------------------------           Adj R-squared =  0.0012
       Total |   748140192  1535  487387.748           Root MSE      =   697.7

-------------+----------------------------------------------------------------
      milk120 |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
  herdsz_100 |   -49.04796    28.91242     -1.70    0.090       -105.76     7.664098
       _cons |    3338.164    74.69789     44.69    0.000      3191.643     3484.685
-------------+----------------------------------------------------------------

.
. * DETECTING CONFOUNDING
. reg wpc vag_disch               /* vag_disch adds ~12 days, P=0.04 */

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  1,  1572) =    4.21
       Model |  11186.2576     1  11186.2576           Prob > F      =  0.0404
    Residual |   4176904.3  1572   2657.0638           R-squared     =  0.0027
-------------+------------------------------           Adj R-squared =  0.0020
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.547

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   vag_disch |    11.99647    5.846716      2.05    0.040      .5282858     23.46465
       _cons |    68.17426    1.334494     51.09    0.000      65.55669     70.79184
-------------+----------------------------------------------------------------

. reg wpc rp                      /* rp adds 12 days, P=0.008 */

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  1,  1572) =    7.00
       Model |  18574.5377     1  18574.5377           Prob > F      =  0.0082
    Residual |  4169516.02  1572  2652.36388           R-squared     =  0.0044
-------------+------------------------------           Adj R-squared =  0.0038
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.501

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
          rp |     11.7344    4.434231      2.65    0.008      3.036767     20.43203
       _cons |    67.68842    1.364298     49.61    0.000      65.01239     70.36446
-------------+----------------------------------------------------------------

. reg wpc rp vag_disch    /* vag_disch no sig. ,  rp is a confounder */

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  2,  1571) =    4.65
       Model |  24663.1482     2  12331.5741           Prob > F      =  0.0097
    Residual |  4163427.41  1571  2650.17658           R-squared     =  0.0059
-------------+------------------------------           Adj R-squared =  0.0046
       Total |  4188090.56  1573  2662.48605           Root MSE      =   51.48

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
          rp |     10.2397    4.540774      2.26    0.024      1.333087     19.14632
   vag_disch |    9.066942      5.9819      1.52    0.130     -2.666406     20.80029
       _cons |    67.35756    1.381095     48.77    0.000      64.64857     70.06654
-------------+----------------------------------------------------------------

.
. tab vag_disch rp, chi2

   Vaginal | Retained placenta at
 discharge |        calving
  observed |        no        yes |     Total
-----------+----------------------+----------
        no |     1,373        119 |     1,492
       yes |        52         30 |        82
-----------+----------------------+----------
     Total |     1,425        149 |     1,574

          Pearson chi2(1) =  74.2346   Pr = 0.000

. cs vag_disch rp, or

                 | Retained placenta at   |
                 | calving                |
                 |   Exposed   Unexposed  |      Total
-----------------+------------------------+------------
           Cases |        30          52  |         82
        Noncases |       119        1373  |       1492
-----------------+------------------------+------------
           Total |       149        1425  |       1574
                 |                        |
            Risk |  .2013423    .0364912  |   .0520966
                 |                        |
                 |      Point estimate    |    [95% Conf. Interval]
                 +------------------------+------------------------
 Risk difference |         .1648511       |    .0997315    .2299706
      Risk ratio |         5.517553       |    3.638118    8.367895
 Attr. frac. ex. |         .8187602       |    .7251326    .8804956
 Attr. frac. pop |         .2995464       |
      Odds ratio |         6.656432       |    4.104597    10.79865 (Cornfield)
                 +------------------------+------------------------
                               chi2(1) =    74.23  Pr>chi2 = 0.0000

.
. * CONFOUNDING AND COLLINEARITY
. use bw5k.dta, clear

. corr cig_2 cig_3 /*considering only cig_2 for the example*/
(obs=5000)

             |    cig_2    cig_3
-------------+------------------
       cig_2 |   1.0000
       cig_3 |   0.9451   1.0000


.
. * Model for cig_3 as exposure of interest
. * 1) relationship Z->E
. corr cig_3 cig_2
(obs=5000)

             |    cig_3    cig_2
-------------+------------------
       cig_3 |   1.0000
       cig_2 |   0.9451   1.0000


. * 2) relationship Z-Y in E-
. reg bwt cig_2 if cig_3==0 /*borderline sig* but not the best model*/

      Source |       SS       df       MS              Number of obs =    4656
-------------+------------------------------           F(  1,  4654) =    2.77
       Model |  879610.363     1  879610.363           Prob > F      =  0.0960
    Residual |  1.4771e+09  4654  317380.896           R-squared     =  0.0006
-------------+------------------------------           Adj R-squared =  0.0004
       Total |  1.4780e+09  4655  317501.676           Root MSE      =  563.37

-------------+----------------------------------------------------------------
          bwt |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       cig_2 |   -22.32463    13.41002     -1.66    0.096     -48.61462     3.965367
       _cons |    3310.075    8.263501    400.57    0.000      3293.874     3326.275
-------------+----------------------------------------------------------------

. * 3) not an int. variable
. * 4) change in coef.
. reg bwt cig_3

      Source |       SS       df       MS              Number of obs =    5000
-------------+------------------------------           F(  1,  4998) =   22.55
       Model |  7189497.98     1  7189497.98           Prob > F      =  0.0000
    Residual |  1.5935e+09  4998  318835.965           R-squared     =  0.0045
-------------+------------------------------           Adj R-squared =  0.0043
       Total |  1.6007e+09  4999  320210.372           Root MSE      =  564.66

-------------+----------------------------------------------------------------
          bwt |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       cig_3 |   -12.48752    2.629726     -4.75    0.000     -17.64293    -7.332101
       _cons |    3303.448    8.177729    403.96    0.000      3287.416      3319.48
-------------+----------------------------------------------------------------

. reg bwt cig_3 cig_2

      Source |       SS       df       MS              Number of obs =    5000
-------------+------------------------------           F(  2,  4997) =   12.61
       Model |  8037757.94     2  4018878.97           Prob > F      =  0.0000
    Residual |  1.5927e+09  4997  318730.017           R-squared     =  0.0050
-------------+------------------------------           Adj R-squared =  0.0046
       Total |  1.6007e+09  4999  320210.372           Root MSE      =  564.56

-------------+----------------------------------------------------------------
          bwt |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       cig_3 |   -.0859205    8.043799     -0.01    0.991      -15.8553     15.68346
       cig_2 |   -12.11372    7.425483     -1.63    0.103     -26.67093      2.44348
       _cons |    3304.134    8.187191    403.57    0.000      3288.084     3320.185
-------------+----------------------------------------------------------------

. estat vce, corr /*high correlation*/

Correlation matrix of coefficients of regress model

e(V)   | cig_3    cig_2    _cons
-------------+------------------------------
cig_3   |   1.0000
cig_2   |  -0.9451      1.0000
_cons   |  -0.0218     -0.0514      1.0000

. * try centring
. summ cig_2

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       cig_2 |      5000        .743     3.28979          0         45

. gen cig2_ctr=cig_2-r(mean)

. summ cig_3

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       cig_3 |      5000       .6704    3.036908          0         45

. gen cig3_ctr=cig_3-r(mean)

. reg bwt cig3_ctr cig2_ctr

      Source |       SS       df       MS              Number of obs =    5000
-------------+------------------------------           F(  2,  4997) =   12.61
       Model |  8037757.91     2  4018878.95           Prob > F      =  0.0000
    Residual |  1.5927e+09  4997  318730.017           R-squared     =  0.0050
-------------+------------------------------           Adj R-squared =  0.0046
       Total |  1.6007e+09  4999  320210.372           Root MSE      =  564.56

-------------+----------------------------------------------------------------
          bwt |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    cig3_ctr |   -.0859208    8.043799     -0.01    0.991      -15.8553     15.68346
    cig2_ctr |   -12.11372    7.425483     -1.63    0.103     -26.67093      2.44348
       _cons |    3295.076    7.984109    412.70    0.000      3279.424     3310.728
-------------+----------------------------------------------------------------

. estat vce, corr /*still high correlation since centring will reduce correlation
>                                 on derived variables*/

Correlation matrix of coefficients of regress model

e(V)   | cig3_ctr    cig2_ctr    _cons
-------------+------------------------------
cig3_ctr   |   1.0000
cig2_ctr   |  -0.9451      1.0000
_cons   |   0.0000     -0.0000      1.0000

.
. * DETECTING INTERACTION
. * 2 dichotomous variables
. use daisy2red, clear

. gen parity_1=parity-1

.
. reg wpc vag_disch

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  1,  1572) =    4.21
       Model |  11186.2576     1  11186.2576           Prob > F      =  0.0404
    Residual |   4176904.3  1572   2657.0638           R-squared     =  0.0027
-------------+------------------------------           Adj R-squared =  0.0020
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.547

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   vag_disch |    11.99647    5.846716      2.05    0.040      .5282858     23.46465
       _cons |    68.17426    1.334494     51.09    0.000      65.55669     70.79184
-------------+----------------------------------------------------------------

. reg wpc i.vag_disch i.rp vag_disch#rp

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  3,  1570) =    4.53
       Model |  35915.9774     3  11971.9925           Prob > F      =  0.0036
    Residual |  4152174.58  1570  2644.69719           R-squared     =  0.0086
-------------+------------------------------           Adj R-squared =  0.0067
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.427

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   vag_disch |
        yes  |    .5429296    7.265382      0.07    0.940     -13.70794      14.7938
             |
          rp |
        yes  |    6.339794    4.914322      1.29    0.197     -3.299531     15.97912
             |
vag_disch#rp |
    yes#yes  |    26.34867    12.77367      2.06    0.039      1.293414     51.40392
             |
       _cons |    67.66861    1.387883     48.76    0.000      64.94631     70.39091
-------------+----------------------------------------------------------------

. reg wpc vag_disch##rp //same as above

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  3,  1570) =    4.53
       Model |  35915.9774     3  11971.9925           Prob > F      =  0.0036
    Residual |  4152174.58  1570  2644.69719           R-squared     =  0.0086
-------------+------------------------------           Adj R-squared =  0.0067
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.427

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
   vag_disch |
        yes  |    .5429296    7.265382      0.07    0.940     -13.70794      14.7938
             |
          rp |
        yes  |    6.339794    4.914322      1.29    0.197     -3.299531     15.97912
             |
vag_disch#rp |
    yes#yes  |    26.34867    12.77367      2.06    0.039      1.293414     51.40392
             |
       _cons |    67.66861    1.387883     48.76    0.000      64.94631     70.39091
-------------+----------------------------------------------------------------

. table vag_disch rp, c(mean wpc) // display wpc means by vag_dich and rp

----------+-------------------
Vaginal   | Retained placenta
discharge |     at calving
observed  |       no       yes
----------+-------------------
       no | 67.66861   74.0084
      yes | 68.21154     100.9
----------+-------------------

.
. *Use of margins command as a tool to create plots - this will be explained later
. reg wpc vag_disch#rp //total effects

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  3,  1570) =    4.53
       Model |  35915.9774     3  11971.9925           Prob > F      =  0.0036
    Residual |  4152174.58  1570  2644.69719           R-squared     =  0.0086
-------------+------------------------------           Adj R-squared =  0.0067
       Total |  4188090.56  1573  2662.48605           Root MSE      =  51.427

-------------+----------------------------------------------------------------
          wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
vag_disch#rp |
     no#yes  |    6.339794    4.914322      1.29    0.197     -3.299531     15.97912
     yes#no  |    .5429296    7.265382      0.07    0.940     -13.70794      14.7938
    yes#yes  |    33.23139    9.491195      3.50    0.000      14.61464     51.84814
             |
       _cons |    67.66861    1.387883     48.76    0.000      64.94631     70.39091
-------------+----------------------------------------------------------------

. margins vag_disch#rp //same as table command

Adjusted predictions                              Number of obs   =       1574
Model VCE    : OLS


Expression  : Linear prediction, predict()


-------------+----------------------------------------------------------------
             |            Delta-method
             |     Margin    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
vag_disch#rp |
      no#no  |    67.66861    1.387883     48.76    0.000      64.94631     70.39091
     no#yes  |     74.0084     4.71427     15.70    0.000      64.76147     83.25533
     yes#no  |    68.21154    7.131589      9.56    0.000       54.2231     82.19998
    yes#yes  |       100.9    9.389173     10.75    0.000      82.48336     119.3166
-------------+----------------------------------------------------------------

. marginsplot, legend(title("Retained Placenta")) noci ytitle("Predicted WPC") title("")


Variables that uniquely identify margins: vag_disch rp


. marginsplot, x(rp) legend(title("Vaginal Discharge")) noci ytitle("Predicted WPC") title("")


Variables that uniquely identify margins: vag_disch rp


.
. * dichotomous and continuous variable
. gen milk120k=milk120/1000
(38 missing values generated)

. summ milk120k

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
    milk120k |      1536    3.215096    .6981316     1.1102     5.6303

. gen milk120k_ctr=milk120k-r(mean)
(38 missing values generated)

. reg wpc i.dyst##c.milk120k_ctr, vsquish

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  3,  1532) =    3.83
       Model |  30572.8752     3  10190.9584           Prob > F      =  0.0095
    Residual |  4073791.78  1532  2659.13302           R-squared     =  0.0074
-------------+------------------------------           Adj R-squared =  0.0055
       Total |  4104364.66  1535   2673.8532           Root MSE      =  51.567

--------------------+----------------------------------------------------------------
                 wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
--------------------+----------------------------------------------------------------
               dyst |
               yes  |     8.20714    5.718528      1.44    0.151      -3.00983     19.42411
       milk120k_ctr |   -3.446531    1.928535     -1.79    0.074     -7.229379     .3363161
dyst#c.milk120k_ctr |
               yes  |    29.14238    9.468101      3.08    0.002      10.57057     47.71419
              _cons |    68.75682    1.357147     50.66    0.000      66.09475     71.41888
--------------------+----------------------------------------------------------------

. margins dyst, at(milk120k_ctr=(-2(1)3))

Adjusted predictions                              Number of obs   =       1536
Model VCE    : OLS


Expression  : Linear prediction, predict()


1._at  : milk120k_ctr    =          -2


2._at  : milk120k_ctr    =          -1


3._at  : milk120k_ctr    =           0


4._at  : milk120k_ctr    =           1


5._at  : milk120k_ctr    =           2


6._at  : milk120k_ctr    =           3


-------------+----------------------------------------------------------------
             |            Delta-method
             |     Margin    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    _at#dyst |
       1#no  |    75.64988    4.106318     18.42    0.000      67.59528     83.70448
      1#yes  |    25.57227    17.96398      1.42    0.155     -9.664321     60.80885
       2#no  |    72.20335     2.37331     30.42    0.000      67.54807     76.85863
      2#yes  |    51.26811    9.531863      5.38    0.000      32.57123     69.96499
       3#no  |    68.75682    1.357147     50.66    0.000      66.09475     71.41888
      3#yes  |    76.96396    5.555152     13.85    0.000      66.06745     87.86046
       4#no  |    65.31028    2.342987     27.87    0.000      60.71448     69.90609
      4#yes  |    102.6598    11.94631      8.59    0.000      79.22694     126.0927
       5#no  |    61.86375    4.071342     15.19    0.000      53.87776     69.84975
      5#yes  |    128.3556    20.64995      6.22    0.000      87.85048     168.8608
       6#no  |    58.41722    5.924572      9.86    0.000      46.79609     70.03835
      6#yes  |    154.0515    29.69811      5.19    0.000      95.79823     212.3047
-------------+----------------------------------------------------------------

. marginsplot, noci title("") legend(order(1 "dyst=0" 2 "dyst=1")) scheme(s2mono)


Variables that uniquely identify margins: milk120k_ctr dyst


.
. * two continuous variables
. reg wpc c.parity_1##c.milk120k_ctr

      Source |       SS       df       MS              Number of obs =    1536
-------------+------------------------------           F(  3,  1532) =    2.26
       Model |  18084.1899     3  6028.06329           Prob > F      =  0.0797
    Residual |  4086280.47  1532   2667.2849           R-squared     =  0.0044
-------------+------------------------------           Adj R-squared =  0.0025
       Total |  4104364.66  1535   2673.8532           Root MSE      =  51.646

--------------------------+----------------------------------------------------------------
                       wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
--------------------------+----------------------------------------------------------------
                 parity_1 |    2.072164    .9549532      2.17    0.030      .1990103     3.945318
             milk120k_ctr |   -2.542834    3.091716     -0.82    0.411     -8.607278     3.521609
                          |
c.parity_1#c.milk120k_ctr |   -.8764358    1.363504     -0.64    0.520     -3.550968     1.798096
                          |
                    _cons |    65.73655    2.207989     29.77    0.000      61.40555     70.06755
--------------------------+----------------------------------------------------------------

. margins, at(milk120k_ctr=(-2(1)3) parity=(0(1)3))

Adjusted predictions                              Number of obs   =       1536
Model VCE    : OLS


Expression  : Linear prediction, predict()


1._at  : parity_1        =           0


     milk120k_ctr    =          -2


2._at  : parity_1        =           0


     milk120k_ctr    =          -1


3._at  : parity_1        =           0


     milk120k_ctr    =           0


4._at  : parity_1        =           0


     milk120k_ctr    =           1


5._at  : parity_1        =           0


     milk120k_ctr    =           2


6._at  : parity_1        =           0


     milk120k_ctr    =           3


7._at  : parity_1        =           1


     milk120k_ctr    =          -2


8._at  : parity_1        =           1


     milk120k_ctr    =          -1


9._at  : parity_1        =           1


     milk120k_ctr    =           0


10._at  : parity_1        =           1


     milk120k_ctr    =           1


11._at  : parity_1        =           1


     milk120k_ctr    =           2


12._at  : parity_1        =           1


     milk120k_ctr    =           3


13._at  : parity_1        =           2


     milk120k_ctr    =          -2


14._at  : parity_1        =           2


     milk120k_ctr    =          -1


15._at  : parity_1        =           2


     milk120k_ctr    =           0


16._at  : parity_1        =           2


     milk120k_ctr    =           1


17._at  : parity_1        =           2


     milk120k_ctr    =           2


18._at  : parity_1        =           2


     milk120k_ctr    =           3


19._at  : parity_1        =           3


     milk120k_ctr    =          -2


20._at  : parity_1        =           3


     milk120k_ctr    =          -1


21._at  : parity_1        =           3


     milk120k_ctr    =           0


22._at  : parity_1        =           3


     milk120k_ctr    =           1


23._at  : parity_1        =           3


     milk120k_ctr    =           2


24._at  : parity_1        =           3


     milk120k_ctr    =           3


-------------+----------------------------------------------------------------
             |            Delta-method
             |     Margin    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |    70.82222    5.665012     12.50    0.000      59.71022     81.93422
          2  |    68.27938    2.987487     22.86    0.000      62.41939     74.13938
          3  |    65.73655    2.207989     29.77    0.000      61.40555     70.06755
          4  |    63.19371    4.465733     14.15    0.000      54.43412     71.95331
          5  |    60.65088    7.357156      8.24    0.000      46.21972     75.08204
          6  |    58.10805    10.36485      5.61    0.000      37.77725     78.43884
          7  |    74.64725    4.302751     17.35    0.000      66.20735     83.08716
          8  |    71.22798     2.33446     30.51    0.000      66.64891     75.80706
          9  |    67.80871    1.601972     42.33    0.000      64.66642       70.951
         10  |    64.38944    3.140622     20.50    0.000      58.22907     70.54982
         11  |    60.97017    5.228888     11.66    0.000      50.71364     71.22671
         12  |     57.5509    7.416173      7.76    0.000      43.00398     72.09783
         13  |    78.47229    4.592419     17.09    0.000       69.4642     87.48038
         14  |    74.17658    2.691774     27.56    0.000      68.89663     79.45653
         15  |    69.88088    1.442666     48.44    0.000      67.05107     72.71069
         16  |    65.58517    2.365847     27.72    0.000      60.94453     70.22581
         17  |    61.28947    4.218233     14.53    0.000      53.01534     69.56359
         18  |    56.99376    6.218525      9.17    0.000      44.79604     69.19148
         19  |    82.29732    6.310492     13.04    0.000      69.91921     94.67544
         20  |    77.12518    3.783241     20.39    0.000       69.7043     84.54606
         21  |    71.95304    1.849358     38.91    0.000       68.3255     75.58058
         22  |     66.7809    2.672818     24.99    0.000      61.53813     72.02367
         23  |    61.60876    5.048207     12.20    0.000      51.70663     71.51089
         24  |    56.43662    7.644701      7.38    0.000      41.44143      71.4318
-------------+----------------------------------------------------------------

. marginsplot, noci title("") scheme(s2mono)


Variables that uniquely identify margins: milk120k_ctr parity_1


.
. * interaction between 2 cont. variables assumes both effect are linear
. * is this true for -milk120k- ?  - generate a smoothed scatterplot
. twoway (scatter wpc milk120k) (lowess wpc milk120k)

. twoway (scatter wpc parity) (lowess wpc parity)

.
. * CAUSAL INTERPRETATION
. use daisy2red.dta, clear

.
. * model to evaluate effect of - rp and vag_disch
. gen calv_mth=month(calv_dt)

. tab calv_mth, summ(wpc)

            |    Summary of Interval from wait
            |        period to conception
   calv_mth |        Mean   Std. Dev.       Freq.
------------+------------------------------------
          1 |    77.00885   50.850533         113
          2 |   60.009615   45.765017         104
          3 |   69.402516   54.240687         159
          4 |   60.385827   53.046258         127
          5 |          63   49.882911         106
          6 |   64.350365   51.665154         137
          7 |   63.581818   45.047453         110
          8 |   69.514019   54.277478         107
          9 |   74.664773   52.827873         176
         10 |   72.477011   49.332856         174
         11 |   72.026846   54.231479         149
         12 |   73.508929   53.222801         112
------------+------------------------------------
      Total |   68.799238   51.599283        1574

. gen aut_calv=(calv_mth>=2 & calv_mth<=7) if !missing(calv_mth)

. tab aut_calv, summ(wpc)

            |    Summary of Interval from wait
            |        period to conception
   aut_calv |        Mean   Std. Dev.       Freq.
------------+------------------------------------
          0 |   73.233454   52.236588         831
          1 |   63.839838   50.451973         743
------------+------------------------------------
      Total |   68.799238   51.599283        1574

. gen hs100=(herd_size/100)

. gen parity_1=parity-1

.
. reg wpc c.hs100##c.hs100 parity_1 i.aut_calv twin dyst i.rp##vag_disch , vsquish

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  9,  1564) =   13.22
       Model |  296062.681     9  32895.8535           Prob > F      =  0.0000
    Residual |  3892027.88  1564  2488.50887           R-squared     =  0.0707
-------------+------------------------------           Adj R-squared =  0.0653
       Total |  4188090.56  1573  2662.48605           Root MSE      =  49.885

----------------+----------------------------------------------------------------
             wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
----------------+----------------------------------------------------------------
          hs100 |   -36.05705    15.05032     -2.40    0.017     -65.57798     -6.53612
c.hs100#c.hs100 |    11.13827    3.111145      3.58    0.000      5.035818     17.24073
       parity_1 |     1.13721    .8583103      1.32    0.185       -.54635      2.82077
     1.aut_calv |   -8.263839    2.537751     -3.26    0.001     -13.24159    -3.286086
           twin |    20.68314    9.845165      2.10    0.036       1.37203     39.99425
           dyst |    11.70041    5.462576      2.14    0.032      .9856659     22.41516
             rp |
           yes  |     5.98687    4.811976      1.24    0.214     -3.451734     15.42547
      vag_disch |
           yes  |    1.228195    7.161395      0.17    0.864     -12.81875     15.27514
   rp#vag_disch |
       yes#yes  |    22.85194    12.51605      1.83    0.068     -1.698056     47.40194
          _cons |    84.66125    17.61671      4.81    0.000      50.10639     119.2161
----------------+----------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of regress model

   |    c.hs100#      1.         1.   1.
e(V)   | hs100    c.hs100    parity_1    aut_calv    twin    dyst    rp    vag_di~h
-------------+--------------------------------------------------------------------------------
hs100   |   1.0000
c.hs100#  |
c.hs100   |  -0.9907      1.0000
parity_1   |   0.0426     -0.0468      1.0000
1.aut_calv   |   0.0349     -0.0265     -0.0500      1.0000
twin   |  -0.0435      0.0464     -0.0666     -0.0487      1.0000
dyst   |  -0.0579      0.0717      0.1303      0.0023     -0.0214      1.0000
1.rp   |  -0.0527      0.0540      0.0318      0.0438     -0.0807     -0.0656      1.0000
1.vag_disch   |  -0.0680      0.0698      0.0649      0.0387     -0.0383     -0.1188      0.0742      1.0000
1.rp#  |
1.vag_disch   |   0.0566     -0.0571     -0.0644     -0.0024     -0.0429      0.0861     -0.3873     -0.5752
_cons   |  -0.9772      0.9458     -0.1201     -0.1090      0.0417      0.0132      0.0235      0.0427

   | 1.rp#
e(V)   | 1.vag_~h    _cons
-------------+--------------------
1.rp#  |
1.vag_disch   |   1.0000
_cons   |  -0.0410      1.0000

. *centre hs100
. summ hs100

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
       hs100 |      1574    2.510076    .6201691       1.25       3.33

. gen hs100_ctr=hs100-r(mean)

.
. reg wpc c.hs100_ctr##c.hs100_ctr parity_1 i.aut_calv i.twin i.dyst i.rp##vag_disch , vsquish

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  9,  1564) =   13.22
       Model |  296062.682     9  32895.8535           Prob > F      =  0.0000
    Residual |  3892027.88  1564  2488.50887           R-squared     =  0.0707
-------------+------------------------------           Adj R-squared =  0.0653
       Total |  4188090.56  1573  2662.48605           Root MSE      =  49.885

------------------------+----------------------------------------------------------------
                     wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
------------------------+----------------------------------------------------------------
              hs100_ctr |    19.85878    2.163552      9.18    0.000      15.61501     24.10255
c.hs100_ctr#c.hs100_ctr |    11.13827    3.111145      3.58    0.000      5.035818     17.24073
               parity_1 |     1.13721    .8583103      1.32    0.185       -.54635      2.82077
             1.aut_calv |   -8.263839    2.537751     -3.26    0.001     -13.24159    -3.286086
                   twin |
                   yes  |    20.68314    9.845165      2.10    0.036       1.37203     39.99425
                   dyst |
                   yes  |    11.70041    5.462576      2.14    0.032      .9856659     22.41516
                     rp |
                   yes  |     5.98687    4.811976      1.24    0.214     -3.451734     15.42547
              vag_disch |
                   yes  |    1.228195    7.161395      0.17    0.864     -12.81875     15.27514
           rp#vag_disch |
               yes#yes  |    22.85194    12.51605      1.83    0.068     -1.698056     47.40194
                  _cons |     64.3318    2.634086     24.42    0.000      59.16509     69.49851
------------------------+----------------------------------------------------------------

. estat vce, corr

Correlation matrix of coefficients of regress model

   |    c.hs10~r#      1.   1.   1.   1.   1.
e(V)   | hs100_~r    c.hs10~r    parity_1    aut_calv    twin    dyst    rp    vag_di~h
-------------+--------------------------------------------------------------------------------
hs100_ctr   |   1.0000
c.hs100_ctr#  |
c.hs100_ctr   |   0.3271      1.0000
parity_1   |  -0.0415     -0.0468      1.0000
1.aut_calv   |   0.0521     -0.0265     -0.0500      1.0000
1.twin   |   0.0326      0.0464     -0.0666     -0.0487      1.0000
1.dyst   |   0.1146      0.0717      0.1303      0.0023     -0.0214      1.0000
1.rp   |   0.0230      0.0540      0.0318      0.0438     -0.0807     -0.0656      1.0000
1.vag_disch   |   0.0305      0.0698      0.0649      0.0387     -0.0383     -0.1188      0.0742      1.0000
1.rp#  |
1.vag_disch   |  -0.0184     -0.0571     -0.0644     -0.0024     -0.0429      0.0861     -0.3873     -0.5752
_cons   |  -0.1716     -0.4415     -0.5404     -0.4246      0.0004     -0.2091     -0.1974     -0.1711

   | 1.rp#
e(V)   | 1.vag_~h    _cons
-------------+--------------------
1.rp#  |
1.vag_disch   |   1.0000
_cons   |   0.1133      1.0000

.
. *Plot to show herd size effect
. margins i.rp, at(hs100=(-1.26 -0.66 -0.5 -0.16 0.12 0.43 0.82) vag_disch=0 twin=0 aut_calv=1)

Predictive margins                                Number of obs   =       1574
Model VCE    : OLS


Expression  : Linear prediction, predict()


1._at  : hs100_ctr       =       -1.26


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


2._at  : hs100_ctr       =        -.66


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


3._at  : hs100_ctr       =         -.5


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


4._at  : hs100_ctr       =        -.16


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


5._at  : hs100_ctr       =         .12


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


6._at  : hs100_ctr       =         .43


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


7._at  : hs100_ctr       =         .82


     aut_calv        =           1


     twin            =           0


     vag_disch       =           0


-------------+----------------------------------------------------------------
             |            Delta-method
             |     Margin    Std. Err.       t    P>|t|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
      _at#rp |
       1#no  |    51.39514    4.179809     12.30    0.000      43.19652     59.59376
      1#yes  |    57.38201    6.237152      9.20    0.000      45.14794     69.61607
       2#no  |    50.47911    2.305193     21.90    0.000      45.95752     55.00071
      2#yes  |    56.46598    5.017018     11.25    0.000      46.62519     66.30677
       3#no  |    51.58925    2.272508     22.70    0.000      47.13177     56.04674
      3#yes  |    57.57612    4.979707     11.56    0.000      47.80852     67.34373
       4#no  |    55.84181    2.307135     24.20    0.000      51.31641     60.36721
      4#yes  |    61.82868    4.975561     12.43    0.000      52.06921     71.58815
       5#no  |    61.27752    2.227896     27.50    0.000      56.90754      65.6475
      5#yes  |    67.26439    4.951049     13.59    0.000        57.553     76.97578
       6#no  |    69.33282    2.148793     32.27    0.000        65.118     73.54764
      6#yes  |    75.31969     4.95891     15.19    0.000      65.59287      85.0465
       7#no  |    82.50765    2.927494     28.18    0.000      76.76542     88.24987
      7#yes  |    88.49452    5.433098     16.29    0.000      77.83759     99.15144
-------------+----------------------------------------------------------------

. marginsplot, noci xlabel(-1.26 "125" -0.66 "185" -0.5 "201" -0.16 "235" 0.12 "263" 0.43 "294" 0.82 "333") ///
>         xtitle("Herd Size") ytitle("Days") title("Preditive WPC by RP")


Variables that uniquely identify margins: hs100_ctr rp


.
. * dyst conf for rp
. reg wpc c.hs100_ctr##c.hs100_ctr parity_1 i.aut_calv i.twin  i.rp

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  6,  1567) =   18.07
       Model |  270961.954     6  45160.3256           Prob > F      =  0.0000
    Residual |  3917128.61  1567  2499.76299           R-squared     =  0.0647
-------------+------------------------------           Adj R-squared =  0.0611
       Total |  4188090.56  1573  2662.48605           Root MSE      =  49.998

------------------------+----------------------------------------------------------------
                     wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
------------------------+----------------------------------------------------------------
              hs100_ctr |    19.30525    2.151998      8.97    0.000      15.08415     23.52635
                        |
c.hs100_ctr#c.hs100_ctr |    10.71722    3.099622      3.46    0.001      4.637372     16.79706
                        |
               parity_1 |    .9394592    .8495005      1.11    0.269     -.7268182     2.605737
             1.aut_calv |   -8.459954    2.540778     -3.33    0.001     -13.44364    -3.476272
                        |
                   twin |
                   yes  |    23.09719    9.826032      2.35    0.019      3.823631     42.37074
                        |
                     rp |
                   yes  |    11.18504     4.35328      2.57    0.010      2.646174     19.72391
                  _cons |    65.59313    2.527825     25.95    0.000      60.63485      70.5514
------------------------+----------------------------------------------------------------

. reg wpc c.hs100_ctr##c.hs100_ctr parity_1 i.aut_calv i.twin  i.rp dyst

      Source |       SS       df       MS              Number of obs =    1574
-------------+------------------------------           F(  7,  1566) =   16.16
       Model |  282216.669     7   40316.667           Prob > F      =  0.0000
    Residual |  3905873.89  1566  2494.17234           R-squared     =  0.0674
-------------+------------------------------           Adj R-squared =  0.0632
       Total |  4188090.56  1573  2662.48605           Root MSE      =  49.942

------------------------+----------------------------------------------------------------
                     wpc |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
------------------------+----------------------------------------------------------------
              hs100_ctr |    19.85311    2.165007      9.17    0.000      15.60649     24.09973
                        |
c.hs100_ctr#c.hs100_ctr |    11.25323     3.10642      3.62    0.000      5.160047     17.34641
                        |
               parity_1 |    1.194524    .8570034      1.39    0.164     -.4864711     2.875519
             1.aut_calv |   -8.425575    2.537986     -3.32    0.001     -13.40378    -3.447366
                        |
                   twin |
                   yes  |    22.58687    9.817977      2.30    0.022        3.3291     41.84463
                        |
                     rp |
                   yes  |    10.69412    4.354546      2.46    0.014      2.152766     19.23548
                   dyst |    11.53206    5.428789      2.12    0.034      .8836013     22.18052
                  _cons |    64.29614    2.597768     24.75    0.000      59.20067     69.39161
------------------------+----------------------------------------------------------------

.
end of do-file

. exit, clear