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Inputting the Surgical Unit data, table 8.1, p. 335.
clear input x1 x2 x3 x4 y logy 6.7 62 81 2.59 200 2.3010 5.1 59 66 1.70 101 2.0043 7.4 57 83 2.16 204 2.3096 6.5 73 41 2.01 101 2.0043 7.8 65 115 4.30 509 2.7067 5.8 38 72 1.42 80 1.9031 5.7 46 63 1.91 80 1.9031 3.7 68 81 2.57 127 2.1038 6.0 67 93 2.50 202 2.3054 3.7 76 94 2.40 203 2.3075 6.3 84 83 4.13 329 2.5172 6.7 51 43 1.86 65 1.8129 5.8 96 114 3.95 830 2.9191 5.8 83 88 3.95 330 2.5185 7.7 62 67 3.40 168 2.2253 7.4 74 68 2.40 217 2.3365 6.0 85 28 2.98 87 1.9395 3.7 51 41 1.55 34 1.5315 7.3 68 74 3.56 215 2.3324 5.6 57 87 3.02 172 2.2355 5.2 52 76 2.85 109 2.0374 3.4 83 53 1.12 136 2.1335 6.7 26 68 2.10 70 1.8451 5.8 67 86 3.40 220 2.3424 6.3 59 100 2.95 276 2.4409 5.8 61 73 3.50 144 2.1584 5.2 52 86 2.45 181 2.2577 11.2 76 90 5.59 574 2.7589 5.2 54 56 2.71 72 1.8573 5.8 76 59 2.58 178 2.2504 3.2 64 65 0.74 71 1.8513 8.7 45 23 2.52 58 1.7634 5.0 59 73 3.50 116 2.0645 5.8 72 93 3.30 295 2.4698 5.4 58 70 2.64 115 2.0607 5.3 51 99 2.60 184 2.2648 2.6 74 86 2.05 118 2.0719 4.3 8 119 2.85 120 2.0792 4.8 61 76 2.45 151 2.1790 5.4 52 88 1.81 148 2.1703 5.2 49 72 1.84 95 1.9777 3.6 28 99 1.30 75 1.8751 8.8 86 88 6.40 483 2.6840 6.5 56 77 2.85 153 2.1847 3.4 77 93 1.48 191 2.2810 6.5 40 84 3.00 123 2.0899 4.5 73 106 3.05 311 2.4928 4.8 86 101 4.10 398 2.5999 5.1 67 77 2.86 158 2.1987 3.9 82 103 4.55 310 2.4914 6.6 77 46 1.95 124 2.0934 6.4 85 40 1.21 125 2.0969 6.4 59 85 2.33 198 2.2967 8.8 78 72 3.20 313 2.4955 end
Generating the interaction of x2 and x3.
gen x2x3=x2*x3
Figure 8.2, page 336Note: In order to create these graphs we need to first perform four different regressions, namely y on x1 x2 x3 x4, logy on x1 x2 x3 x4, y on x2 x3 and logy on x2 x3. Since we don't need to look at the output of the regression at this point we will use the option quietly which will suppress the output of the regression.
Figure 8.2a, page 336.
quietly regress y x1 x2 x3 x4 predict r, resid qnorm r, ylabel(-100(100)300) xlabel(-200(100)200)
Figure 8.2b, page 336.
quietly regress y x2 x3 predict r1, resid graph twoway scatter r1 x2x3, ylabel(-200(100)400) xlabel(0(5000)10000)
Figure 8.2c, page 336.
quietly regress logy x1 x2 x3 x4 predict r2, resid qnorm r2, ylabel(-.15(.6).15) xlabel(-.15(.6).15)
Figure 8.2d, page 336.
quietly regress logy x2 x3 predict r3, resid graph twoway scatter r3 x2x3, ylabel(-.4(.1)0.4) xlabel(0 5000 10000)
Figure 8.3a, page 337.
graph matrix logy x1 x2 x3 x4
Figure 8.4, page 337.
corr logy x1 x2 x3 x4
(obs=54)
| logy x1 x2 x3 x4
-------------+---------------------------------------------
logy | 1.0000
x1 | 0.3464 1.0000
x2 | 0.5929 0.0901 1.0000
x3 | 0.6651 -0.1496 -0.0236 1.0000
x4 | 0.7262 0.5024 0.3690 0.4164 1.0000
Table 8.2, page 338This table is obtained using version 1.1 of rsquare which will calculate not only the Rsquare and Mallow's Cp but also the SSE and MSE. Make sure that when you run this you have the updated version! It was not possible to reproduce the following graphs: figures 8.4-8.7.
You can download rsquare from within Stata by typing findit rsquare (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
rsquare logy x1 x2 x3 x4 Regression models for dependent variable : logy R-squared Mallow's C SEE MSE models with 1 predictor 0.1200 1510.59 3.4961 0.0672 x1 0.3515 1100.01 2.5763 0.0495 x2 0.4424 938.86 2.2153 0.0426 x3 0.5274 788.15 1.8776 0.0361 x4 R-squared Mallow's C SEE MSE models with 2 predictor 0.4381 948.55 2.2325 0.0438 x1 x2 0.6458 580.14 1.4072 0.0276 x1 x3 0.5278 789.34 1.8758 0.0368 x1 x4 0.8130 283.67 0.7430 0.0146 x2 x3 0.6496 573.44 1.3922 0.0273 x2 x4 0.6865 507.90 1.2453 0.0244 x3 x4 R-squared Mallow's C SEE MSE models with 3 predictor 0.9723 3.04 0.1099 0.0022 x1 x2 x3 0.6500 574.71 1.3905 0.0278 x1 x2 x4 0.7192 451.99 1.1156 0.0223 x1 x3 x4 0.8829 161.66 0.4652 0.0093 x2 x3 x4 R-squared Mallow's C SEE MSE models with 4 predictor 0.9724 5.00 0.1098 0.0022 x1 x2 x3 x4
Forward stepwise regression of Surgical unit data, page 349.
Note1: Unlike BMDP, Stata does not provide any output except the output for the final model.
Note2: Tolerance is the equivalent of 1/VIF.
* Stata 8 code.
sw reg logy x1 x2 x3 x4, pe(.01) pr(.05) forward beta
* Stata 9 code and output.
* Note: The beta option does not work with the stepwise prefix.
stepwise, pe(.01) pr(.05) forward: regress logy x1 x2 x3 x4, beta
begin with empty model
p = 0.0000 < 0.0100 adding x4
p = 0.0000 < 0.0100 adding x3
p = 0.0000 < 0.0100 adding x2
p = 0.0000 < 0.0100 adding x1
p = 0.8436 >= 0.0500 removing x4
Source | SS df MS Number of obs = 54
-------------+------------------------------ F( 3, 50) = 586.04
Model | 3.86291372 3 1.28763791 Prob > F = 0.0000
Residual | .109858708 50 .002197174 R-squared = 0.9723
-------------+------------------------------ Adj R-squared = 0.9707
Total | 3.97277243 53 .07495797 Root MSE = .04687
------------------------------------------------------------------------------
logy | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .0692251 .0040779 16.98 0.000 .0610343 .0774159
x3 | .0095236 .0003064 31.08 0.000 .0089082 .0101391
x2 | .0092945 .0003825 24.30 0.000 .0085263 .0100628
_cons | .4836209 .0426287 11.34 0.000 .3979985 .5692432
------------------------------------------------------------------------------
* Stata 8 code.
vif
* Stata 9 code and output.
estat vif
Variable | VIF 1/VIF
-------------+----------------------
x1 | 1.03 0.970108
x3 | 1.02 0.977506
x2 | 1.01 0.991774
-------------+----------------------
Mean VIF | 1.02
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