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Inputting the data shown on page 241.
input x1 x2 y 68.5 16.7 174.4 45.2 16.8 164.4 91.3 18.2 244.2 47.8 16.3 154.6 46.9 17.3 181.6 66.1 18.2 207.5 49.5 15.9 152.8 52.0 17.2 163.2 48.9 16.6 145.4 38.4 16.0 137.2 87.9 18.3 241.9 72.8 17.1 191.1 88.4 17.4 232.0 42.9 15.8 145.3 52.5 17.8 161.1 85.7 18.4 209.7 41.3 16.5 146.4 51.7 16.3 144.0 89.6 18.1 232.6 82.7 19.1 224.1 52.3 16.0 166.5 end label var x1 "targtpop" label var x2 "dispoinc"
Creating the x1x2 variable to be used in Fig. 6.7.
generate x1x2 = x1*x2
Figure 6.4a, page 237. Scatterplot matrix.
graph matrix y x1 x2, half
Fig. 6.4b, p. 237. Correlation matrix.
summarize y x1 x2
Variable | Obs Mean Std. Dev. Min Max
-------------+-----------------------------------------------------
y | 21 181.9048 36.1913 137.2 244.2
x1 | 21 62.01905 18.62033 38.4 91.3
x2 | 21 17.14286 .9703461 15.8 19.1
corr y x1 x2
(obs=21)
| y x1 x2
-------------+---------------------------
y | 1.0000
x1 | 0.9446 1.0000
x2 | 0.8358 0.7813 1.0000
Fig. 6.5a and b, p. 241.
regress y x1 x2
Source | SS df MS Number of obs = 21
-------------+------------------------------ F( 2, 18) = 99.10
Model | 24015.2826 2 12007.6413 Prob > F = 0.0000
Residual | 2180.92749 18 121.162638 R-squared = 0.9167
-------------+------------------------------ Adj R-squared = 0.9075
Total | 26196.2101 20 1309.8105 Root MSE = 11.007
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1.45456 .2117818 6.87 0.000 1.009623 1.899497
x2 | 9.365501 4.063958 2.30 0.033 .8274414 17.90356
_cons | -68.85708 60.01695 -1.15 0.266 -194.948 57.23386
------------------------------------------------------------------------------
predict fitted
predict resid, rresid
Show all variables, including fitted and residual as shown in Fig. 6.5b, p. 24.
list y x1 x2 fitted resid
y x1 x2 fitted resid
1. 174.4 68.5 16.7 187.1841 -12.78413
2. 164.4 45.2 16.8 154.2294 10.17057
3. 244.2 91.3 18.2 234.3963 9.803662
4. 154.6 47.8 16.3 153.3285 1.271483
5. 181.6 46.9 17.3 161.3849 20.21508
6. 207.5 66.1 18.2 197.7414 9.758573
7. 152.8 49.5 15.9 152.0551 .7449242
8. 163.2 52 17.2 167.8666 -4.666642
9. 145.4 48.9 16.6 157.7382 -12.33821
10. 137.2 38.4 16 136.846 .3539732
11. 241.9 87.9 18.3 230.3874 11.51263
12. 191.1 72.8 17.1 197.1849 -6.084922
13. 232 88.4 17.4 222.6857 9.314301
14. 145.3 42.9 15.8 141.5184 3.78156
15. 161.1 52.5 17.8 174.2132 -13.1132
16. 209.7 85.7 18.4 228.1239 -18.42389
17. 146.4 41.3 16.5 145.747 .6530005
18. 144 51.7 16.3 159.0013 -15.00131
19. 232.6 89.6 18.1 230.987 1.612983
20. 224.1 82.7 19.1 230.3161 -6.216054
21. 166.5 52.3 16 157.0644 9.435602
Figure 6.7, page 246, showing 4 different diagnostic plots.
rvfplot, ylabel(-25(10)25) xlabel(120(50)270)
rvpplot x1, ylabel(-25(10)25) xlabel(30(10)100)
rvpplot x2, ylabel(-25(10)25) xlabel(15(1)20)
graph twoway scatter resid x1x2, ylabel(-25(10)25) xlabel(500(500)2000)
Figure 6.8a, page 247.
generate absresid = abs(resid) graph twoway scatter absresid fitted, ylabel(0(5)25) xlabel(120(50)270)
Figure 6.8b, page 247, normal quantile plot.
qnorm resid, ylabel(-30(10)30) xlabel(-30(10)30)
Estimation of Mean Response and Prediction Limits for New Observations, p. 249-251.
Adding extra lines of data in order to predict.
clear input x1 x2 y 68.5 16.7 174.4 45.2 16.8 164.4 91.3 18.2 244.2 47.8 16.3 154.6 46.9 17.3 181.6 66.1 18.2 207.5 49.5 15.9 152.8 52.0 17.2 163.2 48.9 16.6 145.4 38.4 16.0 137.2 87.9 18.3 241.9 72.8 17.1 191.1 88.4 17.4 232.0 42.9 15.8 145.3 52.5 17.8 161.1 85.7 18.4 209.7 41.3 16.5 146.4 51.7 16.3 144.0 89.6 18.1 232.6 82.7 19.1 224.1 52.3 16.0 166.5 65.4 17.6 . 53.1 17.7 . end
Getting the predicted value and the CI's for E[Yh] and Yh(new), p. 249-251.
Upper and Lower CLMean is for E[Yh] and Upper and Lower CL is for Yh(new). Note: This includes observation 22 and 23.
regress y x1 x2
Source | SS df MS Number of obs = 21
-------------+------------------------------ F( 2, 18) = 99.10
Model | 24015.2826 2 12007.6413 Prob > F = 0.0000
Residual | 2180.92749 18 121.162638 R-squared = 0.9167
-------------+------------------------------ Adj R-squared = 0.9075
Total | 26196.2101 20 1309.8105 Root MSE = 11.007
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1.45456 .2117818 6.87 0.000 1.009623 1.899497
x2 | 9.365501 4.063958 2.30 0.033 .8274414 17.90356
_cons | -68.85708 60.01695 -1.15 0.266 -194.948 57.23386
------------------------------------------------------------------------------
predict fitted
predict resid, resid
predict stdp, stdp
predict stdf, stdf
generate umean = fitted+2.101*stdp
generate lmean = fitted -2.101*stdp
generate upre = fitted+2.101*stdf
generate lpre = fitted-2.101*stdf
list y fitted lmean umean lpre upre resid
y fitted lmean umean lpre upre resid
1. 174.4 187.1841 179.1144 195.2539 162.6901 211.6782 -12.78413
2. 164.4 154.2294 146.7588 161.7001 129.9262 178.5326 10.17057
3. 244.2 234.3963 224.7565 244.0361 209.3412 259.4515 9.803662
4. 154.6 153.3285 146.5358 160.1212 129.2251 177.432 1.271483
5. 181.6 161.3849 152.0774 170.6924 136.4557 186.3141 20.21508
6. 207.5 197.7414 188.5421 206.9408 172.8524 222.6305 9.758573
7. 152.8 152.0551 143.2948 160.8153 127.325 176.7852 .7449242
8. 163.2 167.8666 160.8681 174.8651 143.7044 192.0289 -4.666642
9. 145.4 157.7382 151.5134 163.963 133.7886 181.6878 -12.33821
10. 137.2 136.846 128.4265 145.2656 112.2345 161.4575 .3539732
11. 241.9 230.3874 221.5607 239.2141 205.6336 255.1411 11.51263
12. 191.1 197.1849 190.0186 204.3513 172.9735 221.3963 -6.084922
13. 232 222.6857 211.3806 233.9908 196.9439 248.4275 9.314301
14. 145.3 141.5184 132.7499 150.287 116.7854 166.2515 3.78156
15. 161.1 174.2132 163.629 184.7975 148.7797 199.6467 -13.1132
16. 209.7 228.1239 219.4649 236.7829 203.4295 252.8183 -18.42389
17. 146.4 145.747 137.9038 153.5902 121.3267 170.1673 .6530005
18. 144 159.0013 152.167 165.8357 134.8861 183.1165 -15.00131
19. 232.6 230.987 221.7056 240.2685 206.0675 255.9065 1.612983
20. 224.1 230.3161 218.105 242.5271 204.1637 256.4684 -6.216054
21. 166.5 157.0644 148.494 165.6347 132.4009 181.7279 9.435602
22. . 191.1039 185.2909 196.917 167.258 214.9499 .
23. . 174.1494 164.4877 183.8111 149.0858 199.213 .
predict rsta, rsta
predict rstu, rstu
predict cooksd, cooksd
list rsta rstu cooksd
rsta rstu cooksd
1. -1.23931 -1.259317 .0709783
2. .9763196 .9749785 .0370185
3. .9798224 .9786732 .067294
4. .1208419 .1174848 .0004596
5. 2.006145 2.21261 .259292
6. .9662861 .9644076 .0585049
7. .0731241 .0710744 .0002986
8. -.4448118 -.4346749 .0066487
9. -1.163855 -1.176185 .0352674
10. .0345273 .0335556 .0000607
11. 1.13156 1.14101 .0727753
12. -.5814227 -.5704232 .0119696
13. .969979 .9682962 .0984742
14. .3712687 .3621978 .0077142
15. -1.339868 -1.372351 .158554
16. -1.805076 -1.938412 .1770856
17. .0630611 .0612912 .0001723
18. -1.426554 -1.472072 .0649107
19. .1599861 .1555892 .0016381
20. -.6649696 -.6543212 .0569788
21. .9229192 .9189219 .0451999
22. . . .
23. . . .
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