/* Table 7.3, page 189. */
use https://stats.idre.ucla.edu/stat/stata/examples/chp/p189, clear
list
state y x1 x2 x3 region
1. ME 235 3944 325 508 1
2. NH 231 4578 323 564 1
3. VT 270 4011 328 322 1
4. MA 261 5233 305 846 1
5. RI 300 4780 303 871 1
6. CT 317 5889 307 774 1
7. NY 387 5663 301 856 1
8. NJ 285 5759 310 889 1
9. PA 300 4894 300 715 1
10. OH 221 5012 324 753 2
..
[remainder of output deleted]
/* Table 7.4, page 191 */
regress y x1 x2 x3
Source | SS df MS Number of obs = 50
---------+------------------------------ F( 3, 46) = 22.19
Model | 109020.418 3 36340.1394 Prob > F = 0.0000
Residual | 75347.5819 46 1637.99091 R-squared = 0.5913
---------+------------------------------ Adj R-squared = 0.5647
Total | 184368.00 49 3762.61224 Root MSE = 40.472
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | .0723853 .0116024 6.239 0.000 .0490308 .0957398
x2 | 1.552054 .3146716 4.932 0.000 .9186534 2.185456
x3 | -.004269 .0513929 -0.083 0.934 -.1077175 .0991794
_cons | -556.568 123.1953 -4.518 0.000 -804.5472 -308.5889
------------------------------------------------------------------------------
/* Figure 7.3, page 191. */
/* In the book the outlying data point is AL, in our data set that
point corresponds to AK. */
predict p
predict r, rstandard
graph twoway (scatter r p) (scatter r p if state == "AK", mlabel(state)), ///
ylabel(-2.5(1.25)2.5) xlabel(225(75)450)
/* Figure 7.4, page 191 */
graph twoway scatter r region, ylabel(-1.25(1.25)2.5) xlabel(1(1)4)
/* Figure 7.5, page 192 */
graph twoway scatter r x1, ylabel(-1.25(1.25)2.5)
xlabel(3750(750)6000)
/* Figure 7.6, page 192 */
graph twoway scatter r x2, ylabel(-1.25(1.25)2.5) xlabel(300(25)375)
/* Figure 7.7, page 192 */
graph twoway scatter r x3, ylabel(-1.25(1.25)2.5) xlabel(450(150)900)
/* Table 7.5, page 193 */
drop if state=="AK"
regress y x1 x2 x3
Source | SS df MS Number of obs = 49
---------+------------------------------ F( 3, 45) = 14.80
Model | 56943.7919 3 18981.264 Prob > F = 0.0000
Residual | 57699.7591 45 1282.21687 R-squared = 0.4967
---------+------------------------------ Adj R-squared = 0.4631
Total | 114643.551 48 2388.40731 Root MSE = 35.808
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | .0482933 .012147 3.976 0.000 .0238281 .0727586
x2 | .8869283 .33114 2.678 0.010 .219978 1.553879
x3 | .0667917 .04934 1.354 0.183 -.0325841 .1661675
_cons | -277.5773 132.4229 -2.096 0.042 -544.2906 -10.86399
------------------------------------------------------------------------------
/* Figure 7.8, page 194 */
predict p2
predict r2, rstandard
graph twoway scatter r2 p2, ylabel(-1.25 0 1.25) xlabel(240 280 320)
/* Figure 7.9, page 194 */
graph twoway scatter r2 region, ylabel(-2.5(1.25)2.5) xlabel(1(1)4)
/* Part of Table 7.6, page 195 */
/* Computing the weights from the data */
regress y x1 x2 x3
predict e, resid
generate e2 = e^2
bysort region: gen count = _N
gen e2_adj = e2/(count-1)
egen s2 = sum(e2_adj), by(region)
summarize e2
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
e2 | 49 1177.546 1529.095 .0054078 6581.732
generate c = sqrt(s2/r(mean))
table region, contents(freq mean c)
----------------------------------
Region | Freq. mean(c)
----------+-----------------------
1 | 9 1.177438
2 | 12 1.502558
3 | 16 .475338
4 | 12 .9383478
----------------------------------
/* Part of Table 7.7, page 195 */
regress y x1 x2 x3 [aw=1/c^2]
(sum of wgt is 9.6249e+01)
Source | SS df MS Number of obs = 49
-------------+------------------------------ F( 3, 45) = 47.62
Model | 76012.6369 3 25337.5456 Prob > F = 0.0000
Residual | 23943.4288 45 532.076197 R-squared = 0.7605
-------------+------------------------------ Adj R-squared = 0.7445
Total | 99956.0657 48 2082.41804 Root MSE = 23.067
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .0624611 .0078028 8.00 0.000 .0467455 .0781767
x2 | .8739911 .1983961 4.41 0.000 .4744008 1.273581
x3 | .0289241 .0339939 0.85 0.399 -.0395432 .0973914
_cons | -316.0237 77.41892 -4.08 0.000 -471.9535 -160.094
------------------------------------------------------------------------------
/* Figure 7.10, page 196 */
/* Note 1: Predicted values and residuals need to be adjusted for by the weights used in the wls.*/
/* Note 2: For this figure and the next, Stata does not compute standardized residuals for
weighted data, therefore we are going to use the unstandardized residuals.*/
predict p3
predict r3, residual
generate wp = p3*1/c
generate wr = r3*1/c
graph twoway scatter wr wp, xlabel(250(125)750)
/* Figure 7.11, page 196 */
graph twoway scatter wr region, xlabel(1(1)4)
