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Table 7.3, page 189.
use http://www.ats.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.
Note: 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.
Note: Create variable c with weights from book.
generate c = 1.11 if region==1
replace c = 1.439 if region==2
replace c = .46 if region==3
replace c = .898 if region==4
table region, cont(freq mean c)
----------+-----------------------
Region | Freq. mean(c)
----------+-----------------------
1 | 9 1.11
2 | 12 1.439
3 | 16 .46
4 | 12 .898
----------+-----------------------
Computing the weights from the data regress y x1 x2 x3 predict r, resid generate r2 = r^2 egen s2 = mean(r2), by(region) summarize r2 generate c = sqrt(s2/r(mean)) table region, contents(freq mean c) |
Part of Table 7.7, page 195.
regress y x1 x2 x3 [aw=1/c^2]
Source | SS df MS Number of obs = 49
---------+------------------------------ F( 3, 45) = 46.77
Model | 75943.7321 3 25314.5774 Prob > F = 0.0000
Residual | 24354.9225 45 541.2205 R-squared = 0.7572
---------+------------------------------ Adj R-squared = 0.7410
Total | 100298.655 48 2089.5553 Root MSE = 23.264
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
x1 | .0622771 .0078648 7.918 0.000 .0464366 .0781176
x2 | .8742748 .2002008 4.367 0.000 .4710496 1.2775
x3 | .0293526 .0342384 0.857 0.396 -.039607 .0983123
_cons | -315.5311 78.15444 -4.037 0.000 -472.9422 -158.12
------------------------------------------------------------------------------
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)
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