use https://stats.idre.ucla.edu/stat/stata/examples/chp/p203, clear generate index = _n
Table 8.1, page 203.
Note: Create the variable index equal to the observation number.
list
year quarter expendit stock index
1. 1952 1 214.6 159.3 1
2. 1952 2 217.7 161.2 2
3. 1952 3 219.6 162.8 3
4. 1952 4 227.2 164.6 4
5. 1953 1 230.9 165.9 5
6. 1953 2 233.3 167.9 6
7. 1953 3 234.1 168.3 7
8. 1953 4 232.3 169.7 8
9. 1954 1 233.7 170.5 9
10. 1954 2 236.5 171.6 10
11. 1954 3 238.7 173.9 11
12. 1954 4 243.2 176.1 12
13. 1955 1 249.4 178 13
14. 1955 2 254.3 179.1 14
15. 1955 3 260.9 180.2 15
16. 1955 4 263.3 181.2 16
17. 1956 1 265.6 181.6 17
18. 1956 2 268.2 182.5 18
19. 1956 3 270.4 183.3 19
20. 1956 4 275.6 184.3 20
Table 8.2, page 203.
regress expendit stock Source | SS df MS Number of obs = 20 ---------+------------------------------ F( 1, 18) = 403.22 Model | 6395.76619 1 6395.76619 Prob > F = 0.0000 Residual | 285.511158 18 15.861731 R-squared = 0.9573 ---------+------------------------------ Adj R-squared = 0.9549 Total | 6681.27735 19 351.646176 Root MSE = 3.9827 ------------------------------------------------------------------------------ expendit | Coef. Std. Err. t P>|t| [95% Conf. Interval] ---------+-------------------------------------------------------------------- stock | 2.30037 .1145584 20.080 0.000 2.059692 2.541049 _cons | -154.7191 19.85004 -7.794 0.000 -196.4225 -113.0157 ------------------------------------------------------------------------------
Figure 8.1, page 204.
Note: The connect(l) option is used to connect the plotted points with a line.
predict r, rstandard graph twoway scatter r index, c(l) ylabel(-1 0 1) xlabel(4(4)20) yline(0)
Durbin-Watson statistic, page 205.
tsset index *Stata 8 code. dwstat * Stata 9 code and output. estat dwatson Durbin-Watson d-statistic( 2, 20) = .3282105
Equation at the bottom of page 207.
Note: The prais command is used to perform Cochrane-Orcutt transformation. The two option stops the procedure after the first estimate of rho.
prais expendit stock, corc two rhotype(tsc)
Iteration 0: rho = 0.0000
Iteration 1: rho = 0.7506
Cochrane-Orcutt AR(1) regression -- twostep estimates
Source | SS df MS Number of obs = 19
---------+------------------------------ F( 1, 17) = 74.20
Model | 379.837381 1 379.837381 Prob > F = 0.0000
Residual | 87.0261726 17 5.11918663 R-squared = 0.8136
---------+------------------------------ Adj R-squared = 0.8026
Total | 466.863554 18 25.9368641 Root MSE = 2.2626
------------------------------------------------------------------------------
expendit | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
stock | 2.643445 .3068823 8.614 0.000 1.99598 3.29091
_cons | -215.3112 54.59925 -3.943 0.001 -330.5056 -100.1169
------------------------------------------------------------------------------
rho | .7506127
------------------------------------------------------------------------------
Durbin-Watson statistic (original) 0.328210
Durbin-Watson statistic (transformed) 1.425962
Iterative solution; Table 8.1, page 209.
prais expendit stock, corc
Iteration 0: rho = 0.0000
Iteration 1: rho = 0.8745
Iteration 2: rho = 0.8422
Iteration 3: rho = 0.8295
Iteration 4: rho = 0.8255
Iteration 5: rho = 0.8244
Iteration 6: rho = 0.8242
Iteration 7: rho = 0.8241
Iteration 8: rho = 0.8241
Iteration 9: rho = 0.8241
Iteration 10: rho = 0.8241
Iteration 11: rho = 0.8241
Cochrane-Orcutt AR(1) regression -- iterated estimates
Source | SS df MS Number of obs = 19
---------+------------------------------ F( 1, 17) = 39.79
Model | 198.494803 1 198.494803 Prob > F = 0.0000
Residual | 84.8128884 17 4.98899343 R-squared = 0.7006
---------+------------------------------ Adj R-squared = 0.6830
Total | 283.307691 18 15.7393162 Root MSE = 2.2336
------------------------------------------------------------------------------
expendit | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
stock | 2.75306 .4364632 6.308 0.000 1.832204 3.673917
_cons | -235.4889 78.61251 -2.996 0.008 -401.3468 -69.631
------------------------------------------------------------------------------
rho | .8240543
------------------------------------------------------------------------------
Durbin-Watson statistic (original) 0.328210
Durbin-Watson statistic (transformed) 1.601029
Table 8.4, page 211.
use https://stats.idre.ucla.edu/stat/stata/examples/chp/p211, clear
generate index = _n
list
h p d index
1. .0909 2.2 .03635 1
2. .08942 2.222 .03345 2
3. .09755 2.244 .0387 3
4. .0955 2.267 .03745 4
5. .09678 2.28 .04063 5
6. .10327 2.289 .04237 6
7. .10513 2.289 .04715 7
8. .1084 2.29 .04883 8
9. .10822 2.299 .04836 9
10. .10741 2.3 .0516 10
11. .10751 2.3 .04879 11
12. .11429 2.34 .05523 12
13. .11048 2.386 .0477 13
14. .11604 2.433 .05282 14
15. .11688 2.482 .05473 15
16. .12044 2.532 .05531 16
17. .12125 2.58 .05898 17
18. .1208 2.605 .06267 18
19. .12368 2.631 .05462 19
20. .12679 2.658 .05672 20
21. .12996 2.684 .06674 21
22. .13445 2.711 .06451 22
23. .13325 2.738 .06313 23
24. .13863 2.766 .06573 24
25. .13964 2.793 .07229 25
Table 8.5, page 212.
regress h p
Source | SS df MS Number of obs = 25
---------+------------------------------ F( 1, 23) = 284.51
Model | .004736628 1 .004736628 Prob > F = 0.0000
Residual | .000382913 23 .000016648 R-squared = 0.9252
---------+------------------------------ Adj R-squared = 0.9220
Total | .005119541 24 .000213314 Root MSE = .00408
------------------------------------------------------------------------------
h | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
p | .0714097 .0042336 16.867 0.000 .0626518 .0801675
_cons | -.060884 .010416 -5.845 0.000 -.0824311 -.0393369
------------------------------------------------------------------------------
Figure 8.3, page 212.
predict r1, rstandard graph twoway scatter r1 index, c(l) ylabel(-2(1)1) xlabel(5(5)25) yline(0)
Table 8.6, page 213.
regress h p d
Source | SS df MS Number of obs = 25
---------+------------------------------ F( 2, 22) = 397.58
Model | .004981709 2 .002490854 Prob > F = 0.0000
Residual | .000137833 22 6.2651e-06 R-squared = 0.9731
---------+------------------------------ Adj R-squared = 0.9706
Total | .005119541 24 .000213314 Root MSE = .0025
------------------------------------------------------------------------------
h | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
p | .0346557 .0064248 5.394 0.000 .0213315 .0479798
d | .7604638 .1215875 6.254 0.000 .5083067 1.012621
_cons | -.0104272 .0102913 -1.013 0.322 -.0317699 .0109156
------------------------------------------------------------------------------
Figure 8.4, page 213.
predict r2, rstandard graph twoway scatter r2 index, c(l) ylabel(-2(1)1) xlabel(5(5)25) yline(0)
Equation top of page 214.
regress h p d, beta
Source | SS df MS Number of obs = 25
---------+------------------------------ F( 2, 22) = 397.58
Model | .004981709 2 .002490854 Prob > F = 0.0000
Residual | .000137833 22 6.2651e-06 R-squared = 0.9731
---------+------------------------------ Adj R-squared = 0.9706
Total | .005119541 24 .000213314 Root MSE = .0025
------------------------------------------------------------------------------
h | Coef. Std. Err. t P>|t| Beta
---------+--------------------------------------------------------------------
p | .0346557 .0064248 5.394 0.000 .4668058
d | .7604638 .1215875 6.254 0.000 .5412634
_cons | -.0104272 .0102913 -1.013 0.322 .
------------------------------------------------------------------------------
use https://stats.idre.ucla.edu/stat/stata/examples/chp/p217, clear generate index = _n
Table 8.7, page 215.
regress sales pdi
Source | SS df MS Number of obs = 40
---------+------------------------------ F( 1, 38) = 152.55
Model | 1390.73632 1 1390.73632 Prob > F = 0.0000
Residual | 346.433325 38 9.11666646 R-squared = 0.8006
---------+------------------------------ Adj R-squared = 0.7953
Total | 1737.16965 39 44.5428115 Root MSE = 3.0194
------------------------------------------------------------------------------
sales | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
pdi | .1979142 .0160241 12.351 0.000 .1654752 .2303533
_cons | 12.39215 2.539425 4.880 0.000 7.251353 17.53295
------------------------------------------------------------------------------
Figure 8.5, page 215.
predict r3, rstandard
graph twoway (scatter r3 index if season == 1, msymbol(X) yvarlabel("Q1 & Q4")) ///
(scatter r3 index if season == 0, msymbol(Oh) yvarlabel("Q2 & Q3")), ///
ylabel(-1.5(.75)1.5)
Table 8.8, page 217.
list
quarter sales pdi season index
1. Q1/64 37 109 1 1
2. Q2/64 33.5 115 0 2
3. Q3/64 30.8 113 0 3
4. Q4/64 37.9 116 1 4
5. Q1/65 37.4 118 1 5
6. Q2/65 31.6 120 0 6
7. Q3/65 34 122 0 7
8. Q4/65 38.1 124 1 8
9. Q1/66 40 126 1 9
10. Q2/66 35 128 0 10
..
[remainder of output omitted]
Table 8.9, page 217.
regress sales pdi season
Source | SS df MS Number of obs = 40
---------+------------------------------ F( 2, 37) = 652.94
Model | 1689.30565 2 844.652823 Prob > F = 0.0000
Residual | 47.8640016 37 1.29362167 R-squared = 0.9724
---------+------------------------------ Adj R-squared = 0.9710
Total | 1737.16965 39 44.5428115 Root MSE = 1.1374
------------------------------------------------------------------------------
sales | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------+--------------------------------------------------------------------
pdi | .1986837 .0060363 32.915 0.000 .186453 .2109145
season | 5.464342 .3596822 15.192 0.000 4.735557 6.193127
_cons | 9.540204 .9748254 9.787 0.000 7.56502 11.51539
------------------------------------------------------------------------------
Figure 8.7, page 218.
predict r4, rstandard
graph twoway (scatter r4 index if season == 1, msymbol(X) yvarlabel("Q1 & Q4")) ///
(scatter r4 index if season == 0, msymbol(Oh) yvarlabel("Q2 & Q3")), ///
ylabel(-1.25 0 1.25)
