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Table 7.1, p. 261.
input x1 x2 x3 y 19.5 43.1 29.1 11.9 24.7 49.8 28.2 22.8 30.7 51.9 37.0 18.7 29.8 54.3 31.1 20.1 19.1 42.2 30.9 12.9 25.6 53.9 23.7 21.7 31.4 58.5 27.6 27.1 27.9 52.1 30.6 25.4 22.1 49.9 23.2 21.3 25.5 53.5 24.8 19.3 31.1 56.6 30.0 25.4 30.4 56.7 28.3 27.2 18.7 46.5 23.0 11.7 19.7 44.2 28.6 17.8 14.6 42.7 21.3 12.8 29.5 54.4 30.1 23.9 27.7 55.3 25.7 22.6 30.2 58.6 24.6 25.4 22.7 48.2 27.1 14.8 25.2 51.0 27.5 21.1 end label var x1 "Triceps" label var x2 "Thigh cir." label var x3 "Midarm cir." label var y "body fat" save chch7tab01
Table 7.2, p. 262-263.
regress y x1
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 1, 18) = 44.30
Model | 352.269824 1 352.269824 Prob > F = 0.0000
Residual | 143.119689 18 7.95109386 R-squared = 0.7111
-------------+------------------------------ Adj R-squared = 0.6950
Total | 495.389513 19 26.0731323 Root MSE = 2.8198
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .8571866 .1287808 6.66 0.000 .5866282 1.127745
_cons | -1.496107 3.319235 -0.45 0.658 -8.46956 5.477347
------------------------------------------------------------------------------
regress y x2
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 1, 18) = 60.62
Model | 381.965845 1 381.965845 Prob > F = 0.0000
Residual | 113.423669 18 6.30131492 R-squared = 0.7710
-------------+------------------------------ Adj R-squared = 0.7583
Total | 495.389513 19 26.0731323 Root MSE = 2.5102
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x2 | .8565467 .1100156 7.79 0.000 .6254124 1.087681
_cons | -23.63449 5.657414 -4.18 0.000 -35.52028 -11.74871
------------------------------------------------------------------------------
regress y x1 x2
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 2, 17) = 29.80
Model | 385.438738 2 192.719369 Prob > F = 0.0000
Residual | 109.950775 17 6.46769267 R-squared = 0.7781
-------------+------------------------------ Adj R-squared = 0.7519
Total | 495.389513 19 26.0731323 Root MSE = 2.5432
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .2223526 .3034389 0.73 0.474 -.4178475 .8625527
x2 | .6594218 .2911873 2.26 0.037 .0450704 1.273773
_cons | -19.17425 8.36064 -2.29 0.035 -36.81366 -1.534839
------------------------------------------------------------------------------
regress y x1-x3
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 3, 16) = 21.52
Model | 396.984607 3 132.328202 Prob > F = 0.0000
Residual | 98.4049068 16 6.15030667 R-squared = 0.8014
-------------+------------------------------ Adj R-squared = 0.7641
Total | 495.389513 19 26.0731323 Root MSE = 2.48
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 4.334085 3.015511 1.44 0.170 -2.058512 10.72668
x2 | -2.856842 2.582015 -1.11 0.285 -8.330468 2.616785
x3 | -2.186056 1.595499 -1.37 0.190 -5.568362 1.19625
_cons | 117.0844 99.78238 1.17 0.258 -94.44474 328.6136
------------------------------------------------------------------------------
Table 7.4, p. 267.The first test is for the example of testing one variable, p. 269. The second test is for the example of testing two variables at once, p. 270-271.
test x3
( 1) x3 = 0.0
F( 1, 16) = 1.88
Prob > F = 0.1896
test x2 x3
( 1) x2 = 0.0
( 2) x3 = 0.0
F( 2, 16) = 3.64
Prob > F = 0.0500
Coefficients of partial determination, p. 275.
ry1.2 and ry2.1 are from the first model. ry3.12 is the coefficient from X3 in the second model.
pcorr y x1 x2
(obs=20)
Partial correlation of y with
Variable | Corr. Sig.
-------------+------------------
x1 | 0.1750 0.474
x2 | 0.4814 0.037
display 0.1750^2
.30625
display 0.4814^2
.23174596
pcorr y x1-x3
(obs=20)
Partial correlation of y with
Variable | Corr. Sig.
-------------+------------------
x1 | 0.3381 0.170
x2 | -0.2666 0.285
x3 | -0.3241 0.190
display 0.3381^2
.11431161
display -0.2666^2
-.07107556
display -0.3241^2
-.10504081
Inputting the Dwaine Studio Data from Ch. 6, Table 5 (p. 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 y "sales" label var x1 "targtpop" label var x2 "dispoinc"
Creating the standardized variables of the Dwaine Studios Data, p. 282. Table 7.5b, p. 283.
egen yprime = std(y)
egen x1prime = std(x1)
egen x2prime = std(x2)
list yprime x1prime x2prime
yprime x1prime x2prime
1. -.2073638 .3480579 -.4563901
2. -.4836733 -.9032627 -.3533356
3. 1.721276 1.572526 1.08945
4. -.7544563 -.7636304 -.8686157
5. -.0084207 -.8119646 .1619444
6. .7072207 .2191664 1.08945
7. -.8041921 -.6723323 -1.280839
8. -.5168304 -.5380704 .05889
9. -1.008661 -.7045551 -.5594465
10. -1.235235 -1.268455 -1.177783
11. 1.657725 1.38993 1.192505
12. .2540733 .5789885 -.0441664
13. 1.384179 1.416782 .2650008
14. -1.011424 -1.026784 -1.383895
15. -.5748551 -.5112181 .6772245
16. .7680086 1.271779 1.295561
17. -.9810303 -1.112711 -.6625029
18. -1.047344 -.5541818 -.8686157
19. 1.400758 1.481228 .9863937
20. 1.165895 1.110665 2.016954
21. -.4256482 -.5219591 -1.177783
regress yprime x1prime x2prime, beta
Source | SS df MS Number of obs = 21
-------------+------------------------------ F( 2, 18) = 99.10
Model | 18.3349289 2 9.16746445 Prob > F = 0.0000
Residual | 1.66507101 18 .092503945 R-squared = 0.9167
-------------+------------------------------ Adj R-squared = 0.9075
Total | 19.9999999 20 .999999995 Root MSE = .30414
------------------------------------------------------------------------------
yprime | Coef. Std. Err. t P>|t| Beta
-------------+----------------------------------------------------------------
x1prime | .7483669 .1089611 6.87 0.000 .7483669
x2prime | .2511039 .1089611 2.30 0.033 .2511039
_cons | -4.72e-09 .0663698 -0.00 1.000 .
------------------------------------------------------------------------------
Inputting the data of the Work Crew data.
input x1 x2 y 4 2 42 4 2 39 4 3 48 4 3 51 6 2 49 6 2 53 6 3 61 6 3 60 end label var x1 "Crew size" label var x2 "Bonus Pay" label var y "Crew productivity"
Table 7.6, p. 286.
list
x1 x2 y
1. 4 2 42
2. 4 2 39
3. 4 3 48
4. 4 3 51
5. 6 2 49
6. 6 2 53
7. 6 3 61
8. 6 3 60
Table 7.7, p. 287.
regress y x1 x2
Source | SS df MS Number of obs = 8
-------------+------------------------------ F( 2, 5) = 57.06
Model | 402.25 2 201.125 Prob > F = 0.0004
Residual | 17.625 5 3.525 R-squared = 0.9580
-------------+------------------------------ Adj R-squared = 0.9412
Total | 419.875 7 59.9821429 Root MSE = 1.8775
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 5.375 .6637959 8.10 0.000 3.668658 7.081342
x2 | 9.25 1.327592 6.97 0.001 5.837317 12.66268
_cons | .375 4.740451 0.08 0.940 -11.81072 12.56072
------------------------------------------------------------------------------
regress y x1
Source | SS df MS Number of obs = 8
-------------+------------------------------ F( 1, 6) = 7.35
Model | 231.125 1 231.125 Prob > F = 0.0351
Residual | 188.75 6 31.4583333 R-squared = 0.5505
-------------+------------------------------ Adj R-squared = 0.4755
Total | 419.875 7 59.9821429 Root MSE = 5.6088
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 5.375 1.983001 2.71 0.035 .5227722 10.22723
_cons | 23.5 10.11136 2.32 0.059 -1.241604 48.2416
------------------------------------------------------------------------------
regress y x2
Source | SS df MS Number of obs = 8
-------------+------------------------------ F( 1, 6) = 4.13
Model | 171.125 1 171.125 Prob > F = 0.0885
Residual | 248.75 6 41.4583333 R-squared = 0.4076
-------------+------------------------------ Adj R-squared = 0.3088
Total | 419.875 7 59.9821429 Root MSE = 6.4388
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x2 | 9.25 4.552929 2.03 0.088 -1.890617 20.39062
_cons | 27.25 11.60774 2.35 0.057 -1.153112 55.65311
------------------------------------------------------------------------------
Fig. 7.3, p. 290. The graph matrix command can be used for making a scatterplot matrix.
input x1 x2 x3 y 19.5 43.1 29.1 11.9 24.7 49.8 28.2 22.8 30.7 51.9 37.0 18.7 29.8 54.3 31.1 20.1 19.1 42.2 30.9 12.9 25.6 53.9 23.7 21.7 31.4 58.5 27.6 27.1 27.9 52.1 30.6 25.4 22.1 49.9 23.2 21.3 25.5 53.5 24.8 19.3 31.1 56.6 30.0 25.4 30.4 56.7 28.3 27.2 18.7 46.5 23.0 11.7 19.7 44.2 28.6 17.8 14.6 42.7 21.3 12.8 29.5 54.4 30.1 23.9 27.7 55.3 25.7 22.6 30.2 58.6 24.6 25.4 22.7 48.2 27.1 14.8 25.2 51.0 27.5 21.1 end label var x1 "Triceps" label var x2 "Thigh cir." label var x3 "Midarm cir." label var y "body fat" graph matrix x1 x2 x3, half
Showing correlations of x1 to x3.
corr x1-x3
(obs=20)
| x1 x2 x3
-------------+---------------------------
x1 | 1.0000
x2 | 0.9238 1.0000
x3 | 0.4578 0.0847 1.0000
Inputting data in table 7.9, p. 302.
input y x1 x2 150 0.6 10 86 1.0 10 49 1.4 10 288 0.6 20 157 1.0 20 131 1.0 20 184 1.0 20 109 1.4 20 279 0.6 30 235 1.0 30 224 1.4 30 end label var y "cycles" label var x1 "Charge rate" label var x2 "Temperature" /* Creating new variables */ generate lx1 = round((x1-1)/.4,1) generate lx2 = round((x2-20)/10,1) generate lx1sq = lx1^2 generate lx2sq = lx2^2 generate lx1x2 = lx1*lx2 generate x1sq = x1^2 generate x2sq = x2^2
Correlations at the bottom of page 302.
corr x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq
(obs=11)
| x1 x1sq x2 x2sq lx1 lx1sq lx2 lx2sq
-------------+------------------------------------------------------------------------
x1 | 1.0000
x1sq | 0.9910 1.0000
x2 | 0.0000 0.0000 1.0000
x2sq | 0.0000 0.0059 0.9861 1.0000
lx1 | 1.0000 0.9910 0.0000 0.0000 1.0000
lx1sq | 0.0000 0.1336 0.0000 0.0443 0.0000 1.0000
lx2 | 0.0000 0.0000 1.0000 0.9861 0.0000 0.0000 1.0000
lx2sq | 0.0000 0.0356 0.0000 0.1662 0.0000 0.2667 0.0000 1.0000
Table 7.9, p. 303.
list y x1 x2 x1sq x2sq
y x1 x2 x1sq x2sq
1. 150 .6 10 .36 100
2. 86 1 10 1 100
3. 49 1.4 10 1.96 100
4. 288 .6 20 .36 400
5. 157 1 20 1 400
6. 131 1 20 1 400
7. 184 1 20 1 400
8. 109 1.4 20 1.96 400
9. 279 .6 30 .36 900
10. 235 1 30 1 900
11. 224 1.4 30 1.96 900
list lx1 lx2 lx1sq lx2sq lx1x2
lx1 lx2 lx1sq lx2sq lx1x2
1. -1 -1 1 1 1
2. 0 -1 0 1 0
3. 1 -1 1 1 -1
4. -1 0 1 0 0
5. 0 0 0 0 0
6. 0 0 0 0 0
7. 0 0 0 0 0
8. 1 0 1 0 0
9. -1 1 1 1 -1
10. 0 1 0 1 0
11. 1 1 1 1 1
summarize x1 x2
Variable | Obs Mean Std. Dev. Min Max
-------------+-----------------------------------------------------
x1 | 11 1 .3098386 .6 1.4
x2 | 11 20 7.745967 10 30
Table 7.7, p. 304.,Fig. 7.8a-7.8c, p. 304.
Test1 is the Partial F-test on p. 306.
regress y lx1 lx2 lx1sq lx2sq lx1x2
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 5, 5) = 10.57
Model | 55365.5614 5 11073.1123 Prob > F = 0.0109
Residual | 5240.4386 5 1048.08772 R-squared = 0.9135
-------------+------------------------------ Adj R-squared = 0.8271
Total | 60606.00 10 6060.60 Root MSE = 32.374
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 | -55.83333 13.2167 -4.22 0.008 -89.80795 -21.85871
lx2 | 75.5 13.2167 5.71 0.002 41.52538 109.4746
lx1sq | 27.39474 20.34008 1.35 0.236 -24.8911 79.68058
lx2sq | -10.60526 20.34008 -0.52 0.624 -62.8911 41.68058
lx1x2 | 11.5 16.18709 0.71 0.509 -30.11024 53.11024
_cons | 162.8421 16.60761 9.81 0.000 120.1509 205.5333
------------------------------------------------------------------------------
predict resid, resid
test lx1sq lx2sq lx1x2
( 1) lx1sq = 0.0
( 2) lx2sq = 0.0
( 3) lx1x2 = 0.0
F( 3, 5) = 0.78
Prob > F = 0.5527
Fig. 7.8a, p. 304.
rvfplot, ylabel(-40(20)60) xlabel(0(100)300)
Fig. 7.8b, p. 304.
rvpplot lx1, ylabel(-40(20)60) xlabel(-2(1)2)
Fig. 7.8c, p. 304.
rvpplot lx2, ylabel(-40(20)60) xlabel(-2(1)2)
Fig. 7.8d, p. 304.
qnorm resid, ylabel(-50(20)50) xlabel(-60(20)60)
First Order Models using transformed and not transformed variables, p. 306 and p. 307.
regress y lx1 lx2
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 2, 8) = 27.48
Model | 52905.6667 2 26452.8333 Prob > F = 0.0003
Residual | 7700.33333 8 962.541667 R-squared = 0.8729
-------------+------------------------------ Adj R-squared = 0.8412
Total | 60606.00 10 6060.60 Root MSE = 31.025
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lx1 | -55.83333 12.66584 -4.41 0.002 -85.04082 -26.62584
lx2 | 75.5 12.66584 5.96 0.000 46.29251 104.7075
_cons | 172 9.354346 18.39 0.000 150.4288 193.5712
------------------------------------------------------------------------------
regress y x1 x2
Source | SS df MS Number of obs = 11
-------------+------------------------------ F( 2, 8) = 27.48
Model | 52905.6667 2 26452.8333 Prob > F = 0.0003
Residual | 7700.33333 8 962.541667 R-squared = 0.8729
-------------+------------------------------ Adj R-squared = 0.8412
Total | 60606.00 10 6060.60 Root MSE = 31.025
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | -139.5833 31.66461 -4.41 0.002 -212.6021 -66.56461
x2 | 7.55 1.266584 5.96 0.000 4.629251 10.47075
_cons | 160.5833 41.61545 3.86 0.005 64.61794 256.5487
------------------------------------------------------------------------------
Creating centered variables for the Body Fat dataset from table 7.1, p. 261.
clear input x1 x2 x3 y 19.5 43.1 29.1 11.9 24.7 49.8 28.2 22.8 30.7 51.9 37.0 18.7 29.8 54.3 31.1 20.1 19.1 42.2 30.9 12.9 25.6 53.9 23.7 21.7 31.4 58.5 27.6 27.1 27.9 52.1 30.6 25.4 22.1 49.9 23.2 21.3 25.5 53.5 24.8 19.3 31.1 56.6 30.0 25.4 30.4 56.7 28.3 27.2 18.7 46.5 23.0 11.7 19.7 44.2 28.6 17.8 14.6 42.7 21.3 12.8 29.5 54.4 30.1 23.9 27.7 55.3 25.7 22.6 30.2 58.6 24.6 25.4 22.7 48.2 27.1 14.8 25.2 51.0 27.5 21.1 end egen my = mean(y) egen mx1 = mean(x1) egen mx2 = mean(x2) egen mx3 = mean(x3) generate cy = y - my generate cx1 = x1 - mx1 generate cx2 = x2 - mx2 generate cx3 = x3 - mx3 generate cx1x2 = cx1*cx2 generate cx1x3 = cx1*cx3 generate cx2x3 = cx2*cx3
Fitting the Regression model (7.93), p. 315. The test of cx1x2 cx1x3 cx2x3 is the test of the interaction terms.
regress y cx1 cx2 cx3 cx1x2 cx1x3 cx2x3
Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 6, 13) = 10.07
Model | 407.699483 6 67.9499138 Prob > F = 0.0003
Residual | 87.6900304 13 6.74538696 R-squared = 0.8230
-------------+------------------------------ Adj R-squared = 0.7413
Total | 495.389513 19 26.0731323 Root MSE = 2.5972
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cx1 | 3.437794 3.578665 0.96 0.354 -4.293441 11.16903
cx2 | -2.094706 3.036769 -0.69 0.502 -8.655245 4.465834
cx3 | -1.61633 1.90721 -0.85 0.412 -5.736607 2.503947
cx1x2 | .0088755 .0308505 0.29 0.778 -.0577729 .0755238
cx1x3 | -.0847909 .0734178 -1.15 0.269 -.2434004 .0738186
cx2x3 | .0904155 .0920013 0.98 0.344 -.1083413 .2891723
_cons | 20.5269 1.073625 19.12 0.000 18.20747 22.84632
------------------------------------------------------------------------------
test cx1x2 cx1x3 cx2x3
( 1) cx1x2 = 0.0
( 2) cx1x3 = 0.0
( 3) cx2x3 = 0.0
F( 3, 13) = 0.53
Prob > F = 0.6699
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