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Workshop 7 Minitutorial (p4)

*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 01 Dec 2010 17:39:42 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq.htm/, Retrieved Wed, 01 Dec 2010 18:44:02 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1 162556 162556 807 807 213118 213118 6282154 1 29790 29790 444 444 81767 81767 4321023 1 87550 87550 412 412 153198 153198 4111912 0 84738 0 428 0 -26007 0 223193 1 54660 54660 315 315 126942 126942 1491348 1 42634 42634 168 168 157214 157214 1629616 0 40949 0 263 0 129352 0 1398893 1 45187 45187 267 267 234817 234817 1926517 1 37704 37704 228 228 60448 60448 983660 1 16275 16275 129 129 47818 47818 1443586 0 25830 0 104 0 245546 0 1073089 0 12679 0 122 0 48020 0 984885 1 18014 18014 393 393 -1710 -1710 1405225 0 43556 0 190 0 32648 0 227132 1 24811 24811 280 280 95350 95350 929118 0 6575 0 63 0 151352 0 1071292 0 7123 0 102 0 288170 0 638830 1 21950 21950 265 265 114337 114337 856956 1 37597 37597 234 234 37884 37884 992426 0 17821 0 277 0 122844 0 444477 1 12988 12988 73 73 82340 82340 857217 1 22330 22330 67 67 79801 79801 711969 0 13326 0 103 0 165548 0 702380 0 16189 0 290 0 116384 0 358589 0 7146 0 83 0 134028 0 297978 0 15824 0 56 0 63838 0 585715 1 27664 27664 236 236 74996 etc...
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time18 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 195390.249959622 + 13727.2209540143Group[t] + 5.0507577283188Costs[t] + 18.1676444126807Costs_g[t] -186.494340070026Orders[t] + 2735.48083994377Orders_g[t] + 1.89878042590143Dividends[t] -1.74203696507324Dividends_g[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)195390.24995962227782.9337887.032700
Group13727.220954014349618.7187490.27670.7821810.39109
Costs5.05075772831882.8546341.76930.0775610.038781
Costs_g18.16764441268073.4811655.218800
Orders-186.494340070026415.008435-0.44940.6533910.326696
Orders_g2735.48083994377532.4763085.137300
Dividends1.898780425901430.3894444.87562e-061e-06
Dividends_g-1.742036965073240.636243-2.7380.0064420.003221


Multiple Linear Regression - Regression Statistics
Multiple R0.903579223349188
R-squared0.816455412868321
Adjusted R-squared0.813418031993802
F-TEST (value)268.802447436717
F-TEST (DF numerator)7
F-TEST (DF denominator)423
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation185959.742030784
Sum Squared Residuals14627773852553.9


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821546073845.00762885208308.992371153
243210232045360.119199492275662.88080051
341119123316083.80101808795828.198981917
4223193494180.19825551-270987.19825551
514913482301063.40780535-809715.40780535
616296161651882.82622244-22266.8262224406
71398893598776.762389333800116.237610667
819265171975672.83316656-49155.8331665625
99836601675187.85592924-691527.855929238
101443586923311.383051998520274.616948002
111073089772693.849173205300395.150826795
12984885327855.933760219657029.066239781
1314052251628857.43021397-223632.430213965
14227132441938.5123058-214806.512305800
159291181513850.95538859-584732.95538859
161071292504234.053619939567057.946380061
17638830759515.929903308-120685.929903308
188569561412164.39745583-555208.397455829
199924261684460.64644927-692034.646449266
20444477466994.653876028-22517.6538760284
21857217709660.348976314147556.651023686
22711969910874.771131246-198905.771131246
23702380557827.032367115144552.967632885
24358589444061.269291179-85472.2692911787
25297978470493.677383092-172515.677383092
26585715386084.102037312199630.897962688
276579541464747.29430072-806793.29430072
28209458300995.290893086-91537.2908930861
29786690293404.303353873493285.696646127
30439798336946.755795499102851.244204501
31688779367275.833512626321503.166487374
32574339678597.339668132-104258.339668132
33741409485863.072100253255545.927899747
34597793437106.916094432160686.083905568
35644190777170.091117332-132980.091117332
36377934444062.030873152-66128.0308731523
37640273401937.117639859238335.882360141
38697458554559.81897148142898.181028520
39550608505654.81889732844953.1811026723
40207393343041.297715615-135648.297715615
41301607444752.378627765-143145.378627765
42345783437366.435950118-91583.4359501182
43501749379773.422948271121975.577051729
44379983436817.078521217-56834.0785212168
45387475342809.63293846744665.3670615333
46377305374450.0492732492854.95072675078
47370837480584.171338747-109747.171338747
48430866784272.300188387-353406.300188387
49469107440826.65138795228280.3486120476
50194493344352.433548377-149859.433548377
51530670528839.4343225931830.56567740720
52518365673258.595819358-154893.595819358
53491303655119.828675572-163816.828675572
54527021418951.690302029108069.309697971
55233773632400.528985398-398627.528985398
56405972309557.57376674296414.4262332577
57652925308805.118329077344119.881670923
58446211380313.65469520465897.3453047962
59341340381277.028089447-39937.028089447
60387699656041.716774146-268342.716774146
61493408462723.82756931230684.1724306875
62146494311685.816859181-165191.816859181
63414462360168.88833128454293.1116687158
64364304593863.349750775-229559.349750775
65355178310890.65691451844287.3430854825
66357760387982.190079655-30222.1900796546
67261216350441.871048494-89225.871048494
68397144384680.90507030112463.0949296988
69374943437928.936462127-62985.936462127
70424898535207.304517759-110309.304517759
71202055409001.642711227-206946.642711227
72378525288284.78289499090240.2171050097
73310768399041.728188869-88273.7281888689
74325738347054.726748075-21316.7267480746
75394510424753.604722258-30243.6047222578
76247060313244.578349841-66184.578349841
77368078413012.512838504-44934.5128385044
78236761337968.159201884-101207.159201884
79312378324056.296453471-11678.2964534709
80339836276192.94622225763643.0537777426
81347385312743.38769499234641.6123050084
82426280500070.491586663-73790.4915866628
83352850457535.815075265-104685.815075265
84301881271943.32602576729937.6739742332
85377516390241.143581651-12725.1435816511
86357312524676.741071761-167364.741071761
87458343366523.39440187191819.6055981294
88354228393090.445788716-38862.4457887157
89308636400030.425113989-91394.4251139886
90386212391872.571945381-5660.57194538092
91393343380213.38840677413129.6115932262
92378509392542.501955432-14033.5019554321
93452469314837.135621111137631.864378888
94364839454616.213210829-89777.2132108292
95358649268167.40772820890481.5922717925
96376641365962.60773511710678.3922648827
97429112409638.30122582619473.6987741742
98330546309026.87759299721519.1224070031
99403560451904.284940512-48344.2849405121
100317892275646.31251880242245.6874811976
101307528329344.829286999-21816.8292869987
102235133368675.533361962-133542.533361962
103299243408111.713590652-108868.713590652
104314073412814.691721545-98741.6917215452
105368186329122.60610533139063.3938946692
106269661329628.405420849-59967.4054208487
107125390414960.080546457-289570.080546457
108510834312726.504670431198107.495329569
109321896408114.572944107-86218.5729441068
110249898316390.216288781-66492.2162887812
111408881325016.12706710483864.8729328956
112158492380562.808043976-222070.808043976
113292154376605.818155342-84451.818155342
114289513309510.956314473-19997.9563144726
115378049265679.201788172112369.798211828
116343466303477.09684834239988.9031516581
117332743357306.048243208-24563.0482432078
118442882371741.45066274471140.5493372557
119214215301126.827971176-86911.8279711758
120315688312024.4394883273663.56051167286
121375195441117.306681824-65922.3066818242
122334280324790.0194264569489.98057354414
123355864359282.893742161-3418.89374216089
124480382328223.453847911152158.546152089
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154297765307714.039087173-9949.0390871726
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177313267291630.64008377121636.3599162292
178316176220287.35899365595888.641006345
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181359335332788.62128264726546.378717353
182330068260714.55222631069353.4477736903
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186333210261432.26570840271777.7342915977
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188313332312826.083224071505.916775928614
189291787320434.568606761-28647.5686067608
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193315366311818.7840671293547.21593287064
194315380310684.1974203564695.80257964372
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198315380218634.93385512396745.0661448768
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200269587281053.830543781-11466.8305437808
201315380218634.93385512396745.0661448768
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214288985313600.080178237-24615.0801782372
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220322331306352.05180501215978.9481949885
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230315380310684.1974203564695.80257964372
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318297141309661.744313355-12520.7443133550
319315372309754.8776973095617.12230269144
320315380310684.1974203564695.80257964372
321315380310684.1974203564695.80257964372
322315380310684.1974203564695.80257964372
323315380310684.1974203564695.80257964372
324315380218634.93385512396745.0661448768
325315380310684.1974203564695.80257964372
326312502310612.6173111611889.38268883895
327315380218634.93385512396745.0661448768
328315380218634.93385512396745.0661448768
329315380310684.1974203564695.80257964372
330315380310684.1974203564695.80257964372
331315380310684.1974203564695.80257964372
332315380310684.1974203564695.80257964372
333315380310684.1974203564695.80257964372
334313729309775.6086767623953.39132323764
335315388310516.0453009964871.95469900414
336315371311524.1579867683846.84201323173
337296139311606.400128967-15467.4001289666
338315380310684.1974203564695.80257964372
339313880310963.2081361812916.79186381884
340317698307578.40123575710119.5987642430
341295580314252.052866777-18672.0528667772
342315380310684.1974203564695.80257964372
343315380310684.1974203564695.80257964372
344315380310684.1974203564695.80257964372
345308256311396.291548732-3140.29154873190
346315380310684.1974203564695.80257964372
347303677307683.908327522-4006.90832752207
348315380310684.1974203564695.80257964372
349315380310684.1974203564695.80257964372
350319369316875.2125963252493.78740367552
351318690307671.33874761911018.6612523812
352314049310448.8897956293600.11020437062
353325699309647.9208270416051.07917296
354314210313733.415046447476.584953553306
355315380310684.1974203564695.80257964372
356315380310684.1974203564695.80257964372
357322378344774.846283441-22396.8462834415
358315380310684.1974203564695.80257964372
359315380310684.1974203564695.80257964372
360315380310684.1974203564695.80257964372
361315398309947.0683786565450.93162134371
362315380310684.1974203564695.80257964372
363315380310684.1974203564695.80257964372
364308336331078.533071699-22742.533071699
365316386307854.7079887208531.29201127963
366315380310684.1974203564695.80257964372
367315380310684.1974203564695.80257964372
368315380310684.1974203564695.80257964372
369315380310684.1974203564695.80257964372
370315553310479.8022246405073.19777536042
371315380310684.1974203564695.80257964372
372323361309858.52168223113502.4783177685
373336639340761.438546249-4122.43854624877
374307424318788.545991070-11364.5459910695
375315380310684.1974203564695.80257964372
376315380310684.1974203564695.80257964372
377295370300619.640670268-5249.64067026827
378322340311905.29334000010434.7066600004
379319864319991.530114697-127.530114697183
380315380310684.1974203564695.80257964372
381315380310684.1974203564695.80257964372
382317291334143.396449590-16852.3964495896
383280398274419.0275866255978.97241337517
384315380310684.1974203564695.80257964372
385317330312599.8096856104730.19031439036
386238125331298.158081197-93173.1580811967
387327071308775.55519152618295.4448084737
388309038310239.641868781-1201.64186878137
389314210309876.9616594454333.0383405551
390307930308017.886008965-87.8860089653822
391322327314602.9778853427724.0221146576
392292136309189.273663547-17053.2736635471
393263276312770.533504768-49494.5335047677
394367655327007.50556950640647.4944304941
395283910324688.264939876-40778.2649398758
396283587307731.929658870-24144.9296588704
397243650315652.465940225-72002.4659402247
398438493870799.255649715-432306.255649715
399296261318031.746219736-21770.7462197362
400230621366280.009781077-135659.009781077
401304252333892.244579007-29640.2445790068
402333505319776.34999188513728.6500081145
403296919309746.11030031-12827.1103003097
404278990308947.784830045-29957.7848300452
405276898319109.456126981-42211.4561269809
406327007333541.191282400-6534.19128239964
407317046325601.895631564-8555.89563156384
408304555310042.64777046-5487.6477704597
409298096306660.907222566-8564.90722256625
410231861331374.271254753-99513.2712547528
411309422323995.706790381-14573.7067903809
412286963444818.320509747-157855.320509747
413269753283363.023678537-13610.0236785370
414448243379329.76055440868913.2394455916
415165404353837.408482315-188433.408482315
416204325339432.615986805-135107.615986805
417407159274478.157314442132680.842685558
418290476296212.853798829-5736.85379882866
419275311328735.84626784-53424.84626784
420246541323709.912153392-77168.9121533924
421253468332798.083513481-79330.0835134811
422240897333963.081469572-93066.0814695718
423-83265647830.459148747-731095.459148747
424-42143330630.519271306-372773.519271306
425272713307858.58987382-35145.5898738202
426215362547264.948568649-331902.948568649
42742754308988.143361998-266234.143361998
428306275628450.212121089-322175.212121088
429253537387124.073243209-133587.073243209
430372631403346.637644071-30715.6376440710
431-7170325610.81005899-332780.81005899


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1111.85927032485988e-539.29635162429939e-54
1211.00263392570544e-575.0131696285272e-58
1311.10601980010055e-885.53009900050277e-89
1418.16263892189352e-884.08131946094676e-88
1511.05770912546704e-965.28854562733522e-97
1615.7413152061786e-1052.8706576030893e-105
1711.54640562325958e-1117.7320281162979e-112
1815.95794639828382e-1172.97897319914191e-117
1913.57188793742537e-1181.78594396871269e-118
2014.81151002331517e-1192.40575501165758e-119
2114.32343253743218e-1252.16171626871609e-125
2211.33820754234270e-1256.69103771171351e-126
2313.73877916456521e-1271.86938958228260e-127
2411.76526389972943e-1268.82631949864717e-127
2511.11917598573304e-1275.59587992866522e-128
2613.84502639572914e-1291.92251319786457e-129
2711.19201406009211e-1335.96007030046055e-134
2811.64622315941136e-1338.2311157970568e-134
2914.15078246892827e-1432.07539123446414e-143
3013.02355207428962e-1431.51177603714481e-143
3117.80637193659338e-1503.90318596829669e-150
3212.75673353958195e-1501.37836676979097e-150
3311.60273719431306e-1598.01368597156532e-160
3417.72881202109228e-1623.86440601054614e-162
3516.56025167824293e-1623.28012583912147e-162
3613.38842884629086e-1611.69421442314543e-161
3711.88045575241026e-1669.40227876205132e-167
3818.57464565786825e-1724.28732282893413e-172
3913.99812383164209e-1711.99906191582104e-171
4014.76769051238672e-1722.38384525619336e-172
4114.08358264229891e-1722.04179132114946e-172
4215.36396813898839e-1722.68198406949419e-172
4312.23313651114066e-1721.11656825557033e-172
4411.30425897067198e-1716.52129485335988e-172
4513.58343019484389e-1711.79171509742194e-171
4612.67216180413855e-1701.33608090206928e-170
4711.52157373288203e-1727.60786866441016e-173
4814.46986581333374e-1732.23493290666687e-173
4915.12991292281999e-1732.56495646140999e-173
5017.7523036695158e-1743.8761518347579e-174
5113.05009996174115e-1741.52504998087057e-174
5213.62171938597896e-1741.81085969298948e-174
5311.51516660282037e-1737.57583301410187e-174
5418.02064360484783e-1734.01032180242392e-173
5511.11802051604631e-1785.59010258023154e-179
5614.26535138414258e-1782.13267569207129e-178
5713.03937414879899e-1901.51968707439950e-190
5816.00621628803957e-1913.00310814401979e-191
5914.02158432242792e-1902.01079216121396e-190
6017.90582968940891e-1903.95291484470446e-190
6113.54666355024282e-1911.77333177512141e-191
6211.17162029398770e-1935.85810146993848e-194
6313.56497220529922e-1931.78248610264961e-193
6416.99321194136043e-1933.49660597068022e-193
6515.06603030653271e-1922.53301515326635e-192
6614.54134302736806e-1912.27067151368403e-191
6718.52480977484516e-1914.26240488742258e-191
6816.71230100294749e-1903.35615050147374e-190
6913.76716970034019e-1891.88358485017010e-189
7011.54463685424308e-1887.72318427121538e-189
7111.51359929300087e-1877.56799646500437e-188
7215.22765856624178e-1882.61382928312089e-188
7311.50065496475808e-1877.50327482379042e-188
7411.26096886107949e-1866.30484430539743e-187
7519.86294836282537e-1864.93147418141269e-186
7611.17408219985596e-1855.8704109992798e-186
7719.39384606153312e-1854.69692303076656e-185
7819.11019429152963e-1854.55509714576482e-185
7916.65365909765566e-1843.32682954882783e-184
8011.16262912013393e-1845.81314560066966e-185
8118.52335816590092e-1844.26167908295046e-184
8218.74369353771048e-1844.37184676885524e-184
8312.14334602462891e-1831.07167301231446e-183
8411.85875807371569e-1829.29379036857846e-183
8511.58861920325453e-1817.94309601627263e-182
8614.93458899228466e-1822.46729449614233e-182
8716.13365977922775e-1823.06682988961387e-182
8814.97014475280754e-1812.48507237640377e-181
8911.15032019670820e-1805.75160098354099e-181
9019.29086501498095e-1804.64543250749047e-180
9115.68415309470275e-1792.84207654735138e-179
9212.29082129388469e-1781.14541064694234e-178
9312.40004654105336e-1791.20002327052668e-179
9411.37768371543280e-1786.88841857716398e-179
9512.03086227951272e-1781.01543113975636e-178
9614.71313837068924e-1792.35656918534462e-179
9712.22632040224475e-1781.11316020112238e-178
9811.38428720512386e-1776.9214360256193e-178
9919.86038628114007e-1774.93019314057003e-177
10015.38539277285564e-1762.69269638642782e-176
10113.41424291595361e-1751.70712145797680e-175
10215.07370711128602e-1762.53685355564301e-176
10317.42638123564873e-1763.71319061782436e-176
10417.19810894496936e-1763.59905447248468e-176
10513.06571344043405e-1751.53285672021702e-175
10617.38603012784268e-1753.69301506392134e-175
10711.17440049735188e-1765.87200248675938e-177
10811.92678176251249e-1789.63390881256246e-179
10911.17542987875740e-1775.87714939378698e-178
11012.28916063880414e-1771.14458031940207e-177
11111.74172386865118e-1778.70861934325589e-178
11211.8868522846016e-1779.434261423008e-178
11311.02325633370607e-1765.11628166853035e-177
11416.1743533154355e-1763.08717665771775e-176
11511.90702213358560e-1769.53511066792799e-177
11618.8896623715198e-1764.4448311857599e-176
11716.4321445019196e-1753.2160722509598e-175
11812.46399655687796e-1751.23199827843898e-175
11912.19618857556764e-1761.09809428778382e-176
12011.95177340433950e-1759.75886702169751e-176
12117.60814250956001e-1753.80407125478001e-175
12216.03864280822308e-1743.01932140411154e-174
12313.22780794004712e-1731.61390397002356e-173
12413.11101556703685e-1731.55550778351842e-173
12514.21649171481752e-1732.10824585740876e-173
12611.74158839430916e-1738.7079419715458e-174
12711.52212979801707e-1727.61064899008537e-173
12811.34299643374729e-1716.71498216873643e-172
12911.15853699812054e-1705.79268499060268e-171
13019.95592924131067e-1704.97796462065534e-170
13118.62085850948414e-1694.31042925474207e-169
13211.01348220169109e-1685.06741100845543e-169
13318.61461503210679e-1684.30730751605339e-168
13417.36999371242925e-1673.68499685621462e-167
13516.13076139228656e-1663.06538069614328e-166
13615.08585021067142e-1652.54292510533571e-165
13714.23782978621222e-1642.11891489310611e-164
13813.51823785854485e-1631.75911892927242e-163
13912.7501481199883e-1621.37507405999415e-162
14012.24979146101798e-1611.12489573050899e-161
14111.60872142825878e-1608.04360714129391e-161
14211.30186173172098e-1596.5093086586049e-160
14311.05744693057945e-1585.28723465289723e-159
14418.51637274953086e-1584.25818637476543e-158
14516.39807615792072e-1573.19903807896036e-157
14614.94161722676044e-1562.47080861338022e-156
14713.89319248767449e-1551.94659624383724e-155
14813.09262929501e-1541.546314647505e-154
14912.17479510878388e-1531.08739755439194e-153
15011.68510827724014e-1528.42554138620072e-153
15111.26090355721018e-1516.30451778605091e-152
15219.80214937630494e-1514.90107468815247e-151
15317.55707434782121e-1503.77853717391061e-150
15415.76076687826918e-1492.88038343913459e-149
15514.3777911971594e-1482.1888955985797e-148
15613.29165784725398e-1471.64582892362699e-147
15712.46197614950670e-1461.23098807475335e-146
15811.84250735086208e-1459.2125367543104e-146
15911.02925123899639e-1445.14625619498195e-145
16017.58124316519242e-1443.79062158259621e-144
16115.55505253931058e-1432.77752626965529e-143
16214.04919843910621e-1422.02459921955311e-142
16312.93621219295606e-1411.46810609647803e-141
16412.15328461655928e-1401.07664230827964e-140
16511.44461689564268e-1397.2230844782134e-140
16611.03460864942668e-1385.17304324713339e-139
16717.35516499366214e-1383.67758249683107e-138
16811.57630227803331e-1387.88151139016654e-139
16913.48093749026205e-1381.74046874513102e-138
17012.48028202264921e-1371.24014101132460e-137
17111.75824861791493e-1368.79124308957466e-137
17211.26275945533818e-1356.3137972766909e-136
17318.86163674442976e-1354.43081837221488e-135
17416.31155203335042e-1343.15577601667521e-134
17514.38539192464985e-1332.19269596232493e-133
17613.05834879558274e-1321.52917439779137e-132
17711.36345135324092e-1316.81725676620458e-132
17816.3260542358449e-1313.16302711792245e-131
17914.30630631357372e-1302.15315315678686e-130
18012.91651132114958e-1291.45825566057479e-129
18111.43400967259552e-1287.1700483629776e-129
18217.65952689049522e-1283.82976344524761e-128
18313.89809575868878e-1271.94904787934439e-127
18411.37358620997943e-1266.86793104989717e-127
18517.05271278247075e-1263.52635639123538e-126
18613.12553353317253e-1251.56276676658626e-125
18717.53331389610405e-1253.76665694805202e-125
18815.08973009227886e-1242.54486504613943e-124
18912.82312754884148e-1231.41156377442074e-123
19011.84884410035107e-1229.24422050175537e-123
19111.16143311118538e-1215.80716555592691e-122
19217.53084517948145e-1213.76542258974073e-121
19314.94583155734186e-1202.47291577867093e-120
19413.17537711416765e-1191.58768855708382e-119
19512.04284745848874e-1181.02142372924437e-118
19611.01389527679081e-1175.06947638395407e-118
19713.93883089323321e-1171.96941544661661e-117
19811.97799534865924e-1169.88997674329622e-117
19911.00742001393182e-1155.0371000696591e-116
20016.37527194368801e-1163.18763597184401e-116
20113.31447533819798e-1151.65723766909899e-115
20211.74100974265898e-1148.70504871329488e-115
20319.22752669113957e-1144.61376334556978e-114
20415.26574520210657e-1132.63287260105328e-113
20511.18740995750403e-1125.93704978752013e-113
20616.59940720544916e-1123.29970360272458e-112
20713.44229613264928e-1111.72114806632464e-111
20811.86770497462847e-1109.33852487314236e-111
20911.85118277298769e-1109.25591386493847e-111
21011.0528213781508e-1095.264106890754e-110
21116.46549728413016e-1093.23274864206508e-109
21213.95093324053392e-1081.97546662026696e-108
21311.97141947553302e-1079.8570973776651e-108
21411.09178920849215e-1065.45894604246076e-107
21516.73920220581714e-1063.36960110290857e-106
21614.07081273025398e-1052.03540636512699e-105
21712.46773603984548e-1041.23386801992274e-104
21811.43776948254078e-1037.18884741270388e-104
21918.55918054356446e-1034.27959027178223e-103
22013.89051309195672e-1021.94525654597836e-102
22112.30790196720193e-1011.15395098360097e-101
22211.34908176966667e-1006.74540884833336e-101
22317.86633908433918e-1003.93316954216959e-100
22414.68017384952816e-992.34008692476408e-99
22512.69991446279936e-981.34995723139968e-98
22611.59352102859261e-977.96760514296306e-98
22719.27730640205523e-974.63865320102761e-97
22815.26794185098815e-962.63397092549408e-96
22913.05651974165957e-951.52825987082978e-95
23011.71901240986014e-948.59506204930068e-95
23119.42344736051369e-944.71172368025684e-94
23214.8641291405366e-932.4320645702683e-93
23312.69832020188954e-921.34916010094477e-92
23411.51589481910053e-917.57947409550264e-92
23518.33005970644619e-914.16502985322309e-91
23614.55240479979029e-902.27620239989514e-90
23712.47654479038542e-891.23827239519271e-89
23811.35013951653887e-886.75069758269433e-89
23917.27198419034947e-883.63599209517474e-88
24013.89696742115849e-871.94848371057925e-87
24112.07776014607413e-861.03888007303707e-86
24211.12383168777660e-855.61915843888301e-86
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36014.06130112274353e-172.03065056137176e-17
36111.10894017502942e-165.54470087514712e-17
36212.93461523906743e-161.46730761953372e-16
36317.68860221186038e-163.84430110593019e-16
3640.9999999999999992.11451904870682e-151.05725952435341e-15
3650.9999999999999975.58167006473236e-152.79083503236618e-15
3660.9999999999999931.42206842936683e-147.11034214683415e-15
3670.9999999999999823.58497688287385e-141.79248844143692e-14
3680.9999999999999558.94079108878692e-144.47039554439346e-14
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3700.9999999999997245.52768641903634e-132.76384320951817e-13
3710.9999999999993331.33409522430440e-126.67047612152198e-13
3720.9999999999984643.07222715385914e-121.53611357692957e-12
3730.9999999999961897.62204132456135e-123.81102066228067e-12
3740.9999999999905471.89064257496480e-119.45321287482398e-12
3750.9999999999782064.35872184273959e-112.17936092136980e-11
3760.999999999950399.92186944784814e-114.96093472392407e-11
3770.9999999998786332.42734951495829e-101.21367475747915e-10
3780.9999999997387345.22531621214214e-102.61265810607107e-10
3790.9999999995012249.97551152680827e-104.98775576340413e-10
3800.999999998919852.16030105071244e-091.08015052535622e-09
3810.9999999976943844.61123157175551e-092.30561578587776e-09
3820.9999999945795641.08408724356856e-085.4204362178428e-09
3830.999999987917622.41647612928962e-081.20823806464481e-08
3840.9999999751315234.97369546745399e-082.48684773372699e-08
3850.9999999456886141.08622771622549e-075.43113858112746e-08
3860.9999998963772632.07245473038351e-071.03622736519176e-07
3870.999999804728033.90543941922273e-071.95271970961136e-07
3880.9999996181800827.63639835358148e-073.81819917679074e-07
3890.9999992458893631.50822127419356e-067.5411063709678e-07
3900.9999985091970322.98160593577658e-061.49080296788829e-06
3910.9999971257842165.748431567737e-062.8742157838685e-06
3920.9999941885456311.16229087377653e-055.81145436888267e-06
3930.9999879583310762.40833378470856e-051.20416689235428e-05
3940.9999838149695233.23700609539246e-051.61850304769623e-05
3950.9999745708184255.0858363149929e-052.54291815749645e-05
3960.9999497945427980.0001004109144035305.02054572017652e-05
3970.9999032773256430.0001934453487130779.67226743565383e-05
3980.9998420529357220.0003158941285561940.000157947064278097
3990.9997055708603020.0005888582793963920.000294429139698196
4000.999633491184280.00073301763144180.0003665088157209
4010.9993539493587360.001292101282528610.000646050641264305
4020.9990168733256970.001966253348606590.000983126674303293
4030.9983337838903490.003332432219302980.00166621610965149
4040.997194995124730.0056100097505380.002805004875269
4050.9950440560749660.00991188785006720.0049559439250336
4060.9925095067808420.01498098643831640.0074904932191582
4070.9883788202395750.02324235952084910.0116211797604246
4080.9825882209432890.03482355811342280.0174117790567114
4090.9739988349940790.05200233001184220.0260011650059211
4100.95716303219920.08567393560159850.0428369678007992
4110.9313077057225540.1373845885548930.0686922942774465
4120.915294639767180.1694107204656410.0847053602328206
4130.8692038141171940.2615923717656120.130796185882806
4140.8056023272812780.3887953454374440.194397672718722
4150.7418097033734370.5163805932531270.258190296626563
4160.6467826396224730.7064347207550540.353217360377527
4170.7987506526268090.4024986947463820.201249347373191
4180.6871032085173870.6257935829652250.312896791482613
4190.5494810281469190.9010379437061610.450518971853081
4200.3868022377746770.7736044755493540.613197762225323


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3950.963414634146341NOK
5% type I error level3980.970731707317073NOK
10% type I error level4000.97560975609756NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/10cuvk1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/10cuvk1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/1y2fb1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/1y2fb1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/2y2fb1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/2y2fb1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/3y2fb1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/3y2fb1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/4rtfw1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/4rtfw1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/5rtfw1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/5rtfw1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/6rtfw1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/6rtfw1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/712wh1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/712wh1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/8cuvk1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/8cuvk1291225159.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/9cuvk1291225159.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t1291225441irw503o6hjx1toq/9cuvk1291225159.ps (open in new window)


 
Parameters (Session):
par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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Software written by Ed van Stee & Patrick Wessa


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