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Workshop 4 mini-tutorial link 3

*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 17:45:10 +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/t129122549619ay7b16fj47wlu.htm/, Retrieved Wed, 01 Dec 2010 18:45:08 +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/t129122549619ay7b16fj47wlu.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 time65 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 195390.249959614 + 13727.2209540297Group[t] + 5.05075772831932Costs[t] + 18.1676444126800Costs_g[t] -186.494340070149Orders[t] + 2735.48083994389Orders_g[t] + 1.89878042590157Dividends[t] -1.74203696507352Dividends_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)195390.24995961427782.9337887.032700
Group13727.220954029749618.7187490.27670.7821810.39109
Costs5.050757728319322.8546341.76930.0775610.038781
Costs_g18.16764441268003.4811655.218800
Orders-186.494340070149415.008435-0.44940.6533910.326696
Orders_g2735.48083994389532.4763085.137300
Dividends1.898780425901570.3894444.87562e-061e-06
Dividends_g-1.742036965073520.636243-2.7380.0064420.003221


Multiple Linear Regression - Regression Statistics
Multiple R0.90357922334919
R-squared0.816455412868324
Adjusted R-squared0.813418031993805
F-TEST (value)268.802447436723
F-TEST (DF numerator)7
F-TEST (DF denominator)423
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation185959.742030783
Sum Squared Residuals14627773852553.6


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821546073845.00762884208308.992371156
243210232045360.119199542275662.88080046
341119123316083.80101811795828.198981888
4223193494180.198255496-270987.198255496
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99836601675187.85592924-691527.855929243
101443586923311.383052005520274.616947995
111073089772693.84917323300395.15082677
12984885327855.933760212657029.066239788
1314052251628857.43021399-223632.430213989
14227132441938.512305800-214806.512305800
159291181513850.95538859-584732.955388593
161071292504234.053619946567057.946380054
17638830759515.929903328-120685.929903328
188569561412164.39745583-555208.397455828
199924261684460.64644928-692034.646449276
20444477466994.653876017-22517.6538760166
21857217709660.348976313147556.651023687
22711969910874.771131245-198905.771131245
23702380557827.032367124144552.967632876
24358589444061.269291164-85472.2692911637
25297978470493.677383096-172515.677383096
26585715386084.102037315199630.897962685
276579541464747.29430073-806793.294300725
28209458300995.290893081-91537.2908930815
29786690293404.303353871493285.696646129
30439798336946.755795491102851.244204509
31688779367275.833512624321503.166487376
32574339678597.339668128-104258.339668128
33741409485863.072100253255545.927899747
34597793437106.916094427160686.083905573
35644190777170.091117361-132980.091117361
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37640273401937.11763986238335.882360140
38697458554559.818971475142898.181028525
39550608505654.81889730944953.1811026911
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41301607444752.378627756-143145.378627756
42345783437366.435950124-91583.4359501242
43501749379773.422948268121975.577051732
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45387475342809.63293846644665.3670615337
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47370837480584.171338723-109747.171338723
48430866784272.300188379-353406.300188379
49469107440826.65138795628280.3486120437
50194493344352.433548376-149859.433548376
51530670528839.4343225891830.56567741087
52518365673258.595819351-154893.595819351
53491303655119.828675554-163816.828675554
54527021418951.690302018108069.309697982
55233773632400.528985387-398627.528985387
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58446211380313.65469520565897.345304795
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61493408462723.8275693130684.1724306902
62146494311685.816859179-165191.816859179
63414462360168.88833128154293.111668719
64364304593863.349750775-229559.349750775
65355178310890.65691451344287.3430854868
66357760387982.190079639-30222.1900796393
67261216350441.871048495-89225.8710484952
68397144384680.90507029812463.0949297022
69374943437928.936462129-62985.9364621286
70424898535207.304517757-110309.304517757
71202055409001.642711237-206946.642711237
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79312378324056.296453467-11678.2964534672
80339836276192.9462222563643.05377775
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83352850457535.815075271-104685.815075271
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86357312524676.741071765-167364.741071765
87458343366523.39440186691819.6055981343
88354228393090.44578872-38862.4457887198
89308636400030.425113990-91394.4251139905
90386212391872.571945385-5660.57194538491
91393343380213.38840677513129.6115932247
92378509392542.501955432-14033.5019554316
93452469314837.135621106137631.864378894
94364839454616.21321082-89777.2132108201
95358649268167.40772820190481.5922717986
96376641365962.60773512110678.3922648794
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98330546309026.87759299821519.1224070018
99403560451904.28494052-48344.2849405198
100317892275646.31251880342245.6874811972
101307528329344.829286999-21816.8292869992
102235133368675.533361964-133542.533361964
103299243408111.713590654-108868.713590654
104314073412814.691721551-98741.691721551
105368186329122.6061053339063.3938946702
106269661329628.405420847-59967.4054208474
107125390414960.080546461-289570.080546461
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110249898316390.216288782-66492.216288782
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115378049265679.201788175112369.798211825
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118442882371741.45066274771140.5493372529
119214215301126.827971176-86911.8279711756
120315688312024.4394883253663.56051167455
121375195441117.306681826-65922.3066818263
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319315372309754.8776973085617.12230269194
320315380310684.1974203564695.8025796437
321315380310684.1974203564695.8025796437
322315380310684.1974203564695.8025796437
323315380310684.1974203564695.8025796437
324315380218634.93385512696745.0661448741
325315380310684.1974203564695.8025796437
326312502310612.6173111611889.38268883906
327315380218634.93385512696745.0661448741
328315380218634.93385512696745.0661448741
329315380310684.1974203564695.8025796437
330315380310684.1974203564695.8025796437
331315380310684.1974203564695.8025796437
332315380310684.1974203564695.8025796437
333315380310684.1974203564695.8025796437
334313729309775.6086767623953.391323238
335315388310516.0453009964871.95469900422
336315371311524.1579867683846.84201323198
337296139311606.400128965-15467.400128965
338315380310684.1974203564695.8025796437
339313880310963.2081361812916.79186381886
340317698307578.40123575610119.598764244
341295580314252.052866776-18672.0528667764
342315380310684.1974203564695.8025796437
343315380310684.1974203564695.8025796437
344315380310684.1974203564695.8025796437
345308256311396.291548731-3140.2915487309
346315380310684.1974203564695.8025796437
347303677307683.908327522-4006.90832752165
348315380310684.1974203564695.8025796437
349315380310684.1974203564695.8025796437
350319369316875.2125963242493.78740367566
351318690307671.33874761811018.6612523815
352314049310448.8897956293600.11020437122
353325699309647.92082703916051.0791729608
354314210313733.415046447476.584953553134
355315380310684.1974203564695.8025796437
356315380310684.1974203564695.8025796437
357322378344774.846283442-22396.8462834424
358315380310684.1974203564695.8025796437
359315380310684.1974203564695.8025796437
360315380310684.1974203564695.8025796437
361315398309947.0683786565450.93162134411
362315380310684.1974203564695.8025796437
363315380310684.1974203564695.8025796437
364308336331078.533071702-22742.5330717020
365316386307854.7079887198531.29201128053
366315380310684.1974203564695.8025796437
367315380310684.1974203564695.8025796437
368315380310684.1974203564695.8025796437
369315380310684.1974203564695.8025796437
370315553310479.8022246395073.19777536102
371315380310684.1974203564695.8025796437
372323361309858.52168223113502.4783177691
373336639340761.43854625-4122.43854625005
374307424318788.54599107-11364.5459910698
375315380310684.1974203564695.8025796437
376315380310684.1974203564695.8025796437
377295370300619.640670267-5249.6406702667
378322340311905.29333999910434.7066600008
379319864319991.530114697-127.530114697369
380315380310684.1974203564695.8025796437
381315380310684.1974203564695.8025796437
382317291334143.396449590-16852.3964495895
383280398274419.0275866215978.97241337861
384315380310684.1974203564695.8025796437
385317330312599.8096856094730.19031439133
386238125331298.158081196-93173.1580811959
387327071308775.55519152618295.4448084740
388309038310239.641868781-1201.64186878105
389314210309876.9616594454333.03834055539
390307930308017.886008965-87.8860089646296
391322327314602.9778853427724.02211465815
392292136309189.273663547-17053.2736635465
393263276312770.533504767-49494.5335047673
394367655327007.50556950640647.4944304935
395283910324688.264939874-40778.2649398741
396283587307731.929658870-24144.9296588696
397243650315652.465940224-72002.4659402238
398438493870799.255649713-432306.255649713
399296261318031.746219736-21770.7462197361
400230621366280.009781088-135659.009781088
401304252333892.244579008-29640.2445790082
402333505319776.34999188513728.6500081145
403296919309746.110300309-12827.1103003093
404278990308947.784830047-29957.7848300467
405276898319109.456126981-42211.4561269809
406327007333541.191282400-6534.1912824003
407317046325601.895631564-8555.89563156392
408304555310042.647770459-5487.64777045881
409298096306660.907222565-8564.90722256527
410231861331374.271254754-99513.271254754
411309422323995.706790377-14573.7067903768
412286963444818.320509749-157855.320509749
413269753283363.023678540-13610.0236785405
414448243379329.76055440968913.239445591
415165404353837.408482317-188433.408482317
416204325339432.615986807-135107.615986807
417407159274478.157314439132680.842685561
418290476296212.853798831-5736.85379883143
419275311328735.846267839-53424.8462678392
420246541323709.912153393-77168.9121533933
421253468332798.083513483-79330.0835134826
422240897333963.081469567-93066.081469567
423-83265647830.459148764-731095.459148764
424-42143330630.519271307-372773.519271307
425272713307858.589873819-35145.5898738187
426215362547264.948568653-331902.948568653
42742754308988.143361997-266234.143361997
428306275628450.212121094-322175.212121094
429253537387124.073243213-133587.073243213
430372631403346.637644072-30715.6376440724
431-7170325610.810058989-332780.810058989


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1111.85927032486270e-539.29635162431352e-54
1211.00263392570402e-575.01316962852008e-58
1311.10601980009974e-885.53009900049869e-89
1418.16263892189213e-884.08131946094607e-88
1511.05770912546612e-965.28854562733058e-97
1615.7413152061799e-1052.87065760308995e-105
1711.54640562325818e-1117.73202811629091e-112
1815.95794639828719e-1172.97897319914360e-117
1913.57188793742618e-1181.78594396871309e-118
2014.81151002330783e-1192.40575501165391e-119
2114.32343253743194e-1252.16171626871597e-125
2211.33820754234323e-1256.69103771171616e-126
2313.73877916456563e-1271.86938958228281e-127
2411.76526389972904e-1268.82631949864518e-127
2511.11917598573304e-1275.59587992866521e-128
2613.84502639573044e-1291.92251319786522e-129
2711.19201406009272e-1335.96007030046358e-134
2811.64622315941052e-1338.23111579705262e-134
2914.15078246893108e-1432.07539123446554e-143
3013.02355207428826e-1431.51177603714413e-143
3117.80637193659338e-1503.90318596829669e-150
3212.75673353957511e-1501.37836676978755e-150
3311.60273719431442e-1598.0136859715721e-160
3417.72881202109315e-1623.86440601054657e-162
3516.56025167824294e-1623.28012583912147e-162
3613.38842884629353e-1611.69421442314677e-161
3711.88045575240528e-1669.4022787620264e-167
3818.57464565786874e-1724.28732282893437e-172
3913.99812383164005e-1711.99906191582003e-171
4014.76769051239022e-1722.38384525619511e-172
4114.0835826422996e-1722.0417913211498e-172
4215.36396813898567e-1722.68198406949283e-172
4312.23313651114129e-1721.11656825557065e-172
4411.30425897067176e-1716.52129485335879e-172
4513.58343019484327e-1711.79171509742164e-171
4612.67216180413600e-1701.33608090206800e-170
4711.52157373288246e-1727.60786866441231e-173
4814.46986581333045e-1732.23493290666523e-173
4915.12991292282345e-1732.56495646141173e-173
5017.75230366952452e-1743.87615183476226e-174
5113.0500999617439e-1741.52504998087195e-174
5213.62171938597958e-1741.81085969298979e-174
5311.51516660281884e-1737.57583301409419e-174
5418.02064360485505e-1734.01032180242752e-173
5511.11802051604744e-1785.59010258023721e-179
5614.2653513841337e-1782.13267569206685e-178
5713.03937414880294e-1901.51968707440147e-190
5816.00621628803923e-1913.00310814401961e-191
5914.02158432242633e-1902.01079216121316e-190
6017.90582968941872e-1903.95291484470936e-190
6113.54666355024481e-1911.77333177512241e-191
6211.17162029398809e-1935.85810146994045e-194
6313.56497220529560e-1931.78248610264780e-193
6416.9932119413628e-1933.4966059706814e-193
6515.06603030653099e-1922.53301515326550e-192
6614.5413430273701e-1912.27067151368505e-191
6718.52480977484131e-1914.26240488742065e-191
6816.71230100295204e-1903.35615050147602e-190
6913.76716970033977e-1891.88358485016989e-189
7011.54463685424307e-1887.72318427121535e-189
7111.51359929300156e-1877.56799646500779e-188
7215.22765856624648e-1882.61382928312324e-188
7311.50065496475774e-1877.5032748237887e-188
7411.26096886107977e-1866.30484430539887e-187
7519.86294836283206e-1864.93147418141603e-186
7611.17408219985504e-1855.87041099927518e-186
7719.39384606153521e-1854.69692303076761e-185
7819.11019429152039e-1854.55509714576019e-185
7916.6536590976553e-1843.32682954882765e-184
8011.16262912013458e-1845.81314560067292e-185
8118.52335816589614e-1844.26167908294807e-184
8218.74369353771343e-1844.37184676885671e-184
8312.14334602462963e-1831.07167301231482e-183
8411.85875807371496e-1829.2937903685748e-183
8511.58861920325649e-1817.94309601628247e-182
8614.93458899228632e-1822.46729449614316e-182
8716.13365977922844e-1823.06682988961422e-182
8814.97014475281206e-1812.48507237640603e-181
8911.15032019670800e-1805.75160098354001e-181
9019.29086501497461e-1804.64543250748731e-180
9115.6841530946992e-1792.8420765473496e-179
9212.29082129388156e-1781.14541064694078e-178
9312.40004654105144e-1791.20002327052572e-179
9411.37768371543209e-1786.88841857716046e-179
9512.03086227951388e-1781.01543113975694e-178
9614.71313837069218e-1792.35656918534609e-179
9712.22632040224437e-1781.11316020112219e-178
9811.38428720512386e-1776.9214360256193e-178
9919.86038628113558e-1774.93019314056779e-177
10015.3853927728535e-1762.69269638642675e-176
10113.41424291595555e-1751.70712145797777e-175
10215.07370711128516e-1762.53685355564258e-176
10317.42638123564281e-1763.71319061782141e-176
10417.19810894496649e-1763.59905447248325e-176
10513.06571344043440e-1751.53285672021720e-175
10617.38603012783597e-1753.69301506391798e-175
10711.17440049735094e-1765.8720024867547e-177
10811.92678176251205e-1789.63390881256027e-179
10911.17542987875833e-1775.87714939379166e-178
11012.28916063880557e-1771.14458031940278e-177
11111.74172386865039e-1778.70861934325193e-178
11211.88685228460203e-1779.43426142301015e-178
11311.02325633370607e-1765.11628166853035e-177
11416.17435331543374e-1763.08717665771687e-176
11511.90702213358408e-1769.5351106679204e-177
11618.88966237152536e-1764.44483118576268e-176
11716.43214450192435e-1753.21607225096217e-175
11812.46399655687656e-1751.23199827843828e-175
11912.19618857556626e-1761.09809428778313e-176
12011.95177340433961e-1759.75886702169807e-176
12117.60814250956217e-1753.80407125478109e-175
12216.03864280822274e-1743.01932140411137e-174
12313.22780794004437e-1731.61390397002218e-173
12413.11101556703703e-1731.55550778351851e-173
12514.21649171481776e-1732.10824585740888e-173
12611.74158839430837e-1738.70794197154183e-174
12711.52212979801612e-1727.6106489900806e-173
12811.34299643374797e-1716.71498216873987e-172
12911.15853699812047e-1705.79268499060235e-171
13019.95592924131293e-1704.97796462065647e-170
13118.62085850947924e-1694.31042925473962e-169
13211.01348220169126e-1685.0674110084563e-169
13318.61461503211022e-1684.30730751605511e-168
13417.36999371243218e-1673.68499685621609e-167
13516.130761392289e-1663.0653806961445e-166
13615.08585021067402e-1652.54292510533701e-165
13714.23782978620981e-1642.11891489310491e-164
13813.51823785854465e-1631.75911892927232e-163
13912.75014811998673e-1621.37507405999337e-162
14012.24979146101862e-1611.12489573050931e-161
14111.60872142825778e-1608.04360714128888e-161
14211.30186173172031e-1596.50930865860157e-160
14311.05744693057981e-1585.28723465289903e-159
14418.51637274952747e-1584.25818637476374e-158
14516.39807615791854e-1573.19903807895927e-157
14614.94161722676212e-1562.47080861338106e-156
14713.89319248767604e-1551.94659624383802e-155
14813.09262929500947e-1541.54631464750474e-154
14912.17479510878264e-1531.08739755439132e-153
15011.68510827724081e-1528.42554138620407e-153
15111.26090355721068e-1516.30451778605342e-152
15219.80214937629825e-1514.90107468814913e-151
15317.55707434782895e-1503.77853717391447e-150
15415.7607668782705e-1492.88038343913525e-149
15514.37779119715467e-1482.18889559857733e-148
15613.29165784725473e-1471.64582892362737e-147
15712.46197614950586e-1461.23098807475293e-146
15811.84250735086292e-1459.2125367543146e-146
15911.02925123899616e-1445.14625619498078e-145
16017.58124316519544e-1443.79062158259772e-144
16115.55505253931058e-1432.77752626965529e-143
16214.04919843910667e-1422.02459921955334e-142
16312.93621219295956e-1411.46810609647978e-141
16412.15328461655891e-1401.07664230827946e-140
16511.44461689564375e-1397.22308447821874e-140
16611.03460864942621e-1385.17304324713104e-139
16717.35516499366256e-1383.67758249683128e-138
16811.57630227803420e-1387.88151139017102e-139
16913.48093749026304e-1381.74046874513152e-138
17012.48028202264625e-1371.24014101132312e-137
17111.75824861791463e-1368.79124308957315e-137
17211.26275945533638e-1356.31379727668192e-136
17318.86163674443026e-1354.43081837221513e-135
17416.31155203334145e-1343.15577601667072e-134
17514.38539192465359e-1332.19269596232680e-133
17613.05834879558622e-1321.52917439779311e-132
17711.36345135323960e-1316.81725676619799e-132
17816.32605423584203e-1313.16302711792101e-131
17914.30630631357519e-1302.15315315678759e-130
18012.91651132114942e-1291.45825566057471e-129
18111.43400967259601e-1287.17004836298005e-129
18217.65952689050088e-1283.82976344525044e-128
18313.8980957586879e-1271.94904787934395e-127
18411.37358620997928e-1266.86793104989639e-127
18517.05271278246874e-1263.52635639123437e-126
18613.12553353317164e-1251.56276676658582e-125
18717.53331389610576e-1253.76665694805288e-125
18815.08973009227655e-1242.54486504613827e-124
18912.82312754884116e-1231.41156377442058e-123
19011.84884410035002e-1229.24422050175012e-123
19111.16143311118558e-1215.8071655559279e-122
19217.53084517948787e-1213.76542258974394e-121
19314.94583155734692e-1202.47291577867346e-120
19413.17537711417035e-1191.58768855708518e-119
19512.04284745848828e-1181.02142372924414e-118
19611.01389527679024e-1175.06947638395118e-118
19713.93883089323702e-1171.96941544661851e-117
19811.97799534865823e-1169.88997674329116e-117
19911.00742001393079e-1155.03710006965394e-116
20016.37527194368837e-1163.18763597184419e-116
20113.31447533820006e-1151.65723766910003e-115
20211.74100974265888e-1148.70504871329439e-115
20319.2275266911422e-1144.6137633455711e-114
20415.26574520211181e-1132.63287260105591e-113
20511.18740995750463e-1125.93704978752317e-113
20616.5994072054501e-1123.29970360272505e-112
20713.44229613264977e-1111.72114806632488e-111
20811.86770497462895e-1109.33852487314475e-111
20911.85118277298580e-1109.25591386492899e-111
21011.0528213781511e-1095.2641068907555e-110
21116.46549728413365e-1093.23274864206683e-109
21213.95093324053347e-1081.97546662026673e-108
21311.97141947553313e-1079.85709737766566e-108
21411.09178920849082e-1065.45894604245408e-107
21516.73920220581082e-1063.36960110290541e-106
21614.07081273025502e-1052.03540636512751e-105
21712.46773603984548e-1041.23386801992274e-104
21811.43776948254163e-1037.18884741270817e-104
21918.55918054356397e-1034.27959027178198e-103
22013.89051309195351e-1021.94525654597675e-102
22112.30790196720298e-1011.15395098360149e-101
22211.34908176966660e-1006.74540884833298e-101
22317.86633908434119e-1003.93316954217059e-100
22414.6801738495247e-992.34008692476235e-99
22512.69991446279974e-981.34995723139987e-98
22611.59352102859202e-977.96760514296012e-98
22719.27730640206341e-974.63865320103171e-97
22815.26794185098576e-962.63397092549288e-96
22913.05651974166070e-951.52825987083035e-95
23011.71901240986014e-948.59506204930068e-95
23119.4234473605169e-944.71172368025845e-94
23214.86412914053909e-932.43206457026954e-93
23312.69832020188877e-921.34916010094439e-92
23411.51589481910001e-917.57947409550005e-92
23518.33005970644097e-914.16502985322049e-91
23614.55240479979262e-902.27620239989631e-90
23712.47654479038387e-891.23827239519193e-89
23811.35013951653890e-886.75069758269452e-89
23917.27198419034658e-883.63599209517329e-88
24013.89696742116348e-871.94848371058174e-87
24112.07776014607354e-861.03888007303677e-86
24211.12383168777673e-855.61915843888365e-86
24315.93213269796269e-852.96606634898135e-85
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36014.06130112274402e-172.03065056137201e-17
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36212.93461523906647e-161.46730761953323e-16
36317.68860221185648e-163.84430110592824e-16
3640.9999999999999992.11451904870613e-151.05725952435307e-15
3650.9999999999999975.5816700647342e-152.7908350323671e-15
3660.9999999999999931.42206842936725e-147.11034214683624e-15
3670.9999999999999823.58497688287273e-141.79248844143637e-14
3680.9999999999999558.94079108878715e-144.47039554439357e-14
3690.999999999999892.20545632081789e-131.10272816040894e-13
3700.9999999999997245.52768641903824e-132.76384320951912e-13
3710.9999999999993331.33409522430413e-126.67047612152064e-13
3720.9999999999984643.07222715385874e-121.53611357692937e-12
3730.999999999996197.62204132455834e-123.81102066227917e-12
3740.9999999999905471.89064257496512e-119.4532128748256e-12
3750.9999999999782064.35872184274066e-112.17936092137033e-11
3760.999999999950399.92186944784807e-114.96093472392404e-11
3770.9999999998786332.42734951495819e-101.21367475747909e-10
3780.9999999997387345.22531621214284e-102.61265810607142e-10
3790.9999999995012249.97551152680371e-104.98775576340186e-10
3800.999999998919852.16030105071208e-091.08015052535604e-09
3810.9999999976943844.61123157175478e-092.30561578587739e-09
3820.9999999945795641.08408724356855e-085.42043621784276e-09
3830.999999987917622.41647612928906e-081.20823806464453e-08
3840.9999999751315234.97369546745484e-082.48684773372742e-08
3850.9999999456886141.08622771622535e-075.43113858112674e-08
3860.9999998963772632.07245473038361e-071.03622736519180e-07
3870.9999998047280293.90543941922261e-071.95271970961131e-07
3880.9999996181800827.63639835358126e-073.81819917679063e-07
3890.9999992458893631.50822127419364e-067.5411063709682e-07
3900.9999985091970322.98160593577735e-061.49080296788868e-06
3910.9999971257842165.74843156773689e-062.87421578386845e-06
3920.9999941885456311.16229087377644e-055.8114543688822e-06
3930.9999879583310762.40833378470848e-051.20416689235424e-05
3940.9999838149695233.23700609539253e-051.61850304769626e-05
3950.9999745708184255.08583631499335e-052.54291815749667e-05
3960.9999497945427980.0001004109144035455.02054572017727e-05
3970.9999032773256430.0001934453487130909.6722674356545e-05
3980.9998420529357220.0003158941285562630.000157947064278131
3990.9997055708603020.0005888582793963390.000294429139698169
4000.9996334911842790.0007330176314418390.000366508815720919
4010.9993539493587360.001292101282528630.000646050641264313
4020.9990168733256970.001966253348606720.000983126674303359
4030.9983337838903480.003332432219303160.00166621610965158
4040.9971949951247310.005610009750537870.00280500487526893
4050.9950440560749670.009911887850066480.00495594392503324
4060.9925095067808420.01498098643831560.00749049321915778
4070.9883788202395760.02324235952084860.0116211797604243
4080.9825882209432880.03482355811342390.0174117790567120
4090.973998834994080.05200233001184170.0260011650059208
4100.9571630321992020.08567393560159710.0428369678007986
4110.9313077057225470.1373845885549060.0686922942774532
4120.9152946397671860.1694107204656280.0847053602328138
4130.8692038141172010.2615923717655970.130796185882799
4140.8056023272812820.3887953454374360.194397672718718
4150.7418097033734380.5163805932531230.258190296626562
4160.6467826396224660.7064347207550670.353217360377534
4170.7987506526268190.4024986947463620.201249347373181
4180.687103208517380.6257935829652390.312896791482620
4190.5494810281469320.9010379437061360.450518971853068
4200.3868022377746760.7736044755493530.613197762225324


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/t129122549619ay7b16fj47wlu/10w0fd1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/10w0fd1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/1ph0j1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/1ph0j1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/2ph0j1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/2ph0j1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/3ph0j1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/3ph0j1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/40qhm1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/40qhm1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/50qhm1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/50qhm1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/6shy71291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/6shy71291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/73qfr1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/73qfr1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/83qfr1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/83qfr1291225443.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/93qfr1291225443.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/01/t129122549619ay7b16fj47wlu/93qfr1291225443.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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