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*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, 17 Nov 2010 09:28:57 +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/Nov/17/t1289986052iuu6wbiswsl22l0.htm/, Retrieved Wed, 17 Nov 2010 10:27:32 +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/Nov/17/t1289986052iuu6wbiswsl22l0.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 9 41 38 13 12 14 12 53 1 9 39 32 16 11 18 11 83 1 9 30 35 19 15 11 14 66 1 9 31 33 15 6 12 12 67 1 9 34 37 14 13 16 21 76 1 9 35 29 13 10 18 12 78 1 9 39 31 19 12 14 22 53 1 9 34 36 15 14 14 11 80 1 9 36 35 14 12 15 10 74 1 9 37 38 15 9 15 13 76 1 9 38 31 16 10 17 10 79 1 9 36 34 16 12 19 8 54 1 9 38 35 16 12 10 15 67 1 9 39 38 16 11 16 14 54 1 9 33 37 17 15 18 10 87 1 9 32 33 15 12 14 14 58 1 9 36 32 15 10 14 14 75 1 9 38 38 20 12 17 11 88 1 9 39 38 18 11 14 10 64 1 9 32 32 16 12 16 13 57 1 9 32 33 16 11 18 9.5 66 1 9 31 31 16 12 11 14 68 1 9 39 38 19 13 14 12 54 1 9 37 39 16 11 12 14 56 1 9 39 32 17 12 17 11 86 1 9 41 32 17 13 9 9 80 1 9 36 35 16 10 16 11 76 1 9 33 37 15 14 14 15 69 1 9 33 33 16 12 15 14 78 1 9 34 33 14 10 11 13 67 1 9 31 31 15 12 16 9 80 1 9 27 32 12 8 13 15 54 1 9 37 31 14 10 17 10 71 1 9 34 37 16 12 15 11 84 1 9 34 30 14 12 14 13 74 1 9 32 33 10 7 16 8 71 1 9 29 31 10 9 9 20 63 1 9 36 33 14 12 15 12 71 1 9 29 31 16 10 17 10 76 1 9 35 33 16 10 13 1 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 time11 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Learning[t] = + 2.71036882048956 + 0.267704067574296Pop[t] + 0.298790977527051month[t] + 0.0331344672091642Connected[t] + 0.0409019846242882Separate[t] + 0.552243687717541Software[t] + 0.0669242791647773Happiness[t] -0.0340036411629706Depression[t] + 0.00642778731101736Belonging[t] -0.00640786153072009t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)2.710368820489564.4750420.60570.5452790.27264
Pop0.2677040675742960.4986210.53690.5918140.295907
month0.2987909775270510.4551630.65640.512130.256065
Connected0.03313446720916420.0345720.95840.3387690.169384
Separate0.04090198462428820.0353111.15840.2478090.123905
Software0.5522436877175410.05477310.082400
Happiness0.06692427916477730.0581681.15050.2510070.125503
Depression-0.03400364116297060.042131-0.80710.4203630.210181
Belonging0.006427787311017360.0119980.53580.5925990.296299
t-0.006407861530720090.004338-1.47720.1408620.070431


Multiple Linear Regression - Regression Statistics
Multiple R0.66803004658921
R-squared0.446264143145982
Adjusted R-squared0.42664358128895
F-TEST (value)22.7447178321266
F-TEST (DF numerator)9
F-TEST (DF denominator)254
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation1.85966979909574
Sum Squared Residuals878.426427463874


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
11316.0700655900209-3.07006559002095
21615.69426757576120.305732424238781
31917.04157695216141.95842304783860
41512.15766574793512.84233425206487
51416.2994894725434-2.29948947254338
61314.7950060414932-1.79500604149322
71915.33899918241863.66100081758143
81517.0235065935887-2.02350659358869
91416.0003395028786-2.00033950287857
101514.40388565041040.596114349589618
111614.95168489518791.04831510481213
121616.1473625864268-0.147362586426829
131615.49134287835820.508657121641839
141615.44051983130030.559480168699663
151717.8853580370055-0.88535803700552
161515.4353591932854-0.435359193285363
171514.52537222481920.474627775180776
182016.32147757691413.67852242308589
191815.47492440307922.52507559692076
201615.53025017471970.469749825280298
211615.32321199829480.676788001705164
221615.14547862325910.854521376740856
231916.42149517695532.57850482304467
241615.09623272416200.903767275837978
251716.05148953104050.948510468959527
261716.15764061678720.842359383212759
271614.82628683251441.17371316748563
281516.6963966553163-1.69639665531634
291615.58067148598030.41932851401971
301414.1985115803063-0.198511580306322
311515.6695809188536-0.66958091885361
321212.7906452676818-0.79064526768175
331414.7261551758147-0.726155175814723
341615.88595223138800.114047768611978
351415.3940210428864-1.39402104288639
361012.9674151644339-2.96741516443386
371012.9563513608649-2.95635136086492
381415.6454169049801-1.64541690498012
391614.45477120551221.54522879448782
401614.41628248864881.58371751135121
411614.63523271295971.36476728704028
421415.5781446705218-1.57814467052182
432017.38914206980262.61085793019745
441414.0784398144220-0.0784398144219514
451414.3789815766678-0.378981576667822
461115.3881083294370-4.38810832943697
471416.5151148807080-2.51511488070805
481515.0303079753592-0.0303079753592149
491615.27831766031980.721682339680205
501415.519755748483-1.51975574848301
511616.8799334836024-0.879933483602363
521414.0353329346706-0.0353329346706483
531214.8936198510576-2.89361985105759
541615.90674559128980.093254408710175
55911.2791460966546-2.27914609665465
561412.27868154122731.72131845877269
571615.71617692208310.283823077916920
581615.40252016277070.597479837229299
591514.99453856565310.00546143434686897
601614.09851254499011.90148745500994
611211.47730166975390.522698330246092
621615.5035173128220.496482687177994
631616.3953957461175-0.395395746117497
641414.5856409302666-0.585640930266565
651615.18105571453350.818944285466491
661716.20473724979080.795262750209219
671816.47481698377091.52518301622910
681814.56759237499503.43240762500498
691216.0458555294013-4.04585552940125
701615.78876692786410.211233072135857
711013.5861095198426-3.58610951984262
721415.0685754612093-1.06857546120934
731817.03383730964170.966162690358343
741817.26664876195290.733351238047127
751615.37915248158310.620847518416886
761713.63972728910583.36027271089416
771616.5367045060885-0.536704506088515
781614.67085449112751.32914550887252
791315.3391689355289-2.33916893552889
801615.32169023855240.678309761447573
811615.77739832858270.222601671417309
821615.89474636993240.105253630067610
831515.7687684346207-0.768768434620745
841515.0119944674752-0.0119944674751563
851614.29498244779051.70501755220947
861414.2832878161251-0.283287816125141
871615.49194139671190.508058603288128
881615.00583968477700.99416031522303
891514.63614511055400.363854889445985
901214.0240021293728-2.02400212937277
911716.87528843380160.124711566198416
921615.89682785233660.103172147663437
931515.1564981641270-0.156498164126972
941315.1377201193380-2.13772011933795
951614.85535976144831.14464023855169
961615.89009106113240.109908938867559
971613.80654842575962.19345157424036
981615.86590271510010.134097284899881
991414.5391552576154-0.5391552576154
1001617.0743775085394-1.07437750853939
1011614.77927552728781.22072447271217
1022017.51135704770992.48864295229012
1031514.37257299128350.627427008716497
1041615.03046157371660.969538426283401
1051314.9476625190988-1.94766251909879
1061715.78961305896791.21038694103205
1071615.77713511602720.222864883972845
1081614.47931315328771.52068684671229
1091212.4247306347661-0.424730634766116
1101615.34691877369290.653081226307068
1111616.0648243519389-0.0648243519388998
1121715.12188791679471.87811208320529
1131314.3977845272317-1.39778452723171
1141214.6596712566202-2.65967125662023
1151816.22662708610011.77337291389988
1161415.9393449157931-1.93934491579306
1171413.322417959090.677582040910008
1181314.8839669096552-1.88396690965521
1191615.56733874306570.43266125693432
1201314.5186679408697-1.51866794086971
1211615.45072219444780.549277805552234
1221315.8673321688520-2.86733216885203
1231616.9098249193686-0.909824919368622
1241515.9104307251192-0.910430725119216
1251616.8293600377629-0.829360037762884
1261514.72632119126270.273678808737307
1271715.55329136656311.44670863343687
1281514.10005046476740.899949535232634
1291214.748138474433-2.74813847443299
1301614.01781446024261.9821855397574
1311013.7843416092875-3.78434160928755
1321613.53561396127522.46438603872483
1331214.2217235432609-2.22172354326086
1341415.5859809278217-1.58598092782170
1351515.1154055258866-0.115405525886594
1361312.19349926706440.806500732935584
1371514.58676707809970.413232921900267
1381113.5689474543954-2.56894745439539
1391213.0848157644353-1.08481576443525
1401113.4033024434723-2.40330244347227
1411612.94232240779913.05767759220089
1421513.66833858728391.33166141271611
1431716.84060318142830.159396818571737
1441614.17660541411071.82339458588930
1451013.3169539393641-3.3169539393641
1461815.52551596404442.47448403595558
1471314.9960505112883-1.99605051128828
1481614.88394322895541.11605677104456
1491312.87545214910370.124547850896257
1501012.9339030961619-2.93390309616189
1511515.8823334933492-0.882333493349214
1521613.86415679620932.13584320379074
1531611.91177407052244.08822592947764
1541412.14787439783751.85212560216245
1551012.5114300675364-2.51143006753643
1561716.45877743430480.541222565695222
1571311.75149316759401.24850683240602
1581513.90781461884581.09218538115424
1591614.56116563073251.43883436926753
1601212.704212629745-0.704212629745011
1611312.72078448520950.279215514790499
1621312.71690446362840.283095536371560
1631212.4426974334534-0.442697433453368
1641716.20426135972480.795738640275188
1651513.70393652046011.29606347953990
1661011.6747846515357-1.67478465153568
1671414.3757003960369-0.375700396036854
1681114.2342154864931-3.23421548649315
1691314.8072513414194-1.80725134141935
1701614.40214285667511.5978571433249
1711210.56610304987281.43389695012720
1721615.35360135231640.646398647683617
1731213.8966712518605-1.89667125186049
174911.4024498263592-2.40244982635922
1751214.9322562649427-2.93225626494266
1761514.50118919025140.498810809748587
1771212.3519181544552-0.351918154455236
1781212.6823000987845-0.682300098784452
1791413.82904304814560.170956951854436
1801213.3221032278085-1.32210322780853
1811615.03948352515070.960516474849282
1821111.5257114005642-0.525711400564246
1831916.68749540533712.31250459466286
1841515.1240470477292-0.124047047729155
185814.5815747753204-6.5815747753204
1861614.67736426103431.3226357389657
1871714.39353352173172.60646647826829
1881212.3733411536194-0.373341153619402
1891111.4657753769959-0.465775376995942
1901110.48775435056790.512245649432125
1911414.4712423242103-0.47124232421031
1921615.36786109592260.632138904077387
193129.764478698792842.23552130120716
1941614.09233641012791.90766358987211
1951313.6297538082259-0.629753808225923
1961514.99329643613140.00670356386858984
1971612.89811337343853.10188662656153
1981614.94815087873701.05184912126304
1991412.42314909314051.57685090685951
2001614.43568909214091.56431090785908
2011614.02488115039921.97511884960085
2021413.28674299098190.713257009018119
2031113.3067570218082-2.30675702180818
2041214.493290634375-2.49329063437499
2051512.67813717743032.32186282256971
2061514.38824710780600.61175289219397
2071614.49366072052811.50633927947185
2081614.81831521566771.18168478433225
2091113.5667794673052-2.5667794673052
2101513.85287181353071.14712818646934
2111214.1839074212464-2.18390742124639
2121215.6604102083986-3.6604102083986
2131514.04567500911480.95432499088521
2141512.08162488580502.91837511419496
2151614.42634633184391.57365366815615
2161413.06534608486000.934653915140025
2171714.51628568021132.48371431978866
2181413.86790689631440.132093103685559
2191311.81551683488471.18448316511532
2201515.0571742797099-0.0571742797098508
2211314.5339634850250-1.53396348502497
2221413.86409882778510.135901172214907
2231514.15132320869720.84867679130279
2241213.0285658747232-1.02856587472319
2251312.25703521579820.742964784201789
226811.6272488560834-3.62724885608335
2271413.64557564058340.354424359416577
2281412.79037348548481.20962651451519
2291112.1537442990202-1.15374429902023
2301212.7956608051062-0.795660805106198
2311311.16921622326971.83078377673027
2321013.1695174126745-3.16951741267448
2331611.33911347189764.66088652810242
2341815.69207466708632.30792533291370
2351313.6766507663951-0.676650766395077
2361113.1781146783976-2.17811467839762
237410.9584446281236-6.95844462812359
2381314.1454748455463-1.14547484554629
2391614.07937941772261.92062058227743
2401011.5688475086550-1.56884750865497
2411212.1029187904657-0.102918790465723
2421213.3423212406224-1.34232124062235
243108.801555691220241.19844430877976
2441310.93975238491592.06024761508412
2451513.49840895622161.50159104377838
2461211.73076572139950.269234278600498
2471412.67344392604721.32655607395279
2481012.3174962338769-2.31749623387687
2491210.65708416576771.34291583423234
2501211.47886670279690.521133297203091
2511111.6499964267704-0.649996426770351
2521011.4436163470791-1.44361634707906
2531211.22519950450760.774800495492435
2541612.63273584023853.36726415976152
2551213.1233615268255-1.12336152682551
2561413.63137344639980.368626553600234
2571614.02057929230891.97942070769111
2581411.48659857639562.51340142360441
2591313.9532280855537-0.953228085553718
26049.30524253866037-5.30524253866037
2611513.46126303429461.53873696570543
2621114.6588914363487-3.65889143634869
2631111.0942706014226-0.0942706014226423
2641412.53704727642241.46295272357763


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
130.9174031500106020.1651936999787970.0825968499893984
140.856823094396750.2863538112064990.143176905603249
150.8064556608230210.3870886783539570.193544339176979
160.8361648171242940.3276703657514120.163835182875706
170.7749024140490140.4501951719019730.225097585950986
180.9321377923487760.1357244153024490.0678622076512243
190.9133280210415010.1733439579169980.0866719789584989
200.8775061569640890.2449876860718230.122493843035911
210.8287166708518210.3425666582963570.171283329148179
220.79554605782840.40890788434320.2044539421716
230.7621641646750090.4756716706499830.237835835324991
240.731894807121850.5362103857562990.268105192878149
250.6735138624108230.6529722751783540.326486137589177
260.6247876890631590.7504246218736830.375212310936841
270.5649731442464640.8700537115070720.435026855753536
280.6114003397727810.7771993204544370.388599660227219
290.5504999355423020.8990001289153960.449500064457698
300.5566288696546380.8867422606907230.443371130345362
310.5045601095643910.9908797808712180.495439890435609
320.4968220253151970.9936440506303950.503177974684803
330.4740069835266210.9480139670532420.525993016473379
340.4125713587477270.8251427174954540.587428641252273
350.3968628233936090.7937256467872170.603137176606392
360.496170486778490.992340973556980.50382951322151
370.5721580696694730.8556838606610530.427841930330527
380.545605510838940.908788978322120.45439448916106
390.5907791848025920.8184416303948150.409220815197408
400.5713237921018860.8573524157962280.428676207898114
410.5358856025968670.9282287948062670.464114397403133
420.5026337733433340.9947324533133320.497366226656666
430.5202008822946910.9595982354106180.479799117705309
440.4710501663393880.9421003326787750.528949833660612
450.4293964114551620.8587928229103240.570603588544838
460.6453577064830040.7092845870339920.354642293516996
470.6587901131885790.6824197736228420.341209886811421
480.6210629359238070.7578741281523860.378937064076193
490.6080351347272080.7839297305455830.391964865272792
500.5794207300919790.8411585398160420.420579269908021
510.5342295181195860.9315409637608280.465770481880414
520.4914389717690370.9828779435380730.508561028230963
530.4977236230981510.9954472461963030.502276376901849
540.4667513745972050.933502749194410.533248625402795
550.466011255298170.932022510596340.53398874470183
560.4798038966876190.9596077933752380.520196103312381
570.4374139423601130.8748278847202260.562586057639887
580.4213043019546180.8426086039092360.578695698045382
590.3802173881952820.7604347763905650.619782611804718
600.4053723067413370.8107446134826740.594627693258663
610.3771299950584110.7542599901168220.622870004941589
620.3402752368525530.6805504737051070.659724763147447
630.3043359027697820.6086718055395630.695664097230218
640.2722235042209340.5444470084418680.727776495779066
650.2458327725745350.4916655451490690.754167227425465
660.2133745404919580.4267490809839160.786625459508042
670.1879617030857380.3759234061714760.812038296914262
680.2052032384243250.4104064768486490.794796761575675
690.4346312986486780.8692625972973570.565368701351322
700.3933734917529490.7867469835058980.606626508247051
710.5013012172404590.9973975655190830.498698782759541
720.4651852021656170.9303704043312340.534814797834383
730.4484637867890940.8969275735781880.551536213210906
740.4191948995838880.8383897991677760.580805100416112
750.3817146164998780.7634292329997560.618285383500122
760.4429381952571340.8858763905142680.557061804742866
770.4065606447728330.8131212895456650.593439355227167
780.3793935623142900.7587871246285790.62060643768571
790.4023633013412510.8047266026825030.597636698658749
800.3682630368567160.7365260737134320.631736963143284
810.3331574458083590.6663148916167170.666842554191641
820.298449480465750.59689896093150.70155051953425
830.2733370001211770.5466740002423540.726662999878823
840.2415581771199620.4831163542399230.758441822880038
850.2342078141481840.4684156282963670.765792185851816
860.2050013823169960.4100027646339910.794998617683004
870.1804070988852880.3608141977705770.819592901114712
880.1638748191348120.3277496382696240.836125180865188
890.141648301830060.283296603660120.85835169816994
900.138202987859570.276405975719140.86179701214043
910.1185274622219250.2370549244438490.881472537778075
920.1028042978011980.2056085956023950.897195702198802
930.0879845006217340.1759690012434680.912015499378266
940.09290780925431830.1858156185086370.907092190745682
950.08374494643187810.1674898928637560.916255053568122
960.06999374736015350.1399874947203070.930006252639846
970.07455962359840850.1491192471968170.925440376401592
980.06205976734718950.1241195346943790.93794023265281
990.05153734306604220.1030746861320840.948462656933958
1000.04504002548627710.09008005097255420.954959974513723
1010.04019333476138390.08038666952276780.959806665238616
1020.04954302515456560.09908605030913120.950456974845434
1030.04175105409943710.08350210819887420.958248945900563
1040.03767794126377230.07535588252754460.962322058736228
1050.04375318753796460.08750637507592910.956246812462035
1060.03902767731246640.07805535462493280.960972322687534
1070.03189153816964230.06378307633928470.968108461830358
1080.03063618225653030.06127236451306050.96936381774347
1090.02483561384987170.04967122769974350.975164386150128
1100.02075704203742060.04151408407484120.97924295796258
1110.01654005260934740.03308010521869490.983459947390653
1120.01785300851596470.03570601703192950.982146991484035
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1190.01262208366050960.02524416732101920.98737791633949
1200.01121436852773250.02242873705546510.988785631472268
1210.009116782121600060.01823356424320010.9908832178784
1220.0126954953881350.025390990776270.987304504611865
1230.01038502072513720.02077004145027450.989614979274863
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1480.02658661376562510.05317322753125030.973413386234375
1490.02159213586035250.0431842717207050.978407864139648
1500.02961818443544540.05923636887089080.970381815564555
1510.02492185111007820.04984370222015640.975078148889922
1520.02680161829166030.05360323658332060.97319838170834
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1600.03165398388197820.06330796776395630.968346016118022
1610.02580907659199100.05161815318398210.974190923408009
1620.02078059875145690.04156119750291380.979219401248543
1630.01728223957024990.03456447914049980.98271776042975
1640.01473602000337340.02947204000674690.985263979996627
1650.01244061148863620.02488122297727240.987559388511364
1660.01349200736510750.02698401473021500.986507992634893
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1680.01566394871566700.03132789743133410.984336051284333
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1720.01078860389621030.02157720779242070.98921139610379
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1740.01157651140434480.02315302280868960.988423488595655
1750.01402870295049750.02805740590099510.985971297049502
1760.01134205182168960.02268410364337920.98865794817831
1770.008814623604540050.01762924720908010.99118537639546
1780.00731173299058070.01462346598116140.99268826700942
1790.005692231167673290.01138446233534660.994307768832327
1800.00482866455373710.00965732910747420.995171335446263
1810.004003999065621010.008007998131242020.99599600093438
1820.003022345831752460.006044691663504910.996977654168248
1830.003405047614760520.006810095229521040.99659495238524
1840.002556436883933270.005112873767866540.997443563116067
1850.07245747224464380.1449149444892880.927542527755356
1860.0654080203115880.1308160406231760.934591979688412
1870.07562701898484830.1512540379696970.924372981015152
1880.0628367424399570.1256734848799140.937163257560043
1890.05554130822890880.1110826164578180.944458691771091
1900.04675181829933910.09350363659867830.95324818170066
1910.04005892017442970.08011784034885940.95994107982557
1920.03314862335281230.06629724670562470.966851376647188
1930.03366726822108640.06733453644217280.966332731778914
1940.03216375306092830.06432750612185660.967836246939072
1950.02761922547764790.05523845095529580.972380774522352
1960.02171201857721110.04342403715442220.978287981422789
1970.02916679711845130.05833359423690250.970833202881549
1980.02372836617301670.04745673234603350.976271633826983
1990.02121618960772980.04243237921545970.97878381039227
2000.01795966546282950.03591933092565890.98204033453717
2010.01638919684649660.03277839369299310.983610803153503
2020.01357534583868630.02715069167737260.986424654161314
2030.01500026759805040.03000053519610070.98499973240195
2040.01984674344131630.03969348688263250.980153256558684
2050.02096859095247390.04193718190494790.979031409047526
2060.01617388213145570.03234776426291150.983826117868544
2070.01431230540898230.02862461081796470.985687694591018
2080.01130453386399030.02260906772798070.98869546613601
2090.01309188152387800.02618376304775600.986908118476122
2100.01071293175945570.02142586351891140.989287068240544
2110.01309101702181740.02618203404363490.986908982978183
2120.02308789984641130.04617579969282270.976912100153589
2130.01778461084100960.03556922168201920.98221538915899
2140.02226457370744890.04452914741489780.977735426292551
2150.01873149191322610.03746298382645230.981268508086774
2160.01426379609671830.02852759219343650.985736203903282
2170.01596069154060030.03192138308120060.9840393084594
2180.01329666828356290.02659333656712590.986703331716437
2190.01226965916253910.02453931832507820.98773034083746
2200.009004208928150340.01800841785630070.99099579107185
2210.007304318884684750.01460863776936950.992695681115315
2220.005193191901060940.01038638380212190.99480680809894
2230.003925993928176160.007851987856352320.996074006071824
2240.002931169826585560.005862339653171110.997068830173414
2250.001996579463873350.00399315892774670.998003420536127
2260.004162431243562730.008324862487125450.995837568756437
2270.003236731904821690.006473463809643380.996763268095178
2280.002297808837789650.004595617675579290.99770219116221
2290.001576222135455670.003152444270911350.998423777864544
2300.001077293940849130.002154587881698260.99892270605915
2310.001164089994363040.002328179988726080.998835910005637
2320.004142608361277800.008285216722555610.995857391638722
2330.01680643790976090.03361287581952180.98319356209024
2340.02626001313866740.05252002627733480.973739986861333
2350.01849741501433500.03699483002866990.981502584985665
2360.01455609506978610.02911219013957210.985443904930214
2370.1577479892498280.3154959784996570.842252010750172
2380.1212096039362030.2424192078724050.878790396063797
2390.09862671298740160.1972534259748030.901373287012598
2400.07464536724944630.1492907344988930.925354632750554
2410.06425555395170690.1285111079034140.935744446048293
2420.1012610679507750.202522135901550.898738932049225
2430.08106380816007560.1621276163201510.918936191839924
2440.07919179485587910.1583835897117580.92080820514412
2450.06552186515272680.1310437303054540.934478134847273
2460.05366711595153520.1073342319030700.946332884048465
2470.03244867939591730.06489735879183470.967551320604083
2480.02623108749021210.05246217498042410.973768912509788
2490.01740480564527200.03480961129054410.982595194354728
2500.044724685955690.089449371911380.95527531404431
2510.02996643274143760.05993286548287530.970033567258562


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level160.0669456066945607NOK
5% type I error level1020.426778242677824NOK
10% type I error level1330.556485355648536NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/10dtn01289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/10dtn01289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/1pa8p1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/1pa8p1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/2zk7s1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/2zk7s1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/3zk7s1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/3zk7s1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/4sbpd1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/4sbpd1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/5sbpd1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/5sbpd1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/6sbpd1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/6sbpd1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/73k6g1289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/73k6g1289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/8dtn01289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/8dtn01289986122.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/9dtn01289986122.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/17/t1289986052iuu6wbiswsl22l0/9dtn01289986122.ps (open in new window)


 
Parameters (Session):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = 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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