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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Fri, 15 Feb 2008 19:30:37 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Feb/16/t12031291166k6mlw0pdt2b6mv.htm/, Retrieved Sat, 16 Feb 2008 03:32:10 +0100
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
2 990 40 760.00 2 990 30 389.00 2 990 20 201.00 2 2100 50 987.00 2 2100 40 517.00 2 2100 30 272.00 2 2100 20 144.00 5 500 20 141.00 5 500 30 266.00 5 500 40 504.00 5 500 50 960.00 5 2100 20 72.30 5 2100 30 128.00 5 2100 40 229.00 5 2100 50 413.00 5 2100 60 748.00 7 120 40 795.00 7 120 20 209.00 7 990 60 833.00 7 990 40 252.00 7 990 30 140.00 7 990 20 78.40 10 200 20 128.00 10 200 30 236.00 10 200 40 466.00 10 200 50 844.00 10 500 20 84.20 10 500 40 274.00 10 500 50 501.00 10 500 60 918.00 10 985 20 61.50 10 985 40 189.00 10 985 60 601.00 10 985 70 1076.00 10 990 20 60.00 10 990 40 184.00 10 990 60 580.00 10 990 70 1038.00 10 2100 20 42.90 10 2100 40 124.00 10 2100 60 369.00 10 2100 70 640.00 20 990 80 841.00 20 990 60 287.00 20 990 40 99.70 20 990 20 35.70 40 200 60 400.00 40 200 40 133.00 40 200 20 45.60 50 110 20 50.50 50 110 40 150.00 50 110 50 262.00 50 110 60 460.00 50 110 70 810.00 50 120 20 48.60 50 120 40 143.00 50 120 50 249.00 50 120 60 436.00 50 120 70 766.00 50 500 20 25.40 50 500 40 66.70 50 500 50 109.00 50 500 70 299.00 50 500 90 830.00 50 985 20 18.50 50 985 40 45.80 50 985 60 117.00 50 985 80 304.00 50 985 100 801.00 50 990 20 18.10 50 990 40 44.50 50 990 60 113.00 50 990 80 292.00 50 990 100 766.00 50 2100 20 12.90 50 2100 40 29.90 50 2100 70 111.00 50 2100 90 272.00 50 2100 120 1061.00 75 200 90 1007.00 75 200 75 461.00 75 200 60 212.00 75 200 20 28.60 100 105 20 30.90 100 105 40 84.10 100 105 60 236.00 100 105 80 673.00 100 985 20 11.10 100 985 40 25.00 100 985 60 58.70 100 985 80 137.00 100 985 100 327.00 100 985 120 790.00 100 990 20 10.80 100 990 40 24.20 100 990 65 69.00 100 990 90 202.00 100 990 120 752.00 100 2100 20 7.81 100 2100 40 16.50 100 2100 70 52.90 100 2100 90 118.00 100 2100 120 399.00 110 500 110 798.00 110 500 90 317.00 110 500 60 80.90 110 500 40 33.40 110 500 30 21.70 110 500 20 14.20 150 200 90 435.00 150 200 60 105.00 150 200 40 41.90 150 200 20 17.20 180 2100 20 5.17 180 2100 40 10.10 180 2100 60 20.30 180 2100 80 41.30 180 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Text written by user:
 
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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Ergebnis [t] = + 0.420818243142633 -0.00854984625152386U[t] + 0.0560030435963667nD[t] + 2.4335602121075T[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)0.42081824314263329.940.01410.9887940.494397
U-0.008549846251523860.002306-3.70710.0002460.000123
nD0.05600304359636670.0209752.670.0079610.00398
T2.43356021210750.3761276.4700


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
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266184223.52228469701-39.5222846970101
267418272.19348893916145.806511060840
2683.7534.4377720880463-30.6877720880463
2696.9883.1089763301964-76.1289763301964
27013.2131.780180572347-118.580180572347
27125.2180.451384814497-155.251384814497
27249229.122589056647-180.122589056647
27396.1277.793793298797-181.693793298797
274180269.374644946904-89.3746449469038
27586.3220.703440704754-134.403440704754
27641.7172.032236462604-130.332236462604
27720.4123.361032220453-102.961032220453
27810.274.6898279783034-64.4898279783034
2795.1926.0186237361533-20.8286237361533
28054.8273.724190534982-218.924190534982
28129.6225.052986292832-195.452986292832
28216.1176.381782050682-160.281782050682
2838.9127.710577808532-118.810577808532
2844.9779.0393735663819-74.0693735663819
2852.830.3681693242318-27.5681693242318
2865.977.46285209959996-1.49285209959996
2871256.1340563417501-44.1340563417501
28835.6129.140862704975-93.5408627049752
28975.3177.812066947125-102.512066947125
290236250.818873310351-14.8188733103505
2914.248.91893123310547-4.67893123310547
2928.0557.5901354752556-49.5401354752556
29315.5106.261339717406-90.7613397174057
29430.4154.932543959556-124.532543959556
29560.6203.603748201706-143.003748201706
296122252.274952443856-130.274952443856
2973.1112.2231108052911-9.11311080529114
2985.6260.8943150474412-55.2743150474412
29910.3109.565519289591-99.2655192895913
30019158.236723531741-139.236723531741
30135.5206.907927773892-171.407927773892
30267.2255.579132016042-188.379132016042
3032.9813.0631564592367-10.0831564592367
3045.3461.7343607013867-56.3943607013868
3059.67110.405564943537-100.735564943537
30617.7159.076769185687-141.376769185687
30732.9207.747973427837-174.847973427837
30861.8256.419177669987-194.619177669987
3094.5-35.286379158019439.7863791580194
3108.6213.3848250841307-4.76482508413074
31123.686.391631447356-62.7916314473559
31247.2135.062835689506-87.862835689506
313137208.069642052731-71.0696420527312
3143.3-33.830300024513937.1303000245139
315614.8409042176363-8.84090421763626
31611.163.5121084597864-52.4121084597864
31720.7112.183312701937-91.4833127019365
31839.2160.854516944087-121.654516944087
31975209.525721186237-134.525721186237
32082.4122.571179537492-40.1711795374925
32142.773.8999752953424-31.1999752953424
32222.325.2287710531923-2.92877105319228
32311.8-23.442433188957835.2424331889578
3246.37-72.11363743110878.483637431108
3253.46-120.784841673258124.244841673258
32658.5-5.6765142353655264.1765142353655
32731.3-54.347718477515685.6477184775156
32817-103.018922719666120.018922719666
3299.3-151.690126961816160.990126961816
3305.16-200.361331203966205.521331203966
3312.9-249.032535446116251.932535446116
332698181.628647959880516.37135204012
333230132.95744371773097.0425562822705


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.1408676320734340.2817352641468680.859132367926566
80.05608812955495970.1121762591099190.94391187044504
90.03685162184652150.0737032436930430.963148378153478
100.01953221906977170.03906443813954350.980467780930228
110.01556122360855010.03112244721710010.98443877639145
120.01033133940679610.02066267881359210.989668660593204
130.00806102680215260.01612205360430520.991938973197847
140.01780584331622040.03561168663244090.98219415668378
150.02581450193190160.05162900386380320.974185498068098
160.01605095966849320.03210191933698640.983949040331507
170.04744451334362460.09488902668724910.952555486656375
180.03201059623531330.06402119247062650.967989403764687
190.0235895940683460.0471791881366920.976410405931654
200.02426595296014420.04853190592028840.975734047039856
210.01520960218086230.03041920436172460.984790397819138
220.01139198181288700.02278396362577400.988608018187113
230.01086024177944450.02172048355888910.989139758220555
240.00662381031229480.01324762062458960.993376189687705
250.004298268623424860.008596537246849720.995701731376575
260.0067534040613480.0135068081226960.993246595938652
270.004858600802105490.009717201604210970.995141399197895
280.004442362571855570.008884725143711140.995557637428144
290.003704336933751450.007408673867502890.996295663066249
300.004147016705883570.008294033411767150.995852983294116
310.004021672150731660.008043344301463310.995978327849268
320.003636838245362670.007273676490725340.996363161754637
330.003475278210829960.006950556421659910.99652472178917
340.00625938929404040.01251877858808080.99374061070596
350.005873620846531930.01174724169306390.994126379153468
360.005514000959160750.01102800191832150.99448599904084
370.005986656195332910.01197331239066580.994013343804667
380.01001682188848140.02003364377696270.989983178111519
390.02101458226978510.04202916453957030.978985417730215
400.0158892835095430.0317785670190860.984110716490457
410.01876392139515940.03752784279031870.98123607860484
420.01844332751145280.03688665502290560.981556672488547
430.02631485472110810.05262970944221610.973685145278892
440.02055009486563730.04110018973127470.979449905134363
450.01894836750467230.03789673500934450.981051632495328
460.0612505886843470.1225011773686940.938749411315653
470.1147597555188000.2295195110376000.8852402444812
480.1387847217347430.2775694434694860.861215278265257
490.2452632681498240.4905265362996480.754736731850176
500.3640287300840730.7280574601681470.635971269915927
510.3304181048090740.6608362096181490.669581895190926
520.2961234475005450.5922468950010910.703876552499455
530.2824261664280390.5648523328560780.71757383357196
540.3948883919527350.789776783905470.605111608047265
550.4119094558914840.8238189117829690.588090544108516
560.3720761092573370.7441522185146740.627923890742663
570.3418073774080130.6836147548160260.658192622591987
580.3256533250472070.6513066500944130.674346674952793
590.4044456796730680.8088913593461360.595554320326932
600.4175210959394380.8350421918788760.582478904060562
610.3828720490333650.765744098066730.617127950966635
620.3781590710210710.7563181420421420.621840928978929
630.4285510373179940.8571020746359890.571448962682006
640.4981942046842120.9963884093684250.501805795315788
650.5368174077102620.9263651845794770.463182592289738
660.4974489819482810.9948979638965620.502551018051719
670.5221155106190120.9557689787619760.477884489380988
680.595764735990540.808470528018920.40423526400946
690.660819004515840.678361990968320.33918099548416
700.6879369673137470.6241260653725060.312063032686253
710.6529755890863050.6940488218273890.347024410913695
720.6603561254457340.6792877491085310.339643874554266
730.7052544417825020.5894911164349960.294745558217498
740.7607282900377890.4785434199244230.239271709962211
750.826488231528110.3470235369437810.173511768471891
760.805910284172940.3881794316541190.194089715827059
770.8105512890772220.3788974218455570.189448710922778
780.8348111151898870.3303777696202250.165188884810113
790.9476693905409960.1046612189180080.0523306094590042
800.9972658691848260.005468261630347760.00273413081517388
810.9976438823160880.004712235367824410.00235611768391221
820.9970522007304250.005895598539149660.00294779926957483
830.9980702065716270.003859586856746850.00192979342837342
840.99936979715090.001260405698201180.00063020284910059
850.9993675481665840.001264903666832060.000632451833416032
860.9992685501443340.001462899711331190.000731449855665594
870.99986015184810.000279696303801430.000139848151900715
880.9999431579874640.0001136840250726755.68420125363377e-05
890.9999309998721970.0001380002556060176.90001278030087e-05
900.9999054658911410.0001890682177170039.45341088585016e-05
910.99990162543850.0001967491229998979.83745614999486e-05
920.9999137820980380.0001724358039244268.62179019622128e-05
930.9999835509522373.28980955269440e-051.64490477634720e-05
940.9999915926705641.68146588719529e-058.40732943597644e-06
950.9999891969869772.16060260460195e-051.08030130230097e-05
960.999985647450262.87050994778571e-051.43525497389285e-05
970.9999867240601392.65518797223599e-051.32759398611799e-05
980.9999978573309734.28533805434254e-062.14266902717127e-06
990.9999993508736441.29825271180884e-066.49126355904422e-07
1000.9999992818606581.43627868487984e-067.1813934243992e-07
1010.9999990073814381.98523712332900e-069.92618561664501e-07
1020.9999990342718721.93145625672125e-069.65728128360627e-07
1030.9999994884188391.02316232187739e-065.11581160938697e-07
1040.9999999857452532.85094950228605e-081.42547475114302e-08
1050.9999999857190032.85619945996094e-081.42809972998047e-08
1060.999999977661914.46761807308948e-082.23380903654474e-08
1070.9999999687470616.25058772846464e-083.12529386423232e-08
1080.9999999652178916.95642171123254e-083.47821085561627e-08
1090.9999999719827915.60344174541957e-082.80172087270978e-08
1100.9999999858425042.83149910690596e-081.41574955345298e-08
1110.999999980009983.99800384463975e-081.99900192231988e-08
1120.9999999800759053.98481902552358e-081.99240951276179e-08
1130.999999990370961.92580803537502e-089.62904017687508e-09
1140.9999999994775081.04498370578102e-095.2249185289051e-10
1150.999999999741515.16980427789416e-102.58490213894708e-10
1160.9999999996818676.362656167331e-103.1813280836655e-10
1170.9999999995122069.75588007348257e-104.87794003674128e-10
1180.9999999993683861.26322851698399e-096.31614258491993e-10
1190.9999999994361831.12763332521922e-095.63816662609612e-10
1200.9999999999244651.51069976202865e-107.55349881014326e-11
1210.9999999999499961.00007888902026e-105.00039444510128e-11
1220.999999999939031.21942028836554e-106.09710144182768e-11
1230.9999999999275751.44849052670328e-107.2424526335164e-11
1240.9999999999965316.9372169029214e-123.4686084514607e-12
1250.9999999999979784.04494734865663e-122.02247367432832e-12
1260.9999999999974425.11546309460839e-122.55773154730420e-12
1270.9999999999957868.42723972767653e-124.21361986383827e-12
1280.9999999999935331.29344660912066e-116.4672330456033e-12
1290.9999999999991041.79240835605501e-128.96204178027507e-13
1300.9999999999989872.02554482074901e-121.01277241037451e-12
1310.99999999999833.40128122170279e-121.70064061085140e-12
1320.9999999999971145.77235455301448e-122.88617727650724e-12
1330.9999999999958688.26387672218158e-124.13193836109079e-12
1340.9999999999951749.65257395293575e-124.82628697646788e-12
1350.9999999999974435.11469818937516e-122.55734909468758e-12
1360.9999999999970145.971191815716e-122.985595907858e-12
1370.9999999999952479.50645814736324e-124.75322907368162e-12
1380.9999999999918071.63865705861370e-118.19328529306851e-12
1390.9999999999890382.19234198418195e-111.09617099209097e-11
1400.9999999999997994.02430839357596e-132.01215419678798e-13
1410.9999999999998353.29807740923564e-131.64903870461782e-13
1420.9999999999997784.43241929261823e-132.21620964630911e-13
1430.9999999999996447.11278803639704e-133.55639401819852e-13
1440.9999999999993711.25768941325726e-126.28844706628631e-13
1450.9999999999989972.00536445425573e-121.00268222712787e-12
1460.9999999999988262.34806311906948e-121.17403155953474e-12
1470.9999999999993031.39449512868691e-126.97247564343455e-13
1480.9999999999991571.68655462801720e-128.43277314008598e-13
1490.9999999999985952.81072887258477e-121.40536443629238e-12
1500.9999999999976974.60585495312819e-122.30292747656409e-12
1510.999999999997055.89986656592061e-122.94993328296031e-12
1520.9999999999994381.12439515608719e-125.62197578043595e-13
1530.9999999999996756.5029877239106e-133.2514938619553e-13
1540.9999999999997175.65883071527794e-132.82941535763897e-13
1550.9999999999999061.88504732901967e-139.42523664509835e-14
15613.284577116091e-201.6422885580455e-20
15712.89377522744895e-201.44688761372448e-20
15814.33035861319088e-202.16517930659544e-20
15918.1029357198793e-204.05146785993965e-20
16011.36403441935019e-196.82017209675095e-20
16119.82152823641726e-214.91076411820863e-21
16211.22520290788819e-206.12601453944094e-21
16312.20782866681920e-201.10391433340960e-20
16414.51848392018389e-202.25924196009194e-20
16519.61779614855968e-204.80889807427984e-20
16611.51279431498139e-197.56397157490696e-20
16711.51695503929426e-217.5847751964713e-22
16812.90749356979254e-211.45374678489627e-21
16916.17184438166167e-213.08592219083084e-21
17011.33881008765489e-206.69405043827446e-21
17112.29466140866686e-201.14733070433343e-20
17216.89015910497443e-223.44507955248722e-22
17311.03686170533783e-215.18430852668913e-22
17412.08527299679481e-211.04263649839740e-21
17514.49380245847972e-212.24690122923986e-21
17619.47650306234823e-214.73825153117411e-21
17711.91474890874446e-209.5737445437223e-21
17811.41696079961184e-207.0848039980592e-21
17912.33056393368334e-201.16528196684167e-20
18014.89071399396622e-202.44535699698311e-20
18111.05118805458977e-195.25594027294883e-20
18212.04572163507370e-191.02286081753685e-19
18313.45356832750871e-191.72678416375436e-19
18417.12882035076447e-193.56441017538224e-19
18511.35566023118132e-186.77830115590662e-19
18612.38564167566047e-181.19282083783024e-18
18712.49696304050258e-181.24848152025129e-18
18811.57713030980336e-187.88565154901678e-19
18911.50589732115091e-187.52948660575457e-19
19012.30724061140686e-181.15362030570343e-18
19114.71591642415161e-182.35795821207581e-18
19219.3916886766166e-184.6958443383083e-18
19311.83643173256608e-179.18215866283038e-18
19411.38126392951440e-176.90631964757201e-18
19511.68883523427366e-178.4441761713683e-18
19612.77465494005123e-171.38732747002562e-17
19715.28078864976018e-172.64039432488009e-17
19811.03164244518721e-165.15821222593605e-17
19911.87742208719482e-169.38711043597409e-17
20011.34456809492741e-166.72284047463706e-17
20111.52536397508122e-167.6268198754061e-17
20212.20697562275985e-161.10348781137992e-16
20313.27854906862849e-161.63927453431424e-16
20418.38173433069442e-174.19086716534721e-17
20515.72584923474069e-282.86292461737034e-28
20611.15274145317021e-275.76370726585106e-28
20712.69718274125e-271.348591370625e-27
20817.01413467118744e-273.50706733559372e-27
20911.29780862627549e-266.48904313137744e-27
21017.98373336386829e-293.99186668193414e-29
21111.52929213489331e-287.64646067446657e-29
21213.63330641928631e-281.81665320964315e-28
21319.30058455044838e-284.65029227522419e-28
21412.47269946881983e-271.23634973440992e-27
21516.99587843623438e-273.49793921811719e-27
21611.19041497752371e-265.95207488761855e-27
21712.45600702230275e-261.22800351115138e-26
21815.96906084501984e-262.98453042250992e-26
21911.51792471769677e-257.58962358848387e-26
22013.91546998104052e-251.95773499052026e-25
22111.06577702670845e-245.32888513354226e-25
22212.20643088812109e-241.10321544406055e-24
22314.65318879709110e-242.32659439854555e-24
22411.13799000338543e-235.68995001692714e-24
22512.87166121471276e-231.43583060735638e-23
22617.08161812804792e-233.54080906402396e-23
22711.75285207725708e-228.76426038628538e-23
22814.49301953996623e-222.24650976998312e-22
22915.87290888743549e-222.93645444371774e-22
23011.02207955094486e-215.1103977547243e-22
23112.07391311427415e-211.03695655713707e-21
23214.74419334032995e-212.37209667016498e-21
23311.05403308046653e-205.27016540233266e-21
23412.98936411376013e-211.49468205688006e-21
23514.70508842922013e-212.35254421461007e-21
23619.72225648851222e-214.86112824425611e-21
23712.32592735371971e-201.16296367685986e-20
23815.8545845655599e-202.92729228277995e-20
23911.42736513479789e-197.13682567398945e-20
24013.35582145032893e-191.67791072516447e-19
24117.52092411808614e-193.76046205904307e-19
24211.62483987128376e-188.12419935641882e-19
24313.20113941406587e-181.60056970703293e-18
24415.65354034843447e-182.82677017421723e-18
24519.17405752122393e-184.58702876061196e-18
24611.76777698063132e-178.83888490315661e-18
24713.70501723992511e-171.85250861996256e-17
24818.31139112992132e-174.15569556496066e-17
24911.93265344854607e-169.66326724273035e-17
25011.90652496483119e-169.53262482415596e-17
25113.64789218853683e-161.82394609426841e-16
25217.68358779704356e-163.84179389852178e-16
25311.65292433821235e-158.26462169106174e-16
2540.9999999999999983.5847230211092e-151.7923615105546e-15
2550.9999999999999967.90443543362432e-153.95221771681216e-15
2560.9999999999999921.58845289477109e-147.94226447385543e-15
2570.9999999999999833.38111845683869e-141.69055922841934e-14
2580.9999999999999647.12363842615179e-143.56181921307589e-14
2590.9999999999999291.43135821897578e-137.1567910948789e-14
2600.9999999999998612.77055226930601e-131.38527613465300e-13
2610.999999999999725.58769313482435e-132.79384656741218e-13
2620.9999999999994971.00591160074102e-125.02955800370511e-13
2630.9999999999990051.99030052519111e-129.95150262595556e-13
2640.9999999999979294.14284823451621e-122.07142411725811e-12
2650.9999999999955798.84227597326776e-124.42113798663388e-12
2660.999999999993361.32810826951140e-116.64054134755701e-12
2670.9999999999998762.47486923239015e-131.23743461619508e-13
2680.9999999999997425.16262984936018e-132.58131492468009e-13
2690.9999999999994481.10441201245723e-125.52206006228615e-13
2700.9999999999988322.33609483323242e-121.16804741661621e-12
2710.9999999999975644.87177071272421e-122.43588535636210e-12
2720.9999999999947871.04261312211441e-115.21306561057207e-12
2730.9999999999878732.42546261733232e-111.21273130866616e-11
2740.99999999998083.83996589836929e-111.91998294918464e-11
2750.999999999956678.66614454196166e-114.33307227098083e-11
2760.9999999999036751.92649326727174e-109.63246633635872e-11
2770.9999999997937144.12571946602828e-102.06285973301414e-10
2780.9999999995718958.56210032101094e-104.28105016050547e-10
2790.9999999991443051.71139065057904e-098.5569532528952e-10
2800.9999999985992072.80158630298594e-091.40079315149297e-09
2810.999999998085463.82908233996975e-091.91454116998487e-09
2820.9999999976534984.69300463401848e-092.34650231700924e-09
2830.9999999973060115.38797776658152e-092.69398888329076e-09
2840.9999999971076635.78467454754136e-092.89233727377068e-09
2850.9999999972957475.40850659007342e-092.70425329503671e-09
2860.9999999954795949.04081242680053e-094.52040621340027e-09
2870.9999999914263341.71473312641353e-088.57366563206767e-09
2880.999999982524073.49518599594873e-081.74759299797436e-08
2890.9999999664853636.70292735931329e-083.35146367965665e-08
2900.9999999870361772.59276464714262e-081.29638232357131e-08
2910.9999999737444735.25110548069329e-082.62555274034665e-08
2920.9999999436849071.12630186935557e-075.63150934677784e-08
2930.9999998760379952.47924010717954e-071.23962005358977e-07
2940.9999997258834075.48233185445528e-072.74116592722764e-07
2950.9999994080821471.18383570605857e-065.91917853029284e-07
2960.9999989542252752.09154944920624e-061.04577472460312e-06
2970.9999981164797423.76704051679349e-061.88352025839674e-06
2980.9999967788691976.4422616057082e-063.2211308028541e-06
2990.9999947684791391.04630417217798e-055.23152086088989e-06
3000.9999917968609361.64062781279658e-058.20313906398288e-06
3010.9999871572730282.5685453944563e-051.28427269722815e-05
3020.9999786101230064.27797539870382e-052.13898769935191e-05
3030.9999719419082545.61161834909839e-052.80580917454919e-05
3040.9999703696698845.92606602328317e-052.96303301164158e-05
3050.999975505492934.89890141405716e-052.44945070702858e-05
3060.999984880980133.02380397378067e-051.51190198689033e-05
3070.9999939155356811.21689286377028e-056.08446431885142e-06
3080.9999989703697872.05926042519704e-061.02963021259852e-06
3090.9999978438228134.31235437473888e-062.15617718736944e-06
3100.999994982275291.00354494215834e-055.01772471079171e-06
3110.9999873881047192.52237905629019e-051.26118952814509e-05
3120.999969035158056.19296839011552e-053.09648419505776e-05
3130.9999579328242038.4134351593899e-054.20671757969495e-05
3140.9998936016831670.0002127966336658210.000106398316832910
3150.9997383193388090.0005233613223824350.000261680661191217
3160.9993944385463680.001211122907264070.000605561453632033
3170.9986922595472240.00261548090555290.00130774045277645
3180.9973126216511070.005374756697785390.00268737834889269
3190.9945081289299950.01098374214001070.00549187107000533
3200.9881351640173870.02372967196522680.0118648359826134
3210.9752164545526030.04956709089479380.0247835454473969
3220.9507610563955640.09847788720887120.0492389436044356
3230.9066328371155160.1867343257689670.0933671628844836
3240.8316568510278330.3366862979443350.168343148972167
3250.7146279891686750.5707440216626490.285372010831325
3260.5541882981695940.8916234036608120.445811701830406


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2470.771875NOK
5% type I error level2740.85625NOK
10% type I error level2800.875NOK
 
Charts produced by software:
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Parameters (Session):
par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 4 ; 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')
}
 





Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.


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