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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: Tue, 21 Dec 2010 18:24:11 +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/21/t1292955725wcx4cers13xoe56.htm/, Retrieved Tue, 21 Dec 2010 19:22:17 +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/21/t1292955725wcx4cers13xoe56.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 «
162556 213118 34643609608 6282154 29790 81767 2435838930 4321023 87550 153198 13412484900 4111912 84738 -26007 -2203781166 223193 54660 126942 6938649720 1491348 42634 157214 6702661676 1629616 40949 129352 5296835048 1398893 45187 234817 10610675779 1926517 37704 60448 2279131392 983660 16275 47818 778237950 1443586 25830 245546 6342453180 1073089 12679 48020 608845580 984885 18014 -1710 -30803940 1405225 43556 32648 1422016288 227132 24811 95350 2365728850 929118 6575 151352 995139400 1071292 7123 288170 2052634910 638830 21950 114337 2509697150 856956 37597 37884 1424324748 992426 17821 122844 2189202924 444477 12988 82340 1069431920 857217 22330 79801 1781956330 711969 13326 165548 2206092648 702380 16189 116384 1884140576 358589 7146 134028 957764088 297978 15824 63838 1010172512 585715 27664 74996 2074689344 657954 11920 31080 370473600 209458 8568 32168 275615424 786690 14416 49857 718738512 439798 3369 87161 293645409 688779 11819 106113 1254149547 574339 6984 80570 562 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 time26 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Wealth [t] = + 310866.23589241 + 8.9495259849649Costs[t] -0.0555356719630684Dividends[t] + 0.000138242066637196C_D[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)310866.2358924129331.99953510.598200
Costs8.94952598496491.7908064.99751e-060
Dividends-0.05553567196306840.382646-0.14510.8846720.442336
C_D0.0001382420666371961.1e-0512.143600


Multiple Linear Regression - Regression Statistics
Multiple R0.85967314106619
R-squared0.739037909470608
Adjusted R-squared0.737204452160098
F-TEST (value)403.084328843551
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation220695.308918194
Sum Squared Residuals20797641074618.2


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162821546543033.91854909-260879.918549091
24321023909667.0373736223411355.96262638
341119122940058.913318861171853.08668114
4223193766020.222223153-542827.222223153
514913481752210.79392465-260862.793924654
616296161610279.1436635719336.8563364291
713988931402402.14888282-3509.14888282058
819265172169069.49479786-242552.494797862
9983660960013.97709849223646.0229015077
101443586561449.38907928882136.61092072
1110730891405189.76512906-332100.765129063
12984885505838.524130237479046.475869763
131405225467919.562658458937305.437341542
14227132895441.131520165-668309.131520165
15929118854660.84411093374457.1558890673
161071292498874.0614687572417.9385313
17638830642370.486903773-3540.4869037728
18856956847904.2697866299051.73021337084
19992426842139.24767851150286.752321489
20444477766173.450885791-321696.450885791
21857217570370.35090428286846.649095720
22711969752618.674694785-40649.6746947851
23702380725908.606598555-23528.6065985547
24358589709754.135478494-351165.135478494
25297978499779.500415113-201801.500415113
26585715588586.584570685-2871.58457068479
27657954841090.312030665-183136.312030665
28209458467033.573047103-257575.573047103
29786690423860.94884673362829.05115327
30439798536473.657765226-96675.6577652256
31688779376770.79243047312008.20756953
32574339584123.851999077-9784.85199907709
33741409446684.148831111294724.851168889
34597793409438.951239156188354.048760844
35644190406562.472436158237627.527563842
36377934733845.512005982-355911.512005982
37640273524823.619973343115449.380026657
38697458435344.167202748262113.832797252
39550608384081.721135492166526.278864509
40207393387740.19452568-180347.194525680
41301607534194.329592346-232587.329592346
42345783611183.966489272-265400.966489272
43501749404836.01902454296912.9809754583
44379983477409.17820753-97426.1782075306
45387475392690.691938143-5215.69193814327
46377305390139.323683958-12834.3236839576
47370837485318.189801105-114481.189801105
48430866512112.322573509-81246.322573509
49469107430560.72463734538546.2753626547
50194493351187.717378948-156694.717378948
51530670380363.981005141150306.018994859
52518365417834.692142486100530.307857514
53491303555787.10593378-64484.1059337799
54527021335816.565633101191204.434366899
55233773444700.629033579-210927.629033579
56405972349013.30777785356958.6922221465
57652925367700.747431545285224.252568455
58446211419194.4876458227016.5123541795
59341340334514.5192986116825.4807013889
60387699502200.23037109-114501.230371090
61493408428019.19472004665388.805279954
62146494333933.761564062-187439.761564062
63414462374407.88322508040054.1167749196
64364304460110.662415353-95806.6624153533
65355178353353.0098749441824.99012505599
66357760590839.873273745-233079.873273745
67261216324083.505314616-62867.5053146158
68397144352163.70227188144980.2977281195
69374943342139.80918619632803.1908138036
70424898397362.60177031227535.3982296879
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72378525382137.185521623-3612.18552162252
73310768338881.537990715-28113.5379907151
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76247060341291.102142677-94231.1021426774
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79312378330755.664703712-18377.6647037117
80339836321132.79254532118703.2074546786
81347385331463.68864059515921.3113594049
82426280405992.61550106620287.3844989345
83352850327817.56788741225032.4321125880
84301881320409.512341503-18528.5123415025
85377516317060.66132206560455.3386779354
86357312408787.370587275-51475.3705872753
87458343383892.54444221774450.4555577833
88354228317686.17990071836541.8200992824
89308636354665.901715374-46029.9017153739
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96376641360305.26635217216335.7336478283
97429112311274.073857805117837.926142195
98330546333342.317057775-2796.31705777499
99403560372713.87719233830846.122807662
100317892333176.086418408-15284.0864184081
101307528331192.985571945-23664.985571945
102235133326766.874281656-91633.8742816565
103299243385443.637818836-86200.6378188362
104314073318761.865389364-4688.86538936404
105368186338151.45562025630034.5443797435
106269661320948.378491692-51287.378491692
107125390362511.914243190-237121.914243190
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109321896436253.651455659-114357.651455659
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112158492361775.89888489-203283.89888489
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114289513352735.227860313-63222.2278603132
115378049331148.96908155546900.0309184446
116343466332898.35022672810567.6497732724
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121375195560739.998386112-185544.998386112
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194315380307494.1098908147885.89010918592
195315688307970.9472184107717.05278158951
196315380307494.1098908147885.89010918592
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198315380307494.1098908147885.89010918592
199315380307494.1098908147885.89010918592
200269587315868.015992747-46281.0159927471
201315380307494.1098908147885.89010918592
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326312502307875.5637560874626.43624391303
327315380307494.1098908147885.89010918592
328315380307494.1098908147885.89010918592
329315380307494.1098908147885.89010918592
330315380307494.1098908147885.89010918592
331315380307494.1098908147885.89010918592
332315380307494.1098908147885.89010918592
333315380307494.1098908147885.89010918592
334313729309173.5061526934555.49384730709
335315388307511.0656930767876.93430692403
336315371312939.9953519632431.00464803683
337296139322144.628845303-26005.6288453033
338315380307494.1098908147885.89010918592
339313880307935.9013992965944.09860070388
340317698309699.7777625547998.22223744647
341295580312736.175330998-17156.1753309980
342315380307494.1098908147885.89010918592
343315380307494.1098908147885.89010918592
344315380307494.1098908147885.89010918592
345308256318264.475723214-10008.4757232140
346315380307494.1098908147885.89010918592
347303677309620.610374469-5943.61037446922
348315380307494.1098908147885.89010918592
349315380307494.1098908147885.89010918592
350319369335157.126803339-15788.1268033388
351318690312931.629783725758.37021627965
352314049308515.6395233075533.36047669317
353325699317645.9798841978053.020115803
354314210309785.8995918824424.10040811793
355315380307494.1098908147885.89010918592
356315380307494.1098908147885.89010918592
357322378316689.0169564085688.98304359234
358315380307494.1098908147885.89010918592
359315380307494.1098908147885.89010918592
360315380307494.1098908147885.89010918592
361315398307511.3426802257886.65731977457
362315380307494.1098908147885.89010918592
363315380307494.1098908147885.89010918592
364308336338236.451841432-29900.4518414324
365316386310649.2125880915736.78741190866
366315380307494.1098908147885.89010918592
367315380307494.1098908147885.89010918592
368315380307494.1098908147885.89010918592
369315380307494.1098908147885.89010918592
370315553311275.0112619304277.98873806967
371315380307494.1098908147885.89010918592
372323361315258.0290736188102.97092638241
373336639311046.46371392425592.5362860764
374307424310382.819189289-2958.81918928900
375315380307494.1098908147885.89010918592
376315380307494.1098908147885.89010918592
377295370309768.951258216-14398.9512582159
378322340318013.6064008724326.39359912836
379319864345858.118298654-25994.1182986540
380315380307494.1098908147885.89010918592
381315380307494.1098908147885.89010918592
382317291316911.644395245379.35560475535
383280398316946.999762822-36548.9997628215
384315380307494.1098908147885.89010918592
385317330308758.2989382508571.70106174966
386238125352706.371066927-114581.371066927
387327071309805.75352328417265.2464767156
388309038323350.908486469-14312.9084864686
389314210308757.5254406385452.47455936211
390307930317364.267082998-9434.26708299811
391322327314378.2122391707948.7877608304
392292136315289.4136179-23153.4136179
393263276318288.823012987-55012.8230129868
394367655319827.12510056847827.8748994319
395283910376466.790023157-92556.7900231575
396283587317191.042230696-33604.0422306960
397243650387835.711446489-144185.711446489
398438493341197.26735033797295.732649663
399296261316724.288271323-20463.2882713231
400230621334898.872699268-104277.872699268
401304252326779.246965896-22527.2469658958
402333505321134.33928808012370.6607119204
403296919318046.776627451-21127.7766274513
404278990335301.864368839-56311.8643688388
405276898317854.889671126-40956.8896711258
406327007329070.086479644-2063.08647964356
407317046318485.303388799-1439.30338879875
408304555324501.592274832-19946.5922748319
409298096315078.565353851-16982.5653538513
410231861320500.659985215-88639.6599852153
411309422331231.960768886-21809.9607688861
412286963438625.320027425-151662.320027425
413269753327323.756464213-57570.7564642133
414448243370735.05502887877507.9449711216
415165404344718.717786303-179314.717786303
416204325325225.042080803-120900.042080803
417407159353914.85501897753244.1449810234
418290476327337.720638892-36861.7206388920
419275311330539.051368332-55228.051368332
420246541319144.599231298-72603.5992312985
421253468325827.917808456-72359.9178084555
422240897360858.268628349-119961.268628349
423-83265391664.432450494-474929.432450494
424-42143416538.310095989-458681.310095989
425272713345332.198221908-72619.1982219082
426215362400213.87649995-184851.87649995
42742754372142.720461594-329388.720461594
4283062751395502.14155766-1089227.14155766
429253537490946.139425451-237409.139425451
430372631606029.005859414-233398.005859414
431-7170539263.462723035-546433.462723035


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
717.55873921075466e-553.77936960537733e-55
811.6349455564329e-598.1747277821645e-60
913.02427654152587e-791.51213827076293e-79
1014.76221979289045e-932.38110989644522e-93
1113.75378765918281e-941.87689382959140e-94
1213.6307260545363e-1021.81536302726815e-102
1311.26898336828760e-1176.34491684143801e-118
1412.50483699669424e-1291.25241849834712e-129
1512.27682474766907e-1321.13841237383454e-132
1618.94896997573542e-1404.47448498786771e-140
1716.24037964943325e-1393.12018982471663e-139
1811.91891194904391e-1429.59455974521956e-143
1918.87178929415699e-1464.43589464707849e-146
2016.37985889089384e-1483.18992944544692e-148
2111.52624862654519e-1537.63124313272597e-154
2211.20559494629958e-1566.02797473149791e-157
2311.16445614940913e-1575.82228074704566e-158
2412.69755428098908e-1591.34877714049454e-159
2514.65040925634698e-1602.32520462817349e-160
2618.46295379682022e-1624.23147689841011e-162
2715.56296277453947e-1652.78148138726973e-165
2818.26555470311634e-1674.13277735155817e-167
2911.67415089128157e-1768.37075445640787e-177
3018.79340033226167e-1784.39670016613083e-178
3115.96590811419242e-1822.98295405709621e-182
3212.48770592904354e-1831.24385296452177e-183
3312.44711018672766e-1911.22355509336383e-191
3412.20534181194965e-1931.10267090597483e-193
3513.53133480927369e-1931.76566740463684e-193
3618.34182080929548e-1944.17091040464774e-194
3712.35013963839531e-1991.17506981919766e-199
3812.42782881466061e-2051.21391440733031e-205
3911.70020377221244e-2048.5010188610622e-205
4013.72742632551941e-2051.86371316275971e-205
4113.34529124295385e-2051.67264562147692e-205
4213.58548185054094e-2051.79274092527047e-205
4315.04244623550497e-2062.52122311775249e-206
4413.11234225574321e-2051.55617112787161e-205
4515.74123012768446e-2052.87061506384223e-205
4614.48065064477063e-2042.24032532238532e-204
4716.86025820936071e-2053.43012910468036e-205
4815.18469103413741e-2042.59234551706871e-204
4911.71332806579228e-2038.56664032896142e-204
5013.87678620639921e-2041.93839310319960e-204
5114.60970954780128e-2052.30485477390064e-205
5215.10603263914227e-2052.55301631957113e-205
5315.48909198454562e-2042.74454599227281e-204
5417.38967874183562e-2043.69483937091781e-204
5513.11129823319402e-2061.55564911659701e-206
5613.46538553061893e-2061.73269276530946e-206
5712.93088076637861e-2181.46544038318931e-218
5817.68695285372362e-2193.84347642686181e-219
5917.28066904711216e-2183.64033452355608e-218
6014.97388987735067e-2182.48694493867533e-218
6117.67385414511202e-2203.83692707255601e-220
6218.95149236215814e-2224.47574618107907e-222
6312.68680136655168e-2211.34340068327584e-221
6414.33026530517955e-2212.16513265258978e-221
6511.34229425799703e-2206.71147128998517e-221
6613.85555997239390e-2211.92777998619695e-221
6718.98542991685415e-2214.49271495842708e-221
6816.59483955121512e-2203.29741977560756e-220
6916.62729593100205e-2193.31364796550102e-219
7011.16152150566849e-2185.80760752834247e-219
7114.61813304638582e-2182.30906652319291e-218
7218.51228696105988e-2204.25614348052994e-220
7314.00995119967017e-2192.00497559983509e-219
7414.35295452735295e-2182.17647726367648e-218
7514.93510889079457e-2172.46755444539729e-217
7619.62861919577157e-2174.81430959788578e-217
7711.05455356173046e-2155.27276780865231e-216
7811.09526757818779e-2155.47633789093897e-216
7911.13885582146093e-2145.69427910730465e-215
8016.2058927032445e-2143.10294635162225e-214
8113.82227145588469e-2131.91113572794235e-213
8211.77264861384473e-2138.86324306922366e-214
8314.94530017592422e-2132.47265008796211e-213
8413.9419392816039e-2121.97096964080195e-212
8514.41926014568305e-2112.20963007284153e-211
8612.80960207614175e-2111.40480103807087e-211
8712.43097418468100e-2121.21548709234050e-212
8812.44134127021086e-2111.22067063510543e-211
8919.37276620565588e-2114.68638310282794e-211
9011.00451693610666e-2095.0225846805333e-210
9116.52995991309391e-2093.26497995654696e-209
9212.57741840239981e-2081.28870920119990e-208
9311.85377457216141e-2109.26887286080703e-211
9411.66010896280683e-2098.30054481403414e-210
9516.77139381673606e-2103.38569690836803e-210
9613.56517525179589e-2101.78258762589794e-210
9712.39458412838576e-2091.19729206419288e-209
9812.28781783040409e-2081.14390891520204e-208
9912.50537630479148e-2071.25268815239574e-207
10012.57438635044085e-2061.28719317522042e-206
10112.41055639244476e-2051.20527819622238e-205
10213.63170018777041e-2061.81585009388520e-206
10318.82932751130066e-2064.41466375565033e-206
10418.08901419423986e-2064.04450709711993e-206
10512.96863389808848e-2051.48431694904424e-205
10611.05290193643952e-2045.26450968219759e-205
10713.71480383880044e-2071.85740191940022e-207
10811.74565832296801e-2098.72829161484004e-210
10911.52096477474121e-2087.60482387370607e-209
11013.33652590058354e-2081.66826295029177e-208
11111.80009766726739e-2089.00048833633693e-209
11215.54708175051246e-2092.77354087525623e-209
11314.61118546433578e-2082.30559273216789e-208
11413.93657523605417e-2071.96828761802709e-207
11513.20560774772186e-2071.60280387386093e-207
11611.20947833938541e-2066.04739169692707e-207
11711.18023437689862e-2055.9011718844931e-206
11812.26663012896833e-2061.13331506448417e-206
11913.34208070344341e-2071.67104035172170e-207
12013.53412623967084e-2061.76706311983542e-206
12116.0523549602544e-2063.0261774801272e-206
12215.75479622381364e-2052.87739811190682e-205
12316.26282839333829e-2043.13141419666914e-204
12414.02691009639987e-2052.01345504819994e-205
12517.20141759978422e-2053.60070879989211e-205
12614.23417387124166e-2052.11708693562083e-205
12714.70344317822983e-2042.35172158911491e-204
12815.18940594226901e-2032.59470297113450e-203
12915.36613625258553e-2022.68306812629276e-202
13015.8658063596019e-2012.93290317980095e-201
13116.37292304875038e-2003.18646152437519e-200
13214.89776321919855e-2002.44888160959927e-200
13315.31488913319376e-1992.65744456659688e-199
13415.72412963483698e-1982.86206481741849e-198
13516.02873961881942e-1973.01436980940971e-197
13616.36970341489172e-1963.18485170744586e-196
13716.69483712808317e-1953.34741856404158e-195
13817.07492145355548e-1943.53746072677774e-194
13917.01004137582887e-1933.50502068791443e-193
14017.33226599806858e-1923.66613299903429e-192
14116.71316173686032e-1913.35658086843016e-191
14216.95088995279216e-1903.47544497639608e-190
14316.99212588034923e-1893.49606294017462e-189
14417.16113760947905e-1883.58056880473953e-188
14516.50826255423512e-1873.25413127711756e-187
14616.4217963980978e-1863.2108981990489e-186
14716.48245703079734e-1853.24122851539867e-185
14816.51046583174651e-1843.25523291587326e-184
14916.03027645247817e-1833.01513822623908e-183
15015.99400813799575e-1822.99700406899787e-182
15115.43360937647077e-1812.71680468823538e-181
15214.86202152622979e-1802.43101076311489e-180
15314.76420365634352e-1792.38210182817176e-179
15414.47757139409911e-1782.23878569704955e-178
15514.3440593465205e-1772.17202967326025e-177
15614.19312234892229e-1762.09656117446115e-176
15714.02694389795829e-1752.01347194897915e-175
15813.84595440636857e-1741.92297720318428e-174
15912.80327847087799e-1731.40163923543899e-173
16012.65410648774621e-1721.32705324387311e-172
16112.50027776583571e-1711.25013888291785e-171
16212.34358663204669e-1701.17179331602334e-170
16312.18575524784083e-1691.09287762392041e-169
16412.0127775340868e-1681.0063887670434e-168
16511.77967873615135e-1678.89839368075674e-168
16611.63513070129979e-1668.17565350649895e-167
16711.49547136094756e-1657.47735680473778e-166
16813.6465997402891e-1661.82329987014455e-166
16912.17480747811803e-1661.08740373905902e-166
17012.00849246544937e-1651.00424623272468e-165
17111.84578926981029e-1649.22894634905146e-165
17211.68645269685089e-1638.43226348425444e-164
17311.53474854404136e-1627.67374272020681e-163
17411.38300756735722e-1616.91503783678612e-162
17511.24643249878298e-1606.23216249391489e-161
17611.11449388481433e-1595.57246942407167e-160
17719.85552510545624e-1594.92776255272812e-159
17818.7250997684639e-1584.36254988423195e-158
17917.71229950441217e-1573.85614975220609e-157
18016.78410436030931e-1563.39205218015466e-156
18113.19853314657123e-1551.59926657328562e-155
18212.74345672277964e-1541.37172836138982e-154
18311.32709741548595e-1536.63548707742974e-154
18418.77994060901664e-1534.38997030450832e-153
18517.59449515402794e-1523.79724757701397e-152
18614.91027289378744e-1512.45513644689372e-151
18711.11711525266401e-1505.58557626332005e-151
18819.58549414328814e-1504.79274707164407e-150
18916.43362196375518e-1493.21681098187759e-149
19015.46869948183143e-1482.73434974091572e-148
19114.44375713665062e-1472.22187856832531e-147
19213.74177776691092e-1461.87088888345546e-146
19313.13183917916811e-1451.56591958958406e-145
19412.61209305027676e-1441.30604652513838e-144
19512.16657012570818e-1431.08328506285409e-143
19611.78990069074488e-1428.9495034537244e-143
19713.67937267938198e-1421.83968633969099e-142
19813.03054890714611e-1411.51527445357305e-141
19912.48432410802882e-1401.24216205401441e-140
20015.03047396262092e-1402.51523698131046e-140
20114.11188991591159e-1392.05594495795579e-139
20213.34516339798206e-1381.67258169899103e-138
20312.70855517837558e-1371.35427758918779e-137
20412.16609016859548e-1361.08304508429774e-136
20511.55540218189754e-1357.77701090948768e-136
20611.24311764046171e-1346.21558820230855e-135
20719.90028062425629e-1344.95014031212814e-134
20817.83374162355945e-1333.91687081177973e-133
20911.61703019361899e-1328.08515096809494e-133
21011.27144022369735e-1316.35720111848677e-132
21119.97688231076417e-1314.98844115538208e-131
21217.7919252160462e-1303.8959626080231e-130
21314.92663958054817e-1292.46331979027408e-129
21413.33138231898488e-1281.66569115949244e-128
21512.54757402708805e-1271.27378701354402e-127
21611.95588850607851e-1269.77944253039256e-127
21711.49364885314246e-1257.4682442657123e-126
21811.10050636534279e-1245.50253182671393e-125
21918.33114726138475e-1244.16557363069238e-124
22013.66998314292552e-1231.83499157146276e-123
22112.62736019273222e-1221.31368009636611e-122
22211.96648060459344e-1219.8324030229672e-122
22311.46477496300172e-1207.32387481500859e-121
22411.07615671543564e-1195.38078357717821e-120
22517.93642086621439e-1193.96821043310719e-119
22615.79557794323614e-1182.89778897161807e-118
22714.236248392613e-1172.1181241963065e-117
22813.08214720564709e-1161.54107360282355e-116
22912.22350047093046e-1151.11175023546523e-115
23011.60263632714775e-1148.01318163573874e-115
23111.07654513896395e-1135.38272569481973e-114
23216.95786186661672e-1133.47893093330836e-113
23314.94866342961737e-1122.47433171480869e-112
23413.46342846480098e-1111.73171423240049e-111
23512.44038980658514e-1101.22019490329257e-110
23611.71108054765671e-1098.55540273828357e-110
23711.19423029187338e-1085.9711514593669e-109
23818.26472289836239e-1084.13236144918119e-108
23915.71352522092156e-1072.85676261046078e-107
24013.93102074382692e-1061.96551037191346e-106
24112.69171847025896e-1051.34585923512948e-105
24211.83826143782649e-1049.19130718913246e-105
24311.24674349637743e-1036.23371748188716e-104
24418.37877931459649e-1034.18938965729824e-103
24514.88326977302862e-1022.44163488651431e-102
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35411.38797940288443e-266.93989701442215e-27
35515.00538859840025e-262.50269429920012e-26
35611.79009364258351e-258.95046821291754e-26
35716.42042534709465e-253.21021267354732e-25
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35917.87852080896356e-243.93926040448178e-24
36012.72415773877895e-231.36207886938948e-23
36119.33599965768735e-234.66799982884367e-23
36213.17132535237794e-221.58566267618897e-22
36311.06756315345544e-215.33781576727718e-22
36413.39877435496259e-211.69938717748129e-21
36511.10676724378884e-205.53383621894422e-21
36613.62497815353183e-201.81248907676591e-20
36711.17601061319968e-195.88005306599838e-20
36813.77845897143334e-191.88922948571667e-19
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37213.40889460459156e-171.70444730229578e-17
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37413.24835040816121e-161.62417520408060e-16
37519.72248945389316e-164.86124472694658e-16
3760.9999999999999992.87829264844106e-151.43914632422053e-15
3770.9999999999999968.59852777803901e-154.29926388901951e-15
3780.9999999999999882.35726720385880e-141.17863360192940e-14
3790.999999999999975.83526029539177e-142.91763014769588e-14
3800.9999999999999171.65403050105564e-138.27015250527822e-14
3810.9999999999997684.63228738671086e-132.31614369335543e-13
3820.999999999999341.31965253550736e-126.59826267753682e-13
3830.9999999999982423.51660740008501e-121.75830370004250e-12
3840.9999999999952579.48556280655777e-124.74278140327889e-12
3850.9999999999873372.53251202162907e-111.26625601081453e-11
3860.9999999999696936.06143282751082e-113.03071641375541e-11
3870.9999999999253971.49205232896684e-107.4602616448342e-11
3880.9999999998128363.74328261166607e-101.87164130583304e-10
3890.9999999995252189.49564301180715e-104.74782150590357e-10
3900.9999999988230982.35380356287194e-091.17690178143597e-09
3910.9999999971715155.65697000009239e-092.82848500004620e-09
3920.999999992879631.42407396244493e-087.12036981222467e-09
3930.9999999824772473.50455057317004e-081.75227528658502e-08
3940.999999967391216.52175789562742e-083.26087894781371e-08
3950.9999999217798181.56440364591333e-077.82201822956663e-08
3960.9999998117914153.76417170177901e-071.88208585088950e-07
3970.9999995725230228.54953955938248e-074.27476977969124e-07
3980.9999991066019381.78679612458261e-068.93398062291307e-07
3990.999997946792294.10641542175135e-062.05320771087567e-06
4000.9999958298499738.34030005463883e-064.17015002731942e-06
4010.999990723752711.85524945785728e-059.27624728928639e-06
4020.9999819781417353.60437165299645e-051.80218582649823e-05
4030.9999623545898777.52908202448883e-053.76454101224441e-05
4040.9999197459242460.0001605081515076058.02540757538027e-05
4050.9998323348362270.0003353303275458090.000167665163772904
4060.9996772766920270.0006454466159455110.000322723307972756
4070.999379651858350.001240696283299250.000620348141649627
4080.9988706469389360.002258706122128250.00112935306106413
4090.9979484112922710.004103177415457640.00205158870772882
4100.9963258368320240.007348326335951950.00367416316797597
4110.9934303152513940.01313936949721120.0065696847486056
4120.9897730375224670.02045392495506630.0102269624775331
4130.9823028880750780.03539422384984420.0176971119249221
4140.9861369159189070.02772616816218620.0138630840810931
4150.9803968507242530.03920629855149370.0196031492757469
4160.9684617620107930.06307647597841390.0315382379892070
4170.9945327031010540.01093459379789190.00546729689894594
4180.9907649051366070.01847018972678580.00923509486339289
4190.9808067657891320.03838646842173710.0191932342108685
4200.9610995297738390.07780094045232270.0389004702261613
4210.9235743364426750.152851327114650.076425663557325
4220.855176526161220.2896469476775590.144823473838780
4230.8224317097626070.3551365804747850.177568290237392
4240.8561184693265510.2877630613468970.143881530673449


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4040.966507177033493NOK
5% type I error level4120.985645933014354NOK
10% type I error level4140.99043062200957NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/109ipo1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/109ipo1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/12hau1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/12hau1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/22hau1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/22hau1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/3v89f1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/3v89f1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/4v89f1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/4v89f1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/5v89f1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/5v89f1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/6o0801292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/6o0801292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/7g9ql1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/7g9ql1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/8g9ql1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/8g9ql1292955824.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/9g9ql1292955824.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t1292955725wcx4cers13xoe56/9g9ql1292955824.ps (open in new window)


 
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')
}
 




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Software written by Ed van Stee & Patrick Wessa


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