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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: Thu, 02 Dec 2010 14:00:52 +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/02/t1291298417wvmlwsw9pxo9olp.htm/, Retrieved Thu, 02 Dec 2010 15:00:27 +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/02/t1291298417wvmlwsw9pxo9olp.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 807 213118 6282929 5627 37 29790 444 81767 4324047 13346 138 87550 412 153198 4108272 8533 45 84738 428 -26007 -1212617 -2402 -17 54660 312 126942 1485329 4299 24 42634 166 157214 1779876 10127 37 40949 263 129352 1367203 2427 29 42312 237 234817 2519076 7180 55 37704 228 60448 912684 1577 19 16275 129 47818 1443586 11409 76 25830 104 245546 1220017 8870 39 12679 122 48020 984885 7135 62 18014 393 -1710 1457425 5261 70 43556 190 32648 -572920 -3129 -18 24524 275 95350 929144 1467 30 6532 62 151352 1151176 9235 146 7123 102 288170 790090 5414 83 20813 255 114337 774497 1144 28 37597 234 37884 990576 3188 21 17821 277 122844 454195 681 14 12988 73 82340 876607 5686 52 22330 67 79801 711969 6095 23 13326 103 165548 702380 4925 38 16189 290 116384 264449 218 4 7146 83 134028 450033 2381 35 15824 56 63838 541063 5329 22 26088 224 74996 588864 1456 15 11326 64 31080 -37216 -1839 -21 8568 34 32168 783310 15765 68 14416 139 49857 467359 741 19 3369 26 87161 688779 17456 145 11819 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 time10 seconds
R Server'Herman Ole Andreas Wold' @ www.wessa.org


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = -38586.61308433 + 15.8634109045401Costs[t] + 1705.00885637629Orders[t] + 3.44410489813157Dividends[t] + 3.19252902874447`Profit/Trades`[t] + 0.070691761105367`Profit/Cost`[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)-38586.6130843351342.37784-0.75160.4529280.226464
Costs15.86341090454013.0857135.14091e-060
Orders1705.00885637629520.0036233.27880.0011690.000585
Dividends3.444104898131570.5814425.923400
`Profit/Trades`3.192529028744471.0576083.01860.0027650.001382
`Profit/Cost`0.0706917611053671.3889450.05090.9594430.479722


Multiple Linear Regression - Regression Statistics
Multiple R0.756023146596159
R-squared0.571570998189157
Adjusted R-squared0.564184291261384
F-TEST (value)77.378323490826
F-TEST (DF numerator)5
F-TEST (DF denominator)290
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation354393.912397425
Sum Squared Residuals36422563091862.6


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829294668015.881129671614913.11887033
243240471515239.703079172808807.29692083
341082722607593.673950671500678.32604933
4-12126171938150.39810096-3150767.39810096
514853291811398.13302269-326069.133022689
617798761494560.38210241285315.617897592
713672031512673.70406959-145470.704069595
825190761868373.75440755650702.245592445
99126841161494.66521829-248810.665218292
101443586640655.686141247802930.313858753
1112200171422492.88242333-202475.882423333
12984885558725.6489698426159.3510302
131457425928156.775773636529268.224226364
14-5729201078764.23591687-1651684.23591687
159291441152406.07431694-223262.074316937
161151176721509.22715904429666.772840959
177900901258097.29421146-468007.294211456
187744971123798.67076368-349301.67076368
199905761097457.85611715-106881.856117153
204541951141665.40992102-687470.409921015
21876607593657.007600478282949.992399522
22711969724182.051107762-12213.0511077616
23702380934315.682265701-231935.682265701
242644491114213.67295785-849764.672957849
25450033685499.433434602-235466.433434602
26541063544795.807926031-3732.80792603128
275888641020123.50800414-431259.508004144
28-37216351373.180451659-388589.180451659
29783310316426.386203572466883.613796428
30467359601176.294611731-133817.294611731
31688779415118.112576018273660.887423982
32608419649060.53959296-40641.5395929602
33696348448141.274856587248206.725143413
34597793482376.673432694115416.326567306
358217301146314.05406504-324584.05406504
36377934971669.323506285-593735.323506285
37651939572331.17585473479607.8241452656
38697458589455.737738846108002.262261154
39700368821186.103459436-120818.103459436
40225986524743.000208741-298757.000208741
41348695844997.318359624-496302.318359624
42373683615775.232013946-242092.232013946
43501709512302.796676192-10593.796676192
44413743631673.323955609-217930.323955609
45379825348776.5397924831048.4602075198
46336260428991.568184937-92731.5681849374
47636765792749.733982289-155984.733982289
48481231808879.149533286-327648.149533286
49469107568188.497663804-99081.497663804
50211928331843.583503196-119915.583503196
51563925548046.58968591215878.4103140878
52511939729897.64086587-217958.64086587
53521016901776.077805261-380760.077805261
54543856597200.453349969-53344.4533499686
55329304771664.012537326-442360.012537326
56423262349162.23459335774099.7654066427
57509665314361.399453252195303.600546748
58455881441248.89304671714632.1069532832
59367772416419.019951182-48647.0199511823
60406339561901.271328533-155562.271328533
61493408467911.8724766125496.1275233897
62232942250751.5121532-17809.5121531996
63416002399904.60252629716097.3974737034
64337430492761.286739017-155331.286739017
65361517305712.19147211455804.8085278857
66360962912976.5766124-552014.576612401
67235561280739.434315527-45178.4343155274
68408247427419.291790122-19172.2917901225
69450296568559.934936123-118263.934936123
70418799526792.290821062-107993.290821062
71247405189999.72123303157405.2787669688
72378519253495.792459823125023.207540177
73326638423810.852128841-97172.8521288409
74328233295847.55701821332385.4429817874
75386225477146.650951202-90921.6509512021
76283662293855.668719896-10193.6687198956
77370225433760.662892718-63535.6628927185
78269236253079.32243142816156.6775685716
79365732314156.69302467151575.3069753286
80420383404235.30283983216147.6971601678
81345811260689.75181658385121.2481834166
82431809464192.983999688-32383.9839996885
83418876522067.684563624-103191.684563624
84297476153670.020528058143805.979471942
85416776395106.25007341521669.7499265854
86357257395868.841337063-38611.8413370628
87458343510155.987700172-51812.9877001724
88388386393177.231182182-4791.23118218225
89358934446547.974388154-87613.9743881535
90407560410474.789013163-2914.78901316291
91392558395452.779489077-2894.77948907731
92373177375410.981729334-2233.98172933352
93428370339487.52104125388882.4789587472
94369419558799.420873542-189380.420873542
95358649205204.470913997153444.529086003
96376641281642.37009028894998.629909712
97467427477029.439111027-9602.43911102659
98364885265743.15056242899141.8494375724
99436230516986.032541582-80756.0325415817
100329118288358.84872331340759.1512766875
101317365307779.4229193739585.57708062686
102286849333145.254845467-46296.2548454668
103376685489254.142961536-112569.142961536
104407198412770.250447916-5572.25044791569
105377772283336.44278783894435.5572121618
106271483279085.505530967-7602.50553096649
107153661297488.367002527-143827.367002527
108513294408299.415470305104994.584529695
109324881481294.106008416-156413.106008416
110264512283146.247496684-18634.2474966843
111420968271293.629118111149674.370881889
112129302232790.979686852-103488.979686852
113191521414024.202492486-222503.202492486
114268673292197.147493507-23524.1474935068
115353179246161.692752796107017.307247204
116354624251720.590807018102903.409192982
117363713294277.15108328169435.8489167189
118456657370057.1867566586599.8132433503
119211742283835.912198213-72093.9121982127
120338381227904.879468252110476.120531748
121418530673592.733839664-255062.733839664
122351483261064.3996741690418.6003258403
123372928493695.545544933-120767.545544933
124485538432308.27944193753229.7205580632
125279268255932.58426122723335.4157387732
126219060316703.059482389-97643.0594823886
127325314246578.49712438278735.5028756184
128322046220793.83124255101252.16875745
129325599233085.88798579892513.1120142017
130377028229352.532163235147675.467836765
131323850337896.825509136-14046.8255091364
132331514228313.661518123103200.338481877
133325632221118.819454042104513.180545958
134322265210589.616913964111675.383086036
135325906218323.570860306107582.429139694
136325985312847.29445127213137.7055487277
137346145243583.177269773102561.822730227
138325898212939.997289178112958.002710822
139325356250674.91489140974681.0851085906
140325930574433.935022821-248503.935022821
141318020221288.44948309596731.5505169052
142326389281544.74735522944844.2526447706
143302925212412.94052575890512.0594742424
144325540309052.24517011716487.7548298826
145326736380551.82509905-53815.8250990503
146340580250059.76566608490520.2343339155
147331828206123.795428681125704.204571319
148323299235151.87133058888147.1286694117
149387722193029.575436663194692.424563337
150324598278826.15164229945771.8483577008
151328726239007.34018358689718.6598164143
152325043232990.55771561192052.4422843891
153325806573517.120835412-247711.120835412
154387732273613.142504595114118.857495405
155349729283152.74675718666576.2532428135
156332202187910.748416263144291.251583737
157305442272704.33980492232737.6601950775
158329537268854.91395374460682.0860462562
159327055227196.22178942599858.7782105752
160356245244172.297678373112072.702321627
161328451269759.80731020358691.1926897966
162307062268348.17804787838713.8219521217
163331345287498.73150578243846.268494218
164331824258054.59749863273769.4025013675
165325685377627.582537259-51942.5825372585
166404480527433.546347718-122953.546347718
167318314295884.20707079422429.7929292065
168311807173327.284718884138479.715281116
169337724316604.3313282421119.6686717598
170326431385158.042687562-58727.0426875617
171327556294009.50730359633546.4926964039
172356850206538.842598089150311.157401911
173322741195201.280939998127539.719060002
174310902217157.13685617293744.8631438279
175324295250782.35795629973512.6420437007
176326156232325.26487159493830.7351284057
177326960203014.956671375123945.043328625
178333411230705.726935767102705.273064233
179297761257549.23718077840211.7628192225
180325536375413.298781216-49877.2987812162
181325762374059.559269594-48297.5592695939
182327957230558.38071284297398.6192871585
183318521287324.89348259331196.1065174074
184319775241020.01253135278754.9874686481
185325486575282.024153038-249796.024153038
186325838247458.21057458878379.789425412
187331767319671.07912524112095.9208747588
188324523229803.63686117694719.3631388245
189339995363873.987836707-23878.9878367067
190319582236710.59885817982871.401141821
191307245201021.676031454106223.323968546
192317967375392.145188372-57425.1451883717
193331488293279.19208084738208.8079191535
194335452349035.333072115-13583.3330721149
195334184219813.648825115114370.351174885
196313213186168.739461765127044.260538235
197348678277616.89232159171061.107678409
198328727213467.755175908115259.244824092
199387978301820.64476259886157.3552374021
200336704321198.61786882415505.3821311764
201322076237732.90549826984343.0945017311
202334272215761.552684564118510.447315436
203338197240367.70168089797829.2983191035
204321024252223.69278291768800.3072170833
205322145226487.82113056395657.1788694375
206323351210567.695596082112783.304403918
207327748257321.62279759970426.3772024005
208328157283279.32829434544877.671705655
209311594180400.89459747131193.10540253
210335962219065.94954567116896.05045433
211372426306638.40891174165787.5910882594
212319844211736.954191742108107.045808258
213355822210994.913806226144827.086193774
214324047277405.79191519246641.2080848079
215311464348150.88536177-36686.8853617696
216353417213234.746225834140182.253774166
217325590240482.91525025585107.0847497449
218328576249219.41475202279356.5852479783
219326126203150.031225374122975.968774626
220369376328610.96230257640765.0376974237
221332013259726.31529815172286.6847018486
222325871287748.18748035538122.8125196451
223342165230115.652073986112049.347926014
224324967567763.584765331-242796.584765331
225314832233604.45297871481227.5470212858
226325557252362.45020363773194.5497963627
227322649368779.317437936-46130.3174379363
228324598257357.78350156967240.2164984313
229325567381781.895222911-56214.8952229105
230324005236014.61314061487990.386859386
231325748575055.032565067-249307.032565067
232323385216546.8416828106838.1583172
233315409228157.92196223187251.0780377685
234312275231833.35217932180441.6478206787
235320576200820.066743853119755.933256147
236325246224952.882908361100293.117091639
237332961228415.997752809104545.002247191
238323010375439.295545752-52429.2955457521
239345253275405.63618672969847.363813271
240325559290843.41631162134715.5836883792
241319634305358.49012307314275.5098769267
242319951219864.756649066100086.243350934
243318519195825.488739604122693.511260396
244343222291770.00315448951451.9968455113
245317234566856.191573653-249622.191573653
246314025190805.249768781123219.750231219
247320249226040.18726377394208.812736227
248349365261388.24892352287976.7510764783
249289197140763.355173016148433.644826984
250329245224963.096940266104281.903059734
251240869287130.65774045-46261.6577404502
252327182241825.8714712985356.1285287098
253322876237225.44533303385650.5546669669
254323117306827.06188821716289.9381117834
255306351207116.88285825599234.117141745
256335137243908.94026359591228.0597364052
257308271226328.2226320881942.7773679196
258301731241247.31071398860483.6892860117
259382409289869.87290608792539.1270939133
260279230340168.595640173-60938.5956401732
261298731209556.9903434889174.0096565201
262243650268948.306261019-25298.3062610192
263532682818134.134064093-285452.134064093
264319771244217.3257750175553.6742249895
265171493136712.23607396734780.7639260325
266347262319912.32996582627349.6700341737
267343945259652.78018889984292.219811101
268311874229849.81556725582024.1844327454
269302211273334.05174772428876.9482522757
270316708257335.17274190259372.8272580978
271333463275179.07887158458283.9211284155
272344282253042.6433747691239.3566252399
273319635235254.00764338884380.9923566122
274301186213951.24259051487234.7574094857
275300381325895.487337565-25514.4873375648
276318765326106.703605126-7341.7036051263
277286146318599.248863511-32453.2488635112
278306844222941.17140278183902.8285972185
279307705338004.319478115-30299.3194781153
280312448316429.244544924-3981.24454492419
281299715339359.426223795-39644.4262237954
282373399182075.074598496191323.925401504
283299446246717.12469310652728.8753068938
284325586276259.76859074649326.2314092545
285291221297724.490904846-6503.49090484617
286261173317137.356668859-55964.3566688586
287255027385649.868686985-130622.868686985
288-78375197434.49976389-275809.49976389
289-58143259621.111672062-317764.111672062
290227033225049.0059680851983.99403191451
291235098398953.045637305-163855.045637305
29221267218149.348263358-196882.348263358
2932386751484788.00631689-1246113.00631689
294197687436429.487065577-238742.487065577
295418341624196.625525302-205855.625525302
296-297706450898.05919022-748604.05919022


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.9999999999999341.32630558780009e-136.63152793900045e-14
100.9999999999999992.51835458464847e-151.25917729232424e-15
1111.12021850073148e-185.60109250365741e-19
1214.35816540573898e-192.17908270286949e-19
1317.78458745267825e-253.89229372633913e-25
1411.36774444552594e-326.83872222762968e-33
1514.81230339756726e-342.40615169878363e-34
1612.19273936474794e-471.09636968237397e-47
1711.40899670100011e-507.04498350500053e-51
1814.98482298405181e-512.4924114920259e-51
1918.59964217648324e-574.29982108824162e-57
2013.9003620203662e-561.9501810101831e-56
2111.93763992261845e-629.68819961309226e-63
2213.99927139896979e-651.99963569948489e-65
2316.43480704112565e-653.21740352056283e-65
2415.51314630413131e-652.75657315206566e-65
2511.38500257506668e-666.9250128753334e-67
2611.89917704716636e-689.49588523583179e-69
2715.07002968585087e-702.53501484292543e-70
2814.00678318799241e-812.00339159399621e-81
2911.79639544222523e-938.98197721112614e-94
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20912.15592163209583e-461.07796081604791e-46
21011.27683196561622e-456.3841598280811e-46
21117.9352359397853e-453.96761796989265e-45
21214.74855168409255e-442.37427584204628e-44
21311.99048827860229e-439.95244139301144e-44
21411.21170946033892e-426.05854730169461e-43
21517.29094116663289e-423.64547058331645e-42
21613.4167233630559e-411.70836168152795e-41
21711.81498003638794e-409.0749001819397e-41
21811.07053142817235e-395.35265714086174e-40
21915.12696698500425e-392.56348349250212e-39
22012.67870717839001e-381.33935358919501e-38
22111.54682531452019e-377.73412657260096e-38
22218.82864101539432e-374.41432050769716e-37
22314.82663854072478e-362.41331927036239e-36
22412.44413693481041e-351.2220684674052e-35
22511.3612778143985e-346.8063890719925e-35
22617.44205355910779e-343.7210267795539e-34
22714.10516344285203e-332.05258172142601e-33
22812.18602414468881e-321.09301207234441e-32
22911.18218336047574e-315.91091680237872e-32
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23112.94731036474758e-301.47365518237379e-30
23211.47784415016911e-297.38922075084554e-30
23317.64613928805157e-293.82306964402578e-29
23413.88436724397681e-281.94218362198841e-28
23511.82673241237337e-279.13366206186683e-28
23618.92259228743064e-274.46129614371532e-27
23713.90604657521792e-261.95302328760896e-26
23811.9315528241473e-259.6577641207365e-26
23919.29885760450368e-254.64942880225184e-25
24013.5062398964559e-241.75311994822795e-24
24111.52971699947881e-237.64858499739403e-24
24217.20345699898012e-233.60172849949006e-23
24313.19831534225141e-221.59915767112571e-22
24411.42227617606705e-217.11138088033523e-22
24514.04386926702557e-212.02193463351279e-21
24611.79565769849818e-208.9782884924909e-21
24717.70167673324788e-203.85083836662394e-20
24813.35949712914424e-191.67974856457212e-19
24911.03065882360561e-185.15329411802806e-19
25014.52581022862509e-182.26290511431254e-18
25111.79899991352777e-178.99499956763887e-18
25217.69522295446654e-173.84761147723327e-17
25312.97959722872358e-161.48979861436179e-16
25413.18846531662288e-161.59423265831144e-16
25511.36136083684868e-156.80680418424342e-16
2560.9999999999999975.10361550658145e-152.55180775329073e-15
2570.999999999999992.01741410796552e-141.00870705398276e-14
2580.999999999999968.21809763586096e-144.10904881793048e-14
2590.9999999999998343.31221002337455e-131.65610501168727e-13
2600.9999999999993481.30492046960209e-126.52460234801046e-13
2610.999999999997475.06193268558393e-122.53096634279196e-12
2620.9999999999923291.5342683160865e-117.67134158043252e-12
2630.9999999999891522.16953764878465e-111.08476882439232e-11
2640.9999999999611137.77742376471002e-113.88871188235501e-11
2650.9999999998711282.57743717472401e-101.288718587362e-10
2660.999999999521389.57240052507217e-104.78620026253608e-10
2670.9999999982460073.50798548031173e-091.75399274015586e-09
2680.999999993755111.24897818105542e-086.24489090527708e-09
2690.9999999782496924.35006153762548e-082.17503076881274e-08
2700.9999999296093381.40781323792622e-077.03906618963109e-08
2710.9999997664794724.67041056581966e-072.33520528290983e-07
2720.9999993211486541.35770269214091e-066.78851346070457e-07
2730.9999978590653254.28186934990248e-062.14093467495124e-06
2740.9999963412856917.31742861710983e-063.65871430855492e-06
2750.9999898998329072.02003341862437e-051.01001670931218e-05
2760.9999754417109934.91165780141891e-052.45582890070945e-05
2770.9999611162877387.77674245248546e-053.88837122624273e-05
2780.9998826163215930.0002347673568132580.000117383678406629
2790.999668351692150.0006632966156983830.000331648307849191
2800.9990554362653610.001889127469277930.000944563734638965
2810.997439600779760.005120798440477440.00256039922023872
2820.9972317682425110.00553646351497790.00276823175748895
2830.9922901721069360.01541965578612840.00770982789306422
2840.9803935090368960.0392129819262070.0196064909631035
2850.980526182919040.03894763416192120.0194738170809606
2860.9521161274595440.09576774508091130.0478838725404557
2870.897182899401460.2056342011970810.10281710059854


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2740.982078853046595NOK
5% type I error level2770.992831541218638NOK
10% type I error level2780.99641577060932NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/10qpwz1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/10qpwz1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/11ohn1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/11ohn1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/21ohn1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/21ohn1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/3uxg81291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/3uxg81291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/4uxg81291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/4uxg81291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/5uxg81291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/5uxg81291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/6n7xb1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/6n7xb1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/7fyxe1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/7fyxe1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/8fyxe1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/8fyxe1291298442.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/9fyxe1291298442.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291298417wvmlwsw9pxo9olp/9fyxe1291298442.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')
}
 




Copyright

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Software written by Ed van Stee & Patrick Wessa


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