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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 12:32:40 +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/t1291293769sgyoadr6tfsst6x.htm/, Retrieved Thu, 02 Dec 2010 13:43:03 +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/t1291293769sgyoadr6tfsst6x.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 1081 213118 6282929 5627 37 29790 309 81767 4324047 13346 138 87550 458 153198 4108272 8533 45 84738 588 -26007 -1212617 -2402 -17 54660 299 126942 1485329 4299 24 42634 156 157214 1779876 10127 37 40949 481 129352 1367203 2427 29 42312 323 234817 2519076 7180 55 37704 452 60448 912684 1577 19 16275 109 47818 1443586 11409 76 25830 115 245546 1220017 8870 39 12679 110 48020 984885 7135 62 18014 239 -1710 1457425 5261 70 43556 247 32648 -572920 -3129 -18 24524 497 95350 929144 1467 30 6532 103 151352 1151176 9235 146 7123 109 288170 790090 5414 83 20813 502 114337 774497 1144 28 37597 248 37884 990576 3188 21 17821 373 122844 454195 681 14 12988 119 82340 876607 5686 52 22330 84 79801 711969 6095 23 13326 102 165548 702380 4925 38 16189 295 116384 264449 218 4 7146 105 134028 450033 2381 35 15824 64 63838 541063 5329 22 26088 267 74996 588864 1456 15 11326 129 31080 -37216 -1839 -21 8568 37 32168 783310 15765 68 14416 361 49857 467359 741 19 3369 28 87161 688779 17456 145 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 time16 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = -8553.94816625918 + 26.4181507260834Costs[t] -279.798054035501Trades[t] + 3.81781830880396Dividends[t] + 2.27849155604682`Profit/Trades`[t] + 0.0321567525242135`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)-8553.9481662591852022.074846-0.16440.8695080.434754
Costs26.41815072608342.29833611.494500
Trades-279.798054035501257.152446-1.08810.2774710.138735
Dividends3.817818308803960.5882966.489600
`Profit/Trades`2.278491556046821.0725192.12440.034480.01724
`Profit/Cost`0.03215675252421351.4115410.02280.981840.49092


Multiple Linear Regression - Regression Statistics
Multiple R0.746655787766848
R-squared0.557494865405733
Adjusted R-squared0.549865466533418
F-TEST (value)73.0719254211144
F-TEST (DF numerator)5
F-TEST (DF denominator)290
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation360168.709163753
Sum Squared Residuals37619234727598.5


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829294809881.328971981473047.67102802
243240471034569.898861623289477.10113838
341082722780533.583927841327738.41607216
4-12126171960782.56814823-3173399.56814823
514853291846240.05108254-360911.051082543
617798761697398.9548482882477.0451517217
713672031438033.30735781-70830.3073578122
825190761931726.05371454587349.94628546
99126841095420.55967871-182736.559678708
101443586599461.656977396844124.343022604
1112200171599311.59754345-379294.597543454
12984885495214.665105663489670.334894337
131457425405931.8098399061051493.19016009
14-5729201190519.05875768-1763439.05875768
15929144867637.6349443261506.3650556801
161151176734071.21389092417104.78610908
177900901261643.6759087-471553.6759087
18774497839953.7864728-65456.7864727998
199905761067198.08246470-76622.0824647025
20454195828427.417038948-374232.417038948
21876607628585.359719619248021.640280381
22711969876414.185508479-164445.185508479
23702380958209.905153912-255829.905153912
24264449781418.873835901-516969.873835901
25450033667972.127422269-217939.127422269
26541063647444.467613169-106381.467613169
27588864895575.755492279-306711.755492279
28-37216369031.049761035-406247.049761035
29783310366178.424653365417131.575346635
30467359463316.9558375114042.04416248939
31688779445157.329062053243621.670937947
32608419695968.772287561-87549.7722875612
33696348487330.79140339209017.208596610
34597793505529.16062322292263.8393767775
358217301260059.21373835-438329.213738348
36377934831679.541738325-453745.541738325
37651939588291.96776814263647.0322318583
38697458553161.618874258144296.381125742
39700368778433.274405466-78065.2744054664
40225986363456.004547866-137470.004547866
41348695457033.260390069-108338.260390069
42373683711490.78594336-337807.78594336
43501709408951.11775419592757.8822458046
44413743596843.546815562-183100.546815562
45379825367007.15008831112817.8499116887
46336260482795.950792566-146535.950792566
47636765859788.102475198-223023.102475199
48481231624212.791339881-142981.791339881
49469107570188.835779636-101081.835779636
50211928335067.240791989-123139.240791989
51563925465074.68513460498850.3148653958
52511939578338.720910792-66399.7209107922
53521016879168.985927945-358152.985927945
54543856539150.0529129514705.94708704865
55329304670059.301565317-340755.301565317
56423262266750.139828543156511.860171457
57509665358568.978096424151096.021903576
58455881458605.54515239-2724.54515239014
59367772378862.796754019-11090.7967540192
60406339547994.064633228-141655.064633228
61493408499769.125704209-6361.12570420856
62232942253470.527014403-20528.5270144033
63416002440320.719529327-24318.7195293272
64337430479656.521424668-142226.521424668
65361517269988.1865251691528.81347484
66360962423753.394850818-62791.3948508177
67235561303531.568169208-67970.5681692078
68408247423205.427591242-14958.4275912421
69450296509414.829367685-59118.8293676845
70418799471166.192404229-52367.1924042286
71247405161864.05014954885540.9498504516
72378519270315.939935237108203.060064763
73326638436295.04461932-109657.04461932
74328233332269.768282102-4036.7682821023
75386225499821.9022999-113596.902299900
76283662328228.284469391-44566.2844693912
77370225451452.182244108-81227.182244108
78269236287060.39661042-17824.3966104198
79365732260962.432018035104769.567981965
80420383414145.1187184866237.88128151368
81345811266227.73580037479583.2641996257
82431809444095.232953827-12286.2329538265
83418876537107.537735556-118231.537735556
84297476171537.002624787125938.997375213
85416776425955.726385856-9179.72638585645
86357257371902.662162786-14645.6621627861
87458343415049.11208414143293.8879158592
88388386429365.676937386-40979.6769373861
89358934441672.040916273-82738.0409162735
90407560440904.424366857-33344.4243668567
91392558402995.971131599-10437.9711315991
92373177384016.294945421-10839.2949454210
93428370271312.385633667157057.614366333
94369419632718.246545568-263299.246545568
95358649180066.956192034178582.043807966
96376641299496.19403279877144.8059672019
97467427503984.874339025-36557.874339025
98364885243252.808252723121632.191747277
99436230574346.908564449-138116.908564449
100329118331196.974545321-2078.97454532098
101317365314223.0119153093141.98808469127
102286849365017.202384721-78168.2023847213
103376685477173.675174082-100488.675174082
104407198462184.663039737-54986.6630397375
105377772294853.17391829382918.8260817066
106271483285010.171833339-13527.1718333389
107153661285649.315110763-131988.315110763
108513294449298.93344530163995.0665546988
109324881511890.504197599-187009.504197599
110264512315022.424033010-50510.4240330096
111420968283949.215169559137018.784830441
112129302249006.471572907-119704.471572907
113191521435616.868953498-244095.868953498
114268673344625.031213568-75952.031213568
115353179284045.23153813869133.7684618624
116354624244465.450590322110158.549409678
117363713333628.52621265730084.4737873435
118456657410792.47797618445864.5220238162
119211742342395.57871681-130653.578716810
120338381232715.123422568105665.876577432
121418530671734.059956982-253204.059956982
122351483291097.42940704660385.5705929543
123372928358744.81402222714183.1859777735
124485538460308.61934975925229.3806502410
125279268296120.990411943-16852.9904119435
126219060363433.945516343-144373.945516343
127325314264899.59576106160414.4042389392
128322046225886.70764199996159.2923580009
129325599257470.47698712268128.5230128782
130377028233796.437649948143231.562350052
131323850318353.3339955235496.66600447707
132331514261582.07606861069931.9239313903
133325632245578.28749323980053.7125067605
134322265242926.80572528679338.1942747144
135325906249510.96694764476395.0330523562
136325985319837.6442538456147.35574615496
137346145263454.48586781782690.514132183
138325898238462.26355917587435.7364408247
139325356270303.24861866955052.7513813308
140325930511695.569333138-185765.569333138
141318020253198.61040958964821.3895904109
142326389252362.93518860574026.0648113947
143302925245614.46538477757310.5346152232
144325540319332.0298212956207.97017870485
145326736372658.210380028-45922.2103800277
146340580278252.07581194762327.9241880527
147331828240024.01196164191803.9880383586
148323299236207.33476002887091.6652399724
149387722203080.201066024184641.798933976
150324598297405.22197385527192.7780261447
151328726263368.46861950765357.5313804933
152325043259942.79424074565100.2057592548
153325806511660.527682578-185854.527682578
154387732293715.53640734894016.4635926518
155349729310313.35306286239415.6469371382
156332202217707.922356027114494.077643973
157305442294558.84053643110883.1594635685
158329537288687.67993191840849.3200680816
159327055255549.06060785871505.9393921425
160356245275365.57063110780879.4293688927
161328451289406.79891377539044.201086225
162307062295822.33183874611239.6681612543
163331345299583.92794641531761.0720535851
164331824278875.20183176152948.7981682389
165325685367422.985461041-41737.9854610415
166404480476080.131465223-71600.1314652234
167318314317404.351814412909.648185587852
168311807192667.782236885119139.217763115
169337724351898.997197638-14174.9971976377
170326431370984.248337024-44553.2483370239
171327556315500.27624746812055.7237525319
172356850208925.316548811147924.683451189
173322741218360.293383086104380.706616914
174310902247630.97988030863271.020119692
175324295283130.92903303041164.0709669695
176326156258044.71645216268111.2835478378
177326960235976.09219065190983.9078093489
178333411243740.45200711489670.5479928856
179297761284648.70766132913112.2923386714
180325536366993.495183107-41457.4951831069
181325762367038.370969567-41276.3709695673
182327957237172.11281793590784.887182065
183318521312142.6301612226378.36983877847
184319775271652.60121512048122.3987848797
185325486510869.511580004-185383.511580004
186325838269432.53634601856405.4636539817
187331767327472.2208463204294.7791536805
188324523253845.93323600970677.0667639911
189339995409159.877169931-69164.8771699313
190319582252599.70230612066982.2976938802
191307245224301.56567073982943.4343292605
192317967374991.272755184-57024.2727551837
193331488270290.69327884761197.3067211529
194335452310535.86048075224916.1395192484
195334184246372.0325028687811.9674971399
196313213180779.270162132132433.729837868
197348678300381.41113697548296.5888630251
198328727239628.48804913689098.511950864
199387978328776.89745658759201.1025434133
200336704311906.67244372124797.3275562791
201322076246717.00546837275358.9945316284
202334272239146.22040117195125.7795988288
203338197245626.85773006692570.1422699342
204321024250822.07958172670201.9204182738
205322145258353.26609093263791.7339090676
206323351198367.246487201124983.753512799
207327748289352.53830202438395.461697976
208328157301133.03748777227023.9625122276
209311594192187.75918626119406.24081374
210335962241939.5977360894022.40226392
211372426325979.13901229246446.8609877075
212319844235688.69932988084155.3006701196
213355822239226.305322651116595.694677349
214324047294029.92409920530017.0759007954
215311464349994.497405389-38530.4974053894
216353417228867.218900224124549.781099776
217325590254856.82541939170733.174580609
218328576260285.58538153168290.4146184692
219326126217277.962609747108848.037390253
220369376315413.97434411353962.0256558871
221332013272937.65462624159075.3453737593
222325871295407.22163661830463.7783633824
223342165266152.87711214876012.1228878521
224324967505897.099438859-180930.099438859
225314832245337.10024483269494.899755168
226325557272234.57575294453322.4242470561
227322649363202.36969909-40553.3696990897
228324598279921.13336901544676.866630985
229325567369930.584870905-44363.5848709045
230324005264640.75465868159364.2453413194
231325748511012.422741598-185264.422741598
232323385240821.50337357582563.496626425
233315409253227.30137244562181.6986275546
234312275261280.60684524450994.3931547561
235320576239124.95179853581451.0482014654
236325246252199.25119108273046.7488089183
237332961256371.79779852076589.2022014803
238323010371573.74952257-48563.7495225704
239345253297616.13614168147636.8638583188
240325559299726.89863961825832.1013603816
241319634318244.8332993361389.16670066357
242319951245667.53418819474283.4658118061
243318519227082.14953620291436.8504637984
244343222323817.89371273819404.1062872624
245317234510372.379672263-193138.379672263
246314025213260.328927143100764.671072857
247320249260052.59476866360196.4052313371
248349365274693.87403404974671.1259659512
249289197145044.156108142144152.843891858
250329245246866.27031376282378.7296862376
251240869307201.392318007-66332.3923180065
252327182269331.27693967157850.7230603292
253322876272394.03693268550481.9630673151
254323117316659.5185382386457.48146176162
255306351240879.37624324165471.6237567585
256335137269353.93146101265783.0685389876
257308271258432.76089488549838.2391051145
258301731271734.1726201629996.8273798399
259382409319342.92129789463066.0787021061
260279230412862.227754223-133632.227754223
261298731243140.86785540355590.1321445975
262243650313583.025528153-69933.0255281533
263532682465571.84864359667110.1513564039
264319771277076.5595187742694.4404812299
26517149388704.845333802282788.1546661978
266347262354018.998795661-6756.99879566059
267343945291094.99938872352850.0006112771
268311874263194.13379867148679.866201329
269302211298851.3440082593359.65599174118
270316708288493.81798638028214.1820136197
271333463312326.40683950921136.5931604908
272344282283560.585879360721.4141207
273319635264264.62237588555370.3776241151
274301186243561.8590607357624.1409392702
275300381353199.925446047-52818.925446047
276318765279964.61076573638800.3892342638
277286146401922.445803566-115776.445803566
278306844250600.83567192856243.164328072
279307705364309.323936998-56604.3239369977
280312448365390.114642576-52942.1146425762
281299715372407.455121702-72692.4551217022
282373399199562.276042484173836.723957516
283299446267798.90475019331647.0952498071
284325586292946.58546423732639.4145357631
285291221329026.168594497-37805.1685944966
286261173353711.3764464-92538.3764464003
287255027327194.543562954-72167.5435629544
288-78375211816.129639532-290191.129639532
289-58143347100.521317673-405243.521317673
290227033257751.866523830-30718.8665238305
291235098339785.443533488-104687.443533488
29221267270792.419184313-249525.419184313
2932386751471024.32641784-1232349.32641784
294197687525881.841896073-328194.841896073
295418341669951.091976436-251610.091976436
296-297706516402.065375722-814108.065375722


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
90.9999999994066861.18662848112428e-095.93314240562138e-10
100.999999999983223.35598982948078e-111.67799491474039e-11
110.999999999999992.20361514040702e-141.10180757020351e-14
1217.16696248396956e-163.58348124198478e-16
1311.17488097562926e-225.87440487814628e-23
1411.26167395552081e-326.30836977760407e-33
1511.15148007481068e-335.75740037405339e-34
1613.40336130555528e-571.70168065277764e-57
1711.95981922457184e-569.7990961228592e-57
1811.38794516342472e-566.93972581712362e-57
1912.09421145020188e-631.04710572510094e-63
2014.07290914919956e-632.03645457459978e-63
2113.45919307033647e-671.72959653516823e-67
2215.597218490223e-692.7986092451115e-69
2313.0986659195115e-691.54933295975575e-69
2412.69027790243826e-701.34513895121913e-70
2511.40920832034655e-727.04604160173273e-73
2611.98282753192239e-739.91413765961194e-74
2717.94077835103847e-763.97038917551924e-76
2819.85936786162072e-864.92968393081036e-86
2916.41048655975561e-1023.20524327987780e-102
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21611.59725374875231e-417.98626874376153e-42
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21815.39754337462310e-402.69877168731155e-40
21912.57333666695046e-391.28666833347523e-39
22011.29867829787224e-386.49339148936121e-39
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22214.38561952005033e-372.19280976002517e-37
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23811.36223304555804e-256.81116522779022e-26
23916.39260032721333e-253.19630016360666e-25
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24611.57092702922562e-207.85463514612812e-21
24716.81863227430805e-203.40931613715402e-20
24813.06610045724228e-191.53305022862114e-19
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25312.92495517521055e-161.46247758760527e-16
25412.62145191138669e-161.31072595569334e-16
25511.13069841049332e-155.65349205246658e-16
2560.9999999999999984.09884247750424e-152.04942123875212e-15
2570.9999999999999921.60563878959325e-148.02819394796625e-15
2580.9999999999999676.58409346097333e-143.29204673048666e-14
2590.9999999999998662.67886583405655e-131.33943291702828e-13
2600.999999999999481.04008183496357e-125.20040917481783e-13
2610.9999999999979774.04539810677788e-122.02269905338894e-12
2620.999999999993771.24606016549107e-116.23030082745533e-12
2630.9999999999776624.46767819936341e-112.23383909968170e-11
2640.9999999999233561.53287145417679e-107.66435727088393e-11
2650.999999999810133.79739020928962e-101.89869510464481e-10
2660.9999999993049221.39015627492124e-096.95078137460621e-10
2670.9999999974929675.0140650042175e-092.50703250210875e-09
2680.9999999912977851.74044308556664e-088.70221542783322e-09
2690.9999999700930435.98139149125696e-082.99069574562848e-08
2700.999999906769321.86461358726344e-079.3230679363172e-08
2710.9999996923757116.1524857715122e-073.0762428857561e-07
2720.9999991868998181.62620036381166e-068.13100181905831e-07
2730.999997437744925.12451016210336e-062.56225508105168e-06
2740.9999969851963056.02960738959928e-063.01480369479964e-06
2750.9999916821299841.66357400319027e-058.31787001595135e-06
2760.9999755205544334.89588911337182e-052.44794455668591e-05
2770.9999434978325370.0001130043349257255.65021674628625e-05
2780.999838295260390.0003234094792208210.000161704739610411
2790.999550649041370.0008987019172620990.000449350958631049
2800.9988064867834840.002387026433032180.00119351321651609
2810.9968626488321290.006274702335742560.00313735116787128
2820.9969197261196510.00616054776069770.00308027388034885
2830.9916719773010990.01665604539780210.00832802269890106
2840.9804957989680960.03900840206380720.0195042010319036
2850.9929426556773480.01411468864530390.00705734432265196
2860.9882563770487070.02348724590258690.0117436229512934
2870.9558112967532780.0883774064934440.044188703246722


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2740.982078853046595NOK
5% type I error level2780.99641577060932NOK
10% type I error level2791NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/10zp341291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/10zp341291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/1s6oa1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/1s6oa1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/2s6oa1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/2s6oa1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/3lx5v1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/3lx5v1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/4lx5v1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/4lx5v1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/5lx5v1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/5lx5v1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/6e65y1291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/6e65y1291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/77gm11291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/77gm11291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/87gm11291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/87gm11291293142.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/97gm11291293142.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/02/t1291293769sgyoadr6tfsst6x/97gm11291293142.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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