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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Wed, 22 Dec 2010 13:52:50 +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/22/t1293025909u15leheeu69j29g.htm/, Retrieved Wed, 22 Dec 2010 14:51:49 +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/22/t1293025909u15leheeu69j29g.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 «
17.98 586.9642 830.36 1609.84 404.45 2342.32 17.83 582.1727 750 1477.27 387.97 2258.39 19.45 586.19396 830.36 1653.84 390.27 2293.62 21.04 590.49531 803.57 1512.02 384.72 2418.80 20.03 589.70506 830.36 1352.37 371.35 2480.15 20.01 590.07518 803.57 1436.84 367.73 2440.06 19.64 595.2568 830.36 1503.27 375.21 2660.66 18.52 604.1796 830.36 1649.09 365.55 2737.27 19.59 605.00987 803.57 1545.82 361.80 2692.82 20.09 610.71165 830.36 1622.21 366.80 2645.08 19.82 618.31404 803.57 1650.19 394.36 2706.27 21.09 614.74292 830.36 1696.73 409.66 2753.20 22.64 609.16284 544.75 1502.97 410.12 2590.54 22.11 611.73756 492.03 1469.44 416.54 2627.25 20.42 620.77222 544.75 1565.22 393.66 2707.21 18.58 618.00755 527.18 1485.36 374.93 2656.76 18.24 612.3328 544.75 1268.54 368.85 2876.66 16.87 604.04309 527.18 994.85 352.66 2880.69 18.64 605.08732 544.75 1352.65 361.82 2905.20 27.17 569.6086 544.75 1574.06 394.86 2614.36 33.69 595.0899 527.18 1531.7 389.56 2452.48 35.92 598.49214 544.75 1473.81 381.33 2442.33 32 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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
PRICE[t] = -169.944836849113 + 0.249358371013949PRODUCTION[t] + 0.0233130772579997RENEW_RISID[t] -0.0087232698957167RENEW_IND[t] + 0.0917792017482259GOLD[t] + 0.00318761707774345DOWJONES[t] -0.180920339320372t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)-169.94483684911326.474671-6.419100
PRODUCTION0.2493583710139490.0475255.246900
RENEW_RISID0.02331307725799970.0112372.07470.0390560.019528
RENEW_IND-0.00872326989571670.003421-2.54970.0113920.005696
GOLD0.09177920174822590.00662813.848200
DOWJONES0.003187617077743450.000536.016600
t-0.1809203393203720.042638-4.24323.1e-051.6e-05


Multiple Linear Regression - Regression Statistics
Multiple R0.916967581324854
R-squared0.840829545200753
Adjusted R-squared0.836931493246486
F-TEST (value)215.705063725557
F-TEST (DF numerator)6
F-TEST (DF denominator)245
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation9.6357027549884
Sum Squared Residuals22747.4580577103


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
117.9826.1403749707140-8.16037497071395
217.8322.2676010521575-4.43760105215754
319.4523.7459785924967-4.29597859249674
421.0425.1398640152952-4.09986401529525
520.0325.7475879822198-5.71758798221981
620.0123.8375159363709-3.82751593637088
719.6426.3834431964601-6.74344319646006
818.5226.5130867692676-7.99308676926763
919.5926.3296343613763-6.7396343613763
1020.0927.8354065165935-7.7454065165935
1119.8231.4060564212301-11.5860564212301
1221.0932.1070404310160-11.0170404310160
1322.6425.0901738510433-2.45017385104327
1422.1125.3209472014492-3.21094720144916
1520.4225.9414193303606-5.52141933036061
1618.5823.4782952195816-4.89829521958158
1718.2424.3262580593287-6.08625805932872
1816.8722.5830309290855-5.71303092908547
1918.6420.8697488628539-2.22974886285385
2027.1712.015791785933315.1542082140667
2133.6917.146312629479516.5436873705205
2235.9217.940673032316717.9793269676833
2332.320.740763939190411.5592360608096
2427.3419.50223107519087.83776892480922
2524.9619.12538591907185.83461408092817
2620.5219.92589413586270.594105864137272
2719.8621.5972376963016-1.73723769630158
2820.8218.66399490063272.15600509936735
2921.2417.78947188079903.45052811920103
3020.217.64701215398982.55298784601021
3121.4220.91401270567020.505987294329817
3221.6915.00423545906586.68576454093419
3321.8614.62276864476557.2372313552345
3423.2317.29995086633665.93004913366342
3522.4717.50851949347664.96148050652344
3619.5217.85915142090791.66084857909206
3718.8217.75665335455531.06334664544471
381918.12284976772980.877150232270149
3918.9217.17258009469481.74741990530524
4020.2417.80514131009982.43485868990019
4120.9417.25258020299933.68741979700066
4222.3813.93897152444178.44102847555827
4321.7615.44932721502636.31067278497375
4421.3512.45294384367958.89705615632053
4521.913.90566171178847.99433828821163
4621.6914.52643161250077.1635683874993
4720.3412.38146350775067.9585364922494
4819.4114.18855526212715.22144473787285
4919.0810.48322854217478.59677145782526
5020.0511.88214137315868.16785862684137
5120.3510.53611222907989.81388777092021
5220.2711.31484563542258.95515436457755
5319.9417.34568650558392.59431349441609
5419.0716.27881326584522.79118673415485
5517.8718.8125059894788-0.942505989478774
5618.0113.24472169751994.7652783024801
5717.5111.36644063928476.14355936071525
5818.1513.53015827284204.61984172715804
5916.713.43319411442983.26680588557023
6014.5115.7532649919884-1.24326499198842
611512.65169170471382.34830829528615
6214.7814.39537722019880.38462277980122
6314.6614.07168982055950.588310179440534
6416.3813.48503635440432.89496364559567
6517.8818.5251756501387-0.645175650138683
6619.0717.52312614263831.54687385736171
6719.6512.61611079156057.03388920843949
6818.3813.99022394029394.38977605970611
6917.4616.64121675762690.818783242373126
7017.7116.02100352392721.68899647607283
7118.115.49874721141672.60125278858334
7217.1616.62024391948560.539756080514365
7317.9916.40978368005081.58021631994921
7418.5318.9581646112530-0.428164611252952
7518.5516.72289163455661.82710836544335
7619.8717.88565994494371.98434005505632
7719.7420.3279872837084-0.587987283708401
7818.4218.7257150713457-0.305715071345743
7917.316.3497548987340.950245101266018
8018.0315.50901164367282.52098835632724
8118.2318.9636233691282-0.7336233691282
8217.4416.67774634362660.762253656373413
8317.9919.6121877515831-1.62218775158310
8419.0421.4558549269982-2.41585492699824
8518.8822.2254480387213-3.3454480387213
8619.0726.6353682635856-7.56536826358557
8721.3624.331812242654-2.97181224265402
8823.5726.748410268222-3.17841026822198
8921.2525.1484682328803-3.89846823288029
9020.4523.1703347902896-2.72033479028955
9121.3221.23791053349920.0820894665008082
9221.9619.33743104875912.62256895124088
9323.9923.48924281222230.500757187777665
9424.921.53409140916303.36590859083696
9523.7124.1769092988403-0.466909298840285
9625.3927.3535023522573-1.96350235225733
9725.1722.53492595318342.63507404681664
9822.2125.4380115054774-3.22801150547742
9920.9924.1676224603036-3.17762246030363
10019.7225.7494009955928-6.02940099559282
10120.8324.2426745161768-3.41267451617679
10219.1724.9570531421939-5.78705314219389
10319.6324.5403707571359-4.91037075713587
10419.9324.2285294810267-4.29852948102672
10519.7926.2949689667466-6.5049689667466
10621.2622.5811747081200-1.32117470811997
10720.1724.1285785217275-3.95857852172754
10818.3223.3896594661659-5.06965946616591
10916.7122.8291176451252-6.1191176451252
11016.0630.2218287592601-14.1618287592601
11115.0229.6312639134218-14.6112639134218
11215.4430.8560104806671-15.4160104806671
11314.8627.6101154052505-12.7501154052505
11413.6630.5104735178990-16.8504735178990
11514.0825.8435727721557-11.7635727721557
11613.3617.5788848651249-4.21888486512492
11714.9519.0989432303841-4.14894323038413
11814.3921.438572101824-7.04857210182399
11912.8526.9165208745912-14.0665208745912
12011.2824.1318547335490-12.8518547335490
12112.4724.2516649915428-11.7816649915428
12212.0127.6242751263835-15.6142751263835
12314.6629.938316222668-15.278316222668
12417.3426.0373715031557-8.69737150315571
12517.7521.4778912705363-3.72789127053625
12617.8922.1138145718596-4.22381457185956
12720.0722.2494816125324-2.17948161253236
12821.2622.8614395208625-1.60143952086253
12923.8822.835975602861.04402439713998
13022.6431.1689702064054-8.52897020640541
13124.9727.2693469397964-2.29934693979637
13226.0827.9853923670214-1.90539236702141
13327.1830.4587405793625-3.27874057936248
13429.3528.11451277130351.23548722869651
13529.8929.04344046642770.846559533572337
13625.7429.553850681364-3.81385068136399
13728.7830.1602635988104-1.38026359881045
13831.8331.22970546367670.600294536323305
13929.7730.9919030010104-1.22190300101038
14031.2234.2427147360737-3.02271473607373
14133.8832.94851758850140.931482411498647
14233.0832.89465658163760.185343418362355
14334.431.98243296814852.4175670318515
14428.4630.2844897236162-1.82448972361625
14529.5830.9073258357336-1.32732583573365
14629.6128.60050916150051.00949083849947
14727.2428.1408319096338-0.90083190963385
14827.4128.1144698556916-0.70446985569159
14928.6428.52280647340360.117193526596374
15027.622.61418709700214.98581290299793
15126.4526.8974624611557-0.447462461155686
15227.4725.37771610636332.09228389363673
15325.8821.85670861481944.0232913851806
15422.2121.54695397773900.663046022260967
15519.6724.3084937341711-4.63849373417106
15619.3323.662415143757-4.332415143757
15719.6721.8838706250749-2.2138706250749
15820.7424.5405241864900-3.80052418648996
15924.4224.9069895644898-0.486989564489803
16026.2722.41534630184523.8546536981548
16127.0224.19054972174272.82945027825729
16225.5222.64418018504892.87581981495106
16326.9420.15984218343856.78015781656147
16428.3819.83099926181808.54900073818196
16529.6717.387095285291512.2829047147085
16628.8522.31281286296336.53718713703673
16726.2724.89415154876831.37584845123175
16829.4219.70280643212919.7171935678709
16932.9423.48522755494219.45477244505787
17035.8727.24793231239958.62206768760046
17133.5526.95135707235616.59864292764386
17228.2524.31884879577243.93115120422755
17328.1427.99072292709870.149277072901289
17430.7226.23478590102434.48521409897575
17530.7627.29271152014313.46728847985693
17631.5929.83592953280601.75407046719395
17728.2932.8566602888261-4.56666028882613
17830.3336.5155606547614-6.18556065476142
17931.0937.7708755818229-6.68087558182288
18032.1543.6849713776193-11.5349713776193
18134.2743.2931073838521-9.02310738385206
18234.7443.0441195813623-8.30411958136226
18336.7642.2369807084095-5.47698070840954
18436.6940.9311317239534-4.24113172395337
18540.2838.79830119544471.48169880455527
18638.0243.6182771294125-5.59827712941253
18740.6943.9084425586163-3.21844255861634
18844.9441.59250050904363.34749949095636
18945.9543.37759135081792.57240864918208
19053.1345.51114839269257.61885160730755
19148.4647.60853628005160.851463719948414
19243.3347.2132798000787-3.88327980007874
19346.8445.77183742568141.06816257431855
19447.9746.96816688034311.00183311965686
19554.3148.43729163383515.87270836616486
19653.0447.70666724109025.33333275890984
19749.8348.15897860375881.67102139624123
19856.2647.07211286192749.18788713807258
19958.746.834980600754811.8650193992452
20064.9747.499569968724317.4704300312757
20165.5748.336997825408717.2330021745913
20262.3749.147535945898313.2224640541017
20358.352.05696157270796.24303842729211
20459.4354.98013643820314.4498635617969
20565.5156.1334058219539.37659417804702
20661.6357.76219358752723.8678064124728
20762.957.83780607115215.06219392884793
20869.6963.86565456391385.82434543608618
20970.9467.88132494367963.05867505632039
21070.9659.896937093681711.0630629063183
21174.4165.13194523448889.27805476551122
21273.0564.64855335457028.40144664542977
21363.8761.8962432541111.97375674588902
21458.8862.320310458468-3.44031045846804
21559.3765.4277886965468-6.0577886965468
21662.0365.4257924736437-3.39579247364367
21754.5766.2518138567438-11.6818138567438
21859.2669.0555603807603-9.79556038076033
21960.5668.0390927114699-7.47909271146991
22063.9772.8648733097164-8.89487330971638
22163.4672.425290721594-8.96529072159404
22267.4869.4498457391767-1.96984573917671
22374.1870.48928396251143.69071603748858
22472.3969.29418570082763.09581429917240
22579.9377.04362040663462.88637959336538
22686.282.31136864357653.88863135642354
22794.6284.295577663212710.3244223367873
22891.7383.90967211398647.82032788601355
22992.9589.49459790797943.45540209202064
23095.3593.0958816800442.25411831995608
231105.5697.70816696053337.85183303946673
232112.5792.238606539506720.3313934604933
233125.3990.19317926136235.1968207386379
234133.9386.389282687301747.5407173126983
235133.4492.551287348834640.8887126511653
236116.6180.621556569465635.9884434305344
237103.974.777696741268529.1223032587315
23876.6570.75089060207795.89910939792209
23957.4463.4417624242048-6.00176242420476
24041.0267.6087190351272-26.5887190351272
24141.7465.9978467490202-24.2578467490202
24239.1671.7201275050298-32.5601275050297
24347.9871.4975249125932-23.5175249125932
24449.7970.513034023874-20.7230340238741
24559.1673.381632435124-14.2216324351240
24669.6875.1508885122486-5.47088851224857
24764.0977.3597795545729-13.2697795545729
24871.0678.086989522683-7.02698952268302
24969.4684.5018934014139-15.0418934014139
25075.8289.3520695729228-13.5320695729228
25178.0898.6535302372746-20.5735302372746
25274.398.8082349314682-24.5082349314682


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
100.002646382525915730.005292765051831470.997353617474084
110.0003001374412222490.0006002748824444980.999699862558778
123.27035327037567e-056.54070654075134e-050.999967296467296
135.75389915805223e-061.15077983161045e-050.999994246100842
145.84780023795297e-071.16956004759059e-060.999999415219976
157.41461948858214e-081.48292389771643e-070.999999925853805
169.51763401072182e-081.90352680214436e-070.99999990482366
171.03170621917915e-072.06341243835830e-070.999999896829378
183.86773838936181e-087.73547677872362e-080.999999961322616
195.53084972807853e-091.10616994561571e-080.99999999446915
201.77311996837446e-093.54623993674892e-090.99999999822688
211.29244336772600e-082.58488673545200e-080.999999987075566
226.32803071329215e-091.26560614265843e-080.99999999367197
231.26015587996196e-092.52031175992392e-090.999999998739844
242.41108807833235e-094.8221761566647e-090.999999997588912
254.80638153429784e-099.61276306859568e-090.999999995193618
261.55017798837680e-083.10035597675359e-080.99999998449822
272.91958649026353e-085.83917298052706e-080.999999970804135
281.44116147079033e-082.88232294158067e-080.999999985588385
294.0065866210854e-098.0131732421708e-090.999999995993413
303.66286887337373e-097.32573774674745e-090.999999996337131
311.0868841746223e-092.1737683492446e-090.999999998913116
323.75469525381586e-107.50939050763173e-100.99999999962453
331.80733944442488e-103.61467888884977e-100.999999999819266
344.95686120061601e-119.91372240123202e-110.999999999950431
358.36191206084315e-111.67238241216863e-100.99999999991638
363.37973188071617e-116.75946376143234e-110.999999999966203
371.18115279818371e-112.36230559636743e-110.999999999988188
383.31514197279011e-126.63028394558023e-120.999999999996685
399.97260512023614e-131.99452102404723e-120.999999999999003
404.45872772273649e-138.91745544547298e-130.999999999999554
412.70044188665422e-135.40088377330844e-130.99999999999973
429.35122238509349e-141.87024447701870e-130.999999999999907
432.99815782353141e-145.99631564706282e-140.99999999999997
441.03994427079589e-142.07988854159178e-140.99999999999999
453.26672060507497e-156.53344121014993e-150.999999999999997
461.60325636949451e-153.20651273898902e-150.999999999999998
475.96040446341623e-161.19208089268325e-151
483.75648707263206e-167.51297414526413e-161
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1911.0158824846719e-222.0317649693438e-221
1924.98355129537075e-239.9671025907415e-231
1933.24078156095890e-236.48156312191781e-231
1942.31518106841502e-234.63036213683003e-231
1954.90887673938146e-239.81775347876291e-231
1961.00523076671878e-222.01046153343756e-221
1978.48714097653528e-221.69742819530706e-211
1982.09894137370119e-214.19788274740239e-211
1997.19366302453059e-211.43873260490612e-201
2008.6643755846291e-201.73287511692582e-191
2011.01929004368495e-182.03858008736990e-181
2021.77967593254256e-183.55935186508512e-181
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2085.47308422768558e-191.09461684553712e-181
2093.52171638785607e-197.04343277571213e-191
2106.92989130715387e-181.38597826143077e-171
2115.51063464217407e-181.10212692843481e-171
2121.32461463651098e-172.64922927302197e-171
2132.73344686492005e-175.46689372984009e-171
2141.51551753495053e-173.03103506990106e-171
2152.85061804170246e-175.70123608340493e-171
2166.09367120549337e-151.21873424109867e-140.999999999999994
2177.11273938383368e-151.42254787676674e-140.999999999999993
2189.49580678546305e-151.89916135709261e-140.99999999999999
2195.40493691416315e-151.08098738283263e-140.999999999999995
2205.04315523139289e-151.00863104627858e-140.999999999999995
2212.99738022075243e-145.99476044150485e-140.99999999999997
2221.23587278520621e-142.47174557041243e-140.999999999999988
2236.89665298268905e-151.37933059653781e-140.999999999999993
2243.00500867993624e-156.01001735987247e-150.999999999999997
2251.62997746963808e-143.25995493927616e-140.999999999999984
2263.73315856860750e-117.46631713721499e-110.999999999962668
2273.84785365851856e-117.69570731703711e-110.999999999961521
2287.53151675648749e-111.50630335129750e-100.999999999924685
2293.22894230908519e-116.45788461817038e-110.99999999996771
2307.20281164032202e-101.44056232806440e-090.999999999279719
2311.93042978941704e-083.86085957883408e-080.999999980695702
2329.7232086206192e-061.94464172412384e-050.99999027679138
2330.000940376365519610.001880752731039220.99905962363448
2340.003947541707063840.007895083414127690.996052458292936
2350.01815603774261260.03631207548522530.981843962257387
2360.02184761756636690.04369523513273390.978152382433633
2370.03938285723910110.07876571447820210.960617142760899
2380.5241085689145040.9517828621709920.475891431085496
2390.7925743205997550.4148513588004890.207425679400245
2400.8159321433801560.3681357132396880.184067856619844
2410.7590009697939640.4819980604120730.240999030206036
2420.776526740336630.4469465193267390.223473259663369


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level2250.965665236051502NOK
5% type I error level2270.974248927038627NOK
10% type I error level2280.978540772532189NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/10yssy1293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/10yssy1293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/1r9d51293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/1r9d51293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/2kjc81293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/2kjc81293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/3kjc81293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/3kjc81293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/4kjc81293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/4kjc81293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/5kjc81293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/5kjc81293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/6datb1293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/6datb1293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/761be1293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/761be1293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/861be1293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/861be1293025956.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/961be1293025956.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293025909u15leheeu69j29g/961be1293025956.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 





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Software written by Ed van Stee & Patrick Wessa


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