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*The author of this computation has been verified*
R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Tue, 21 Dec 2010 18:18:42 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye.htm/, Retrieved Tue, 21 Dec 2010 19:19:05 +0100
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye.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 131182692 6282154 29790 444 13226760 4321023 87550 412 36070600 4111912 84738 428 36267864 223193 54660 315 17217900 1491348 42634 168 7162512 1629616 40949 263 10769587 1398893 45187 267 12064929 1926517 37704 228 8596512 983660 16275 129 2099475 1443586 25830 104 2686320 1073089 12679 122 1546838 984885 18014 393 7079502 1405225 43556 190 8275640 227132 24811 280 6947080 929118 6575 63 414225 1071292 7123 102 726546 638830 21950 265 5816750 856956 37597 234 8797698 992426 17821 277 4936417 444477 12988 73 948124 857217 22330 67 1496110 711969 13326 103 1372578 702380 16189 290 4694810 358589 7146 83 593118 297978 15824 56 886144 585715 27664 236 6528704 657954 11920 73 870160 209458 8568 34 291312 786690 14416 139 2003824 439798 3369 26 87594 688779 11819 70 827330 574339 6984 40 279360 741409 4519 42 189798 597793 2220 12 26640 644190 18562 211 3916582 377934 10327 74 764198 640273 5336 80 426880 697458 2365 83 196295 550608 4069 131 533039 207393 8636 2 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 time14 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Wealth [t] = + 294344.351351714 + 1.81429466312585Costs[t] + 1798.51378507764Orders[t] + 0.0328503696213768C_O[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0
2-tail p-value1-tail p-value
(Intercept)294344.35135171413017.18860822.61200
Costs1.814294663125852.9864330.60750.5438340.271917
Orders1798.51378507764323.3173495.562700
C_O0.03285036962137680.0036299.05100


Multiple Linear Regression - Regression Statistics
Multiple R0.837395944803322
R-squared0.701231968373049
Adjusted R-squared0.699132895551314
F-TEST (value)334.067480228454
F-TEST (DF numerator)3
F-TEST (DF denominator)427
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation236141.030134022
Sum Squared Residuals23810624270147.3


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast
Residuals
Prediction Error
162821546350069.37929568-67915.3792956825
243210231581436.264833952739586.73516605
341119122379106.07102521732805.9289748
42231932409260.69030673-2186067.69030673
514913481525659.91904153-34311.9190415338
61629616909136.472530012720479.527469988
713988931195431.94260705203461.057392951
819265171252867.44201578673649.55798422
99836601055210.25698251-71550.2569825147
101443586624848.805029943818737.194970057
111073089616499.621069627456589.378930373
12984885587580.67520935397304.32479065
1314052251266407.23038405138817.769615947
14227132986943.221717026-759811.221717026
159291181071156.82184954-142038.821849544
161071292433187.151578073638104.848421927
17638830514583.282962012124246.717037988
188569561001856.65974805-144900.659748045
199924261072416.24462667-79990.2446266724
20444477987028.338065035-542551.338065035
21857217480346.140593959376870.859406041
22711969504505.741273754207463.258726246
23702380548858.256529696153521.743470304
24358589999511.20912771-640922.209127711
25297978476070.090704947-178092.090704947
26585715452880.680003131132834.319996869
27657954983454.591739312-325500.591739312
28209458475847.327676579-266389.327676579
29786690380608.403593158406081.596406842
30439798636318.998397314-196520.998397314
31688779350095.563760418338683.436239582
32574339468861.561229487105477.438770513
33741409388133.015939518353275.984060482
34597793384315.662361039213477.337638961
35644190320829.384771498323360.615228502
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37640273471274.779197477168998.220802523
38697458461929.696264338235528.303735662
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41301607732701.144219423-431094.144219423
42345783445185.534250921-99402.534250921
43501749475851.42668003825897.5733199625
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45387475378812.173584398662.82641561005
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61493408389637.923108895103770.076891105
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63414462347535.39526588266926.6047341177
64364304465673.181393044-101369.181393044
65355178401062.569861576-45884.5698615762
66357760879093.011673228-521333.011673228
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201315380294344.35135171421035.6486482862
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328315380294344.35135171421035.6486482862
329315380294344.35135171421035.6486482862
330315380294344.35135171421035.6486482862
331315380294344.35135171421035.6486482862
332315380294344.35135171421035.6486482862
333315380294344.35135171421035.6486482862
334313729301725.19332161912003.8066783809
335315388296144.71228182419243.2877181757
336315371302149.3550804913221.6449195096
337296139332400.405988154-36261.4059881537
338315380294344.35135171421035.6486482862
339313880296190.89090764317689.1090923571
340317698312597.3389974085100.66100259228
341295580316597.900498615-21017.9004986146
342315380294344.35135171421035.6486482862
343315380294344.35135171421035.6486482862
344315380294344.35135171421035.6486482862
345308256319116.908577478-10860.9085774777
346315380294344.35135171421035.6486482862
347303677299967.5213538143709.47864618639
348315380294344.35135171421035.6486482862
349315380294344.35135171421035.6486482862
350319369315747.2525856373621.74741436304
351318690300336.70058780818353.2994121924
352314049307056.6026822866992.39731771411
353325699313587.31183942312111.6881605774
354314210296392.22971621217817.7702837876
355315380294344.35135171421035.6486482862
356315380294344.35135171421035.6486482862
357322378322507.881934506-129.88193450598
358315380294344.35135171421035.6486482862
359315380294344.35135171421035.6486482862
360315380294344.35135171421035.6486482862
361315398301540.35218816613857.647811834
362315380294344.35135171421035.6486482862
363315380294344.35135171421035.6486482862
364308336349522.964470968-41186.9644709684
365316386310910.7660555625475.2339444381
366315380294344.35135171421035.6486482862
367315380294344.35135171421035.6486482862
368315380294344.35135171421035.6486482862
369315380294344.35135171421035.6486482862
370315553307379.5937478618173.406252139
371315380294344.35135171421035.6486482862
372323361307849.7706154715511.2293845296
373336639307397.99197311529241.0080268847
374307424300072.7278712737351.27212872695
375315380294344.35135171421035.6486482862
376315380294344.35135171421035.6486482862
377295370314391.256483772-19021.2564837722
378322340308174.80592829614165.194071704
379319864317069.359173352794.64082665048
380315380294344.35135171421035.6486482862
381315380294344.35135171421035.6486482862
382317291327992.568180756-10701.568180756
383280398320822.112450199-40424.112450199
384315380294344.35135171421035.6486482862
385317330316098.7797023351231.220297665
386238125353388.203065126-115263.203065126
387327071299990.47550307727080.5244969225
388309038306991.9533832082046.04661679193
389314210299877.6176025314332.3823974699
390307930309920.56147103-1990.56147103041
391322327313180.1801511489146.81984885187
392292136306040.562658564-13904.562658564
393263276310024.416352035-46748.4163520352
394367655306531.34349749261123.6565025075
395283910317757.547282198-33847.5472821976
396283587309899.790494829-26312.7904948294
397243650354226.253575458-110576.253575458
398438493738126.84457507-299633.84457507
399296261308015.354642759-11754.3546427589
400230621374804.04231212-144183.04231212
401304252301769.4220710282482.57792897185
402333505310344.2893855323160.7106144698
403296919306364.397556382-9445.39755638155
404278990335934.477439161-56944.477439161
405276898308144.142219539-31246.1422195389
406327007316699.619785210307.3802148002
407317046315479.0808482531566.91915174728
408304555318110.722381144-13555.7223811435
409298096311455.132636909-13359.1326369092
410231861301128.618737412-69267.6187374115
411309422401663.492849342-92241.4928493418
412286963350691.447680716-63728.447680716
413269753324007.464569346-54254.4645693462
414448243361381.61895944186861.3810405588
415165404318305.248547173-152901.248547173
416204325299755.574485155-95430.5744851549
417407159344077.61031184363081.389688157
418290476333119.55488632-42643.5548863198
419275311340814.115681807-65503.1156818067
420246541297363.828003437-50822.8280034374
421253468298014.023054964-44546.0230549644
422240897439507.782858426-198610.782858426
423-83265463310.013761184-546575.013761184
424-42143346442.344267808-388585.344267808
425272713335909.65490704-63196.6549070396
426215362464853.981310431-249491.981310431
42742754342127.246386618-299373.246386618
4283062751083357.97043348-777082.970433484
429253537378408.458529022-124871.458529022
430372631519702.838269188-147071.838269188
431-7170492197.176350278-499367.176350278


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
712.98613015237419e-791.49306507618709e-79
814.46219785064409e-852.23109892532204e-85
912.29186440249699e-871.14593220124849e-87
1014.578807471886e-952.289403735943e-95
1116.76746192740253e-983.38373096370127e-98
1216.08099821375051e-1023.04049910687525e-102
1311.31687717702996e-1216.58438588514981e-122
1413.78901808439207e-1281.89450904219604e-128
1517.18916994813094e-1333.59458497406547e-133
1613.31073832098131e-1411.65536916049066e-141
1712.98459101831887e-1421.49229550915943e-142
1811.79319606644359e-1468.96598033221794e-147
1917.62246363795378e-1513.81123181897689e-151
2019.85184491203429e-1564.92592245601714e-156
2111.26940046774883e-1596.34700233874415e-160
2211.8212852551907e-1609.1064262759535e-161
2314.13492280245707e-1622.06746140122853e-162
2411.19054024764627e-1665.95270123823135e-167
2511.70251540057217e-1668.51257700286087e-167
2619.28810573112206e-1674.64405286556103e-167
2712.13465848503065e-1691.06732924251532e-169
2819.22793692991852e-1704.61396846495926e-170
2911.96041947538869e-1759.80209737694347e-176
3013.9712793812414e-1751.9856396906207e-175
3119.37104542767694e-1794.68552271383847e-179
3218.59313164616528e-1804.29656582308264e-180
3317.19615807006254e-1863.59807903503127e-186
3416.57117307428559e-1883.28558653714279e-188
3517.83495494288302e-1923.91747747144151e-192
3611.20701293403366e-1926.03506467016828e-193
3718.50688828922994e-1974.25344414461497e-197
3812.86872916058889e-2021.43436458029444e-202
3913.40450253121484e-2031.70225126560742e-203
4013.05806034247551e-2051.52903017123775e-205
4111.19844024259238e-2065.99220121296192e-207
4212.79855185182609e-2061.39927592591304e-206
4311.77251177147585e-2068.86255885737923e-207
4419.9709324585187e-2064.98546622925935e-206
4514.4375587901118e-2052.2187793950559e-205
4612.26988887313231e-2041.13494443656616e-204
4711.41704760095059e-2037.08523800475297e-204
4815.10952390858331e-2032.55476195429165e-203
4912.43219509694149e-2031.21609754847074e-203
5011.4356546212534e-2037.17827310626701e-204
5112.86520073692716e-2041.43260036846358e-204
5212.18561770294818e-2041.09280885147409e-204
5313.43596492638933e-2051.71798246319466e-205
5413.15328620200026e-2061.57664310100013e-206
5511.20047449453104e-2066.00237247265522e-207
5617.31986706030486e-2063.65993353015243e-206
5713.91868066576398e-2151.95934033288199e-215
5815.92991255105934e-2162.96495627552967e-216
5916.40092721971561e-2153.20046360985781e-215
6016.8922349335604e-2153.4461174667802e-215
6111.34301361589333e-2176.71506807946666e-218
6213.18810942756466e-2191.59405471378233e-219
6311.92785420772223e-2199.63927103861113e-220
6414.64855907672846e-2192.32427953836423e-219
6514.0663862180117e-2182.03319310900585e-218
6616.23174655874828e-2193.11587327937414e-219
6714.01124105194519e-2182.0056205259726e-218
6811.50745464228371e-2177.53727321141857e-218
6911.52351754952175e-2167.61758774760873e-217
7012.78738749904954e-2161.39369374952477e-216
7112.05124076643104e-2161.02562038321552e-216
7212.16333686751629e-2161.08166843375815e-216
7312.37878085367177e-2151.18939042683589e-215
7412.68015194255667e-2141.34007597127834e-214
7517.5388496424197e-2143.76942482120985e-214
7614.115888151452e-2132.057944075726e-213
7713.02676955407135e-2121.51338477703568e-212
7811.01661275256637e-2115.08306376283184e-212
7919.38085670685818e-2114.69042835342909e-211
8019.21853020589833e-2104.60926510294917e-210
8118.39737897924716e-2094.19868948962358e-209
8213.48847245543941e-2091.74423622771971e-209
8313.30791248640522e-2081.65395624320261e-208
8413.492357969441e-2071.7461789847205e-207
8511.79020472820308e-2068.9510236410154e-207
8616.220206900108e-2063.110103450054e-206
8713.02623668114672e-2061.51311834057336e-206
8812.35619993990309e-2051.17809996995155e-205
8912.36908319931694e-2041.18454159965847e-204
9018.47937210205245e-2044.23968605102622e-204
9111.88332966238309e-2039.41664831191543e-204
9214.6129103647831e-2032.30645518239155e-203
9311.30554358466939e-2036.52771792334696e-204
9412.31325474568787e-2041.15662737284394e-204
9511.44225031447618e-2037.21125157238091e-204
9612.05089692368169e-2031.02544846184084e-203
9711.03131009071153e-2035.15655045355767e-204
9819.24037508871196e-2034.62018754435598e-203
9912.98834177976409e-2031.49417088988204e-203
10012.81607182055917e-2021.40803591027959e-202
10112.8793936974029e-2011.43969684870145e-201
10217.6686900347865e-2013.83434501739325e-201
10317.10600279596297e-2003.55300139798148e-200
10417.31714972646525e-1993.65857486323263e-199
10512.70530989314223e-1981.35265494657111e-198
10611.49645858555098e-1977.48229292775488e-198
10711.00730520143334e-1995.03652600716671e-200
10812.70360365035165e-2041.35180182517583e-204
10917.18805402536384e-2043.59402701268192e-204
11014.47957976255336e-2032.23978988127668e-203
11113.4912336664293e-2031.74561683321465e-203
11215.85201289588701e-2042.92600644794351e-204
11314.22270670246412e-2032.11135335123206e-203
11414.38456176905953e-2022.19228088452977e-202
11515.95298151387433e-2022.97649075693716e-202
11614.60302101078452e-2012.30151050539226e-201
11714.3123427456988e-2002.1561713728494e-200
11813.03150681616447e-2021.51575340808224e-202
11918.59723619211326e-2024.29861809605663e-202
12019.17452617721249e-2014.58726308860624e-201
12115.88596286875592e-2032.94298143437796e-203
12214.86389430811843e-2022.43194715405922e-202
12314.33053048453809e-2012.16526524226904e-201
12419.14571099135266e-2054.57285549567633e-205
12511.13646801125047e-2045.68234005625236e-205
12615.55198783101717e-2042.77599391550858e-204
12716.11538614113714e-2033.05769307056857e-203
12816.71120323495461e-2023.35560161747731e-202
12917.35071849538284e-2013.67535924769142e-201
13017.96128067394728e-2003.98064033697364e-200
13118.58281392442547e-1994.29140696221273e-199
13211.69552400223302e-1988.47762001116508e-199
13311.81717516883026e-1979.08587584415129e-198
13411.87035854921329e-1969.35179274606646e-197
13511.94668492704843e-1959.73342463524213e-196
13612.04566191727975e-1941.02283095863987e-194
13712.15483288390736e-1931.07741644195368e-193
13812.2500687472239e-1921.12503437361195e-192
13912.14801778848605e-1911.07400889424303e-191
14012.21780587166403e-1901.10890293583202e-190
14112.13270294321306e-1891.06635147160653e-189
14212.17941028464444e-1881.08970514232222e-188
14312.22220598322058e-1871.11110299161029e-187
14412.25243713373112e-1861.12621856686556e-186
14512.0831005196277e-1851.04155025981385e-185
14612.09492106285262e-1841.04746053142631e-184
14712.08562991272063e-1831.04281495636031e-183
14812.06755101827365e-1821.03377550913682e-182
14911.89409865999481e-1819.47049329997403e-182
15011.85606702759523e-1809.28033513797615e-181
15111.67825168879583e-1798.39125844397913e-180
15211.56785599068418e-1787.83927995342088e-179
15311.51676773378671e-1777.58383866893355e-178
15411.40845951575264e-1767.04229757876321e-177
15511.34827435925471e-1756.74137179627356e-176
15611.28239740502748e-1746.41198702513742e-175
15711.21363998557098e-1736.06819992785492e-174
15811.14373475624989e-1725.71867378124947e-173
15918.50568386725057e-1724.25284193362528e-172
16017.93677172678986e-1713.96838586339493e-171
16117.36917893918571e-1703.68458946959285e-170
16216.80830762786786e-1693.40415381393393e-169
16316.25904859636898e-1683.12952429818449e-168
16415.74000201014067e-1672.87000100507034e-167
16514.83561496131508e-1662.41780748065754e-166
16614.38378082904566e-1652.19189041452283e-165
16713.95170549365819e-1641.97585274682909e-164
16817.00532106591733e-1643.50266053295866e-164
16919.19403603799342e-1644.59701801899671e-164
17018.28180684079191e-1634.14090342039596e-163
17117.423850619735e-1623.7119253098675e-162
17216.62116487464311e-1613.31058243732156e-161
17315.87776174471526e-1602.93888087235763e-160
17415.17126966172769e-1592.58563483086384e-159
17514.54625512191347e-1582.27312756095674e-158
17613.98937268269649e-1571.99468634134825e-157
17711.2589680036098e-1566.294840018049e-157
17811.09183240995438e-1555.45916204977189e-156
17919.45179851085553e-1554.72589925542776e-155
18018.14310029785181e-1544.07155014892591e-154
18112.97176393637394e-1531.48588196818697e-153
18212.24494923296882e-1521.12247461648441e-152
18311.32888577260206e-1516.64442886301031e-152
18411.03510623232385e-1505.17553116161925e-151
18518.77278063499438e-1504.38639031749719e-150
18616.05244136492109e-1493.02622068246054e-149
18711.16018988386105e-1485.80094941930526e-149
18819.7724036559527e-1484.88620182797635e-148
18917.3143363770596e-1473.6571681885298e-147
19016.08725355276855e-1463.04362677638427e-146
19114.98631534884565e-1452.49315767442282e-145
19214.11076018267009e-1442.05538009133505e-144
19313.38218995063755e-1431.69109497531878e-143
19412.76200683666061e-1421.3810034183303e-142
19512.2483975882751e-1411.12419879413755e-141
19611.81886400676454e-1409.0943200338227e-141
19711.35391241615145e-1416.76956208075724e-142
19811.10829473037946e-1405.54147365189731e-141
19919.02982452276362e-1404.51491226138181e-140
20014.23392294426351e-1392.11696147213176e-139
20113.42568482919154e-1381.71284241459577e-138
20212.75877044631004e-1371.37938522315502e-137
20312.21130262023493e-1361.10565131011746e-136
20411.6665278729799e-1358.3326393648995e-136
20511.23278087513308e-1346.16390437566539e-135
20619.76528261224279e-1344.88264130612139e-134
20717.64454510465182e-1333.82227255232591e-133
20815.98874727955324e-1322.99437363977662e-132
20912.96189289883732e-1311.48094644941866e-131
21012.30344225066156e-1301.15172112533078e-130
21111.78303136447891e-1298.91515682239455e-130
21211.37375765779905e-1286.86878828899527e-129
21319.78153091022305e-1284.89076545511153e-128
21416.73714260389622e-1273.36857130194811e-127
21515.13462476125999e-1262.56731238063e-126
21613.88934013108887e-1251.94467006554444e-125
21712.93448190855603e-1241.46724095427802e-124
21812.15864024376382e-1231.07932012188191e-123
21911.61237253152373e-1228.06186265761863e-123
22018.93443997746834e-1224.46721998873417e-122
22116.35899934409506e-1213.17949967204753e-121
22214.68647258353567e-1202.34323629176784e-120
22313.43949610300001e-1191.71974805150001e-119
22412.51090593409459e-1181.25545296704729e-118
22511.82494320221142e-1179.1247160110571e-118
22611.31729910771077e-1166.58649553855384e-117
22719.49215242893964e-1164.74607621446982e-116
22816.80089465309156e-1153.40044732654578e-115
22914.85453266975901e-1142.4272663348795e-114
23013.44558855531186e-1131.72279427765593e-113
23112.3561104944204e-1121.1780552472102e-112
23211.51852697612664e-1117.59263488063322e-112
23311.06330611469277e-1105.31653057346383e-111
23417.2798841634246e-1103.6399420817123e-110
23515.05010685527282e-1092.52505342763641e-109
23613.48645605066935e-1081.74322802533467e-108
23712.39584460275439e-1071.1979223013772e-107
23811.64132954871749e-1068.20664774358743e-107
23911.11725377914572e-1055.58626889572862e-106
24017.56918673332762e-1053.78459336666381e-105
24115.10370396936587e-1042.55185198468293e-104
24213.42937267885461e-1031.71468633942731e-103
24312.29042705546292e-1021.14521352773146e-102
24411.52464269012906e-1017.62321345064528e-102
24514.33000736465741e-1012.16500368232871e-101
24612.86414797106236e-1001.43207398553118e-100
24711.88549096272614e-999.42745481363072e-100
24811.21556656324822e-986.07783281624111e-99
24917.92657222444997e-983.96328611222498e-98
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35413.98105954983103e-261.99052977491551e-26
35511.42682868537299e-257.13414342686496e-26
35615.07171587240167e-252.53585793620083e-25
35711.74862076422814e-248.7431038211407e-25
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36112.48593803121566e-221.24296901560783e-22
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36312.80842098475787e-211.40421049237894e-21
36418.99104457081431e-214.49552228540716e-21
36512.95485117686356e-201.47742558843178e-20
36619.62264100235222e-204.81132050117611e-20
36713.1041786474953e-191.55208932374765e-19
36819.9182630603486e-194.9591315301743e-19
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37417.79056854240065e-163.89528427120032e-16
3750.9999999999999992.31996304940519e-151.15998152470259e-15
3760.9999999999999976.83400778559106e-153.41700389279553e-15
3770.999999999999991.99578719117789e-149.97893595588943e-15
3780.9999999999999725.5345875180316e-142.7672937590158e-14
3790.9999999999999341.31000709641924e-136.55003548209618e-14
3800.9999999999998153.70363807571378e-131.85181903785689e-13
3810.9999999999994831.03468802990403e-125.17344014952015e-13
3820.999999999998582.84200196306602e-121.42100098153301e-12
3830.9999999999961287.74482152203135e-123.87241076101567e-12
3840.9999999999895542.08921847331904e-111.04460923665952e-11
3850.9999999999720435.59131669874928e-112.79565834937464e-11
3860.999999999929781.40440813807979e-107.02204069039895e-11
3870.9999999998224583.55083060607574e-101.77541530303787e-10
3880.9999999995524978.95006879842439e-104.47503439921219e-10
3890.999999998864072.27185877354556e-091.13592938677278e-09
3900.999999997160515.67897831347255e-092.83948915673627e-09
3910.999999993149641.37007218059716e-086.85036090298582e-09
3920.9999999830821913.3835617566703e-081.69178087833515e-08
3930.9999999598301018.03397975955706e-084.01698987977853e-08
3940.9999999275782921.44843415266787e-077.24217076333936e-08
3950.999999845752893.08494221962242e-071.54247110981121e-07
3960.999999636170487.27659038458278e-073.63829519229139e-07
3970.999999185845271.62830946193943e-068.14154730969715e-07
3980.9999982428838033.51423239397955e-061.75711619698977e-06
3990.9999960647043727.8705912557163e-063.93529562785815e-06
4000.9999919388807331.61222385343591e-058.06111926717955e-06
4010.999983048871183.39022576397904e-051.69511288198952e-05
4020.9999670521109146.58957781723284e-053.29478890861642e-05
4030.99993134222460.000137315550799296.86577753996451e-05
4040.9998584566712470.0002830866575068240.000141543328753412
4050.9997131621702340.0005736756595321450.000286837829766072
4060.9994810363206960.001037927358607750.000518963679303873
4070.9990340524130130.001931895173973740.00096594758698687
4080.9982225915186550.003554816962689880.00177740848134494
4090.9967418243870520.006516351225896120.00325817561294806
4100.9941257215332550.0117485569334910.00587427846674549
4110.989610628234510.0207787435309780.010389371765489
4120.9867936953575140.02641260928497140.0132063046424857
4130.9772496937500220.04550061249995510.0227503062499775
4140.9829130381157410.03417392376851730.0170869618842586
4150.971530332737230.05693933452554180.0284696672627709
4160.9520032923996660.09599341520066730.0479967076003336
4170.956362600230760.087274799538480.04363739976924
4180.9290470160600110.1419059678799770.0709529839399886
4190.8864333909422980.2271332181154030.113566609057702
4200.824109558601190.3517808827976220.175890441398811
4210.7574573630620940.4850852738758110.242542636937906
4220.639271103682130.7214577926357410.360728896317871
4230.6939125916896180.6121748166207650.306087408310382
4240.636298630735580.7274027385288390.363701369264419


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level4030.964114832535885NOK
5% type I error level4080.976076555023923NOK
10% type I error level4110.983253588516746NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/104l0c1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/104l0c1292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/1xk311292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/1xk311292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/28u241292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/28u241292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/38u241292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/38u241292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/48u241292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/48u241292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/5jljo1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/5jljo1292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/6jljo1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/6jljo1292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/7bu1r1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/7bu1r1292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/8bu1r1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/8bu1r1292955502.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/94l0c1292955502.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/21/t12929555422v7v766iosxixye/94l0c1292955502.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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