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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: Fri, 03 Dec 2010 13:07:36 +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/03/t1291381686k4kbm50lq76dczt.htm/, Retrieved Fri, 03 Dec 2010 14:08:06 +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/03/t1291381686k4kbm50lq76dczt.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 «
1 162556 162556 213118 213118 6282929 1 29790 29790 81767 81767 4324047 1 87550 87550 153198 153198 4108272 0 84738 0 -26007 0 -1212617 1 54660 54660 126942 126942 1485329 1 42634 42634 157214 157214 1779876 0 40949 0 129352 0 1367203 1 42312 42312 234817 234817 2519076 1 37704 37704 60448 60448 912684 1 16275 16275 47818 47818 1443586 0 25830 0 245546 0 1220017 0 12679 0 48020 0 984885 1 18014 18014 -1710 -1710 1457425 0 43556 0 32648 0 -572920 1 24524 24524 95350 95350 929144 0 6532 0 151352 0 1151176 0 7123 0 288170 0 790090 1 20813 20813 114337 114337 774497 1 37597 37597 37884 37884 990576 0 17821 0 122844 0 454195 1 12988 12988 82340 82340 876607 1 22330 22330 79801 79801 711969 0 13326 0 165548 0 702380 0 16189 0 116384 0 264449 0 7146 0 134028 0 450033 0 15824 0 63838 0 541063 1 26088 26088 74996 74996 588864 0 11326 0 31080 0 -37216 0 8568 0 32168 0 783310 0 14416 0 49857 0 467359 1 3369 3369 87161 87161 688779 1 11819 11819 106113 106113 608419 1 6620 6620 80570 80570 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'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 117378.942798089 + 45851.7248740936Group[t] -7.64971774851703Costs[t] + 43.2848436572618GrCosts[t] + 3.42410064392417Dividends[t] -1.61331277750957GrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)117378.94279808931052.1760383.78010.0001799e-05
Group45851.724874093655610.0300350.82450.4101050.205053
Costs-7.649717748517031.720886-4.44521.1e-056e-06
GrCosts43.28484365726182.06466320.964600
Dividends3.424100643924170.416838.214600
GrDiv-1.613312777509570.700046-2.30460.0216710.010836


Multiple Linear Regression - Regression Statistics
Multiple R0.884401241167262
R-squared0.782165555378194
Adjusted R-squared0.779602797206173
F-TEST (value)305.204589304383
F-TEST (DF numerator)5
F-TEST (DF denominator)425
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation210046.470857091
Sum Squared Residuals18750795965795.5


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829296341845.68340864-58916.6834086411
243240471372863.759966812951183.24003319
341082723560495.02054177547776.97945823
4-1212617-619893.425222283-592723.574777717
514853292340911.68318257-855582.683182573
617798761967179.82929611-187303.829296111
71367203247044.9172069441120158.08279306
825190762096227.88955087422848.110449132
99126841616275.95988452-703591.959884524
101443586829780.596033217613805.403966783
111220017760560.950066898459456.049933102
12984885184813.48438588800071.51561412
131457425802065.378540741655359.621459259
14-572920-104022.125633483-468897.874366517
159291441209805.11852087-280661.118520871
161151176585655.467123987565520.532876013
177900901049613.08583503-259523.085835030
187744971111944.59549313-337447.595493133
199905761571604.38399451-581028.383994509
20454195401683.54230398852511.4576960124
21876607775159.955895538101447.044104462
227119691103465.71174220-391496.711742204
23702380582291.817481709120088.182518291
24264449392048.191509817-127599.191509817
25450033521639.420871055-71606.4208710548
26541063214917.546052386326145.453947614
275888641228681.67920914-639817.679209145
28-37216137159.287591548-174375.287591548
29783310161982.630642547621327.369357453
30467359177815.997539594289543.002460406
31688779441115.488083307247663.511916693
32608419776550.353656489-168131.353656489
33696348545030.379585097151317.620414903
34597793509199.75566285788593.2443371431
358217301133345.01064899-311615.010648986
36377934325714.89113192952219.1088680709
37651939341676.870346025310262.129653975
38697458557051.68637196140406.313628040
39700368594777.015891624105590.984108376
40225986359509.169067097-133523.169067097
41348695497691.18696863-148996.18696863
42373683342687.77362913030995.2263708695
43501709403982.27549321997726.7245067805
44413743467233.339257494-53490.3392574938
45379825318783.42549110461041.5745088964
46336260477729.501114902-141469.501114902
47636765589603.08140193547161.9185980652
48481231678172.820150107-196941.820150107
49469107497354.026619842-28247.0266198416
50211928361518.548958214-149590.548958214
51563925471572.96917603692352.030823964
52511939555136.402283639-43197.4022836387
53521016764841.496610713-243825.496610713
54543856468407.05912837775448.9408716234
55329304612802.950338574-283498.950338574
56423262309203.741989084114058.258010916
57509665261111.268098229248553.731901771
58455881376654.41725583279226.582744168
59367772448209.404454616-80437.4044546161
60406339653896.751517143-247557.751517143
61493408532397.032489897-38989.0324898968
62232942312252.469523724-79310.4695237242
63416002445910.818072754-29908.8180727540
64337430573227.073835691-235797.073835691
65361517298996.09552327862520.9044767216
66360962327004.87086398133957.1291360191
67235561387283.706302671-151722.706302671
68408247418234.331071789-9987.33107178909
69450296555440.124752962-105144.124752962
70418799488619.924417402-69820.9244174021
71247405321228.458453421-73823.4584534211
72378519211893.502681586166625.497318414
73326638472417.194025796-145779.194025796
74328233384620.818718938-56387.8187189381
75386225509331.258895117-123106.258895117
76283662349616.226145529-65954.2261455288
77370225502614.611138479-132389.611138479
78269236364617.480581837-95381.4805818374
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80420383400399.41655382919983.5834461708
81345811315630.83777291930180.1622270811
82431809490645.449047493-58836.4490474928
83418876586528.480637174-167652.480637174
84297476246832.06056629150643.939433709
85416776465187.726522461-48411.7265224614
86357257482389.006095365-125132.006095365
87458343398584.84307987359758.1569201268
88388386469217.598156246-80831.5981562463
89358934466368.978993351-107434.978993351
90407560466905.233881023-59345.233881023
91392558429248.098210905-36690.0982109046
92373177418438.400466440-45261.4004664405
93428370317892.960959750110477.039040250
94369419625842.033360689-256423.033360689
95358649231424.850835682127224.149164318
96376641381190.513911278-4549.51391127817
97467427502204.471830704-34777.4718307037
98364885340707.0713235924177.9286764101
99436230543377.524291183-107147.524291183
100329118345101.74517072-15983.74517072
101317365345992.869107391-28627.8691073906
102286849419917.995690315-133068.995690315
103376685463073.006608830-86388.0066088305
104407198502501.818728401-95303.8187284005
105377772342610.4292535435161.5707464598
106271483356704.319537553-85221.3195375525
107153661385319.238408348-231658.238408348
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109324881422962.59613553-98081.5961355297
110264512364181.948934288-99669.9489342882
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112129302372666.2503415-243364.2503415
113191521372980.971579402-181459.971579402
114268673382682.582347452-114009.582347452
115353179316902.48351426136276.5164857391
116354624298877.42571621055746.5742837905
117363713405318.0699903-41605.0699903001
118456657403592.30080440153064.6991955987
119211742382632.362239526-170890.362239526
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322325560325290.333897164269.666102835675
323325560325290.333897164269.666102835675
324325560273181.70692087752378.2930791229
325325560325290.333897164269.666102835675
326322649325128.888307985-2479.8883079848
327325560273181.70692087752378.2930791229
328325560273181.70692087752378.2930791229
329325560325290.333897164269.666102835675
330325560325290.333897164269.666102835675
331325560325290.333897164269.666102835675
332325560325290.333897164269.666102835675
333325560325290.333897164269.666102835675
334324598323388.3426737291209.65732627145
335325567325306.652883923260.347116076707
336325560325290.333897164269.666102835675
337324005325372.647391539-1367.64739153891
338325560325290.333897164269.666102835675
339325748325694.08294903453.9170509664688
340323385320957.9559436902427.04405630955
341315409330665.622049801-15256.6220498006
342325560325290.333897164269.666102835675
343325560325290.333897164269.666102835675
344325560325290.333897164269.666102835675
345325560325290.333897164269.666102835675
346325560325290.333897164269.666102835675
347312275318894.608253524-6619.60825352426
348325560325290.333897164269.666102835675
349325560325290.333897164269.666102835675
350325560325290.333897164269.666102835675
351320576315637.680393224938.31960678007
352325246326214.687492399-968.687492398662
353332961316947.8363543716013.1636456299
354323010328863.037367193-5853.03736719255
355325560325290.333897164269.666102835675
356325560325290.333897164269.666102835675
357345253383197.636603697-37944.6366036971
358325560325290.333897164269.666102835675
359325560325290.333897164269.666102835675
360325560325290.333897164269.666102835675
361325559325289.532380704269.467619296323
362325560325290.333897164269.666102835675
363325560325290.333897164269.666102835675
364319634276842.03754602942791.9624539709
365319951320198.235503774-247.23550377354
366325560325290.333897164269.666102835675
367325560325290.333897164269.666102835675
368325560325290.333897164269.666102835675
369325560325290.333897164269.666102835675
370325560325290.333897164269.666102835675
371325560325290.333897164269.666102835675
372318519318648.029841184-129.029841183903
373343222378079.226622099-34857.2266220995
374317234337998.095649011-20764.0956490114
375325560325290.333897164269.666102835675
376325560325290.333897164269.666102835675
377314025308812.452924895212.54707510983
378320249319674.51064094574.489359059967
379325560325290.333897164269.666102835675
380325560325290.333897164269.666102835675
381325560325290.333897164269.666102835675
382349365364766.574976658-15401.5749766583
383289197255032.37637172834164.6236282718
384325560325290.333897164269.666102835675
385329245331473.37518775-2228.37518774986
386240869330506.515382664-89637.5153826642
387327182320662.0982901936519.9017098071
388322876311039.03306304211836.9669369577
389323117323636.993811928-519.993811927518
390306351313587.119967015-7236.11996701488
391335137329067.3562324126069.64376758787
392308271317071.340512057-8800.34051205743
393301731321319.752605689-19588.7526056893
394382409345114.32850609737294.6714939031
395279230436699.055299222-157469.055299222
396298731313239.028664653-14508.0286646534
397243650260595.45973491-16945.4597349098
398532682434035.11736964998646.882630351
399319771332029.55023656-12258.5502365599
400171493277019.301336747-105526.301336747
401347262350370.639108833-3108.63910883256
402343945331372.74618448912572.2538155111
403311874315377.482367616-3503.48236761644
404302211343189.819132646-40978.819132646
405316708332917.258275973-16209.2582759730
406333463350400.347340917-16937.3473409169
407344282345484.432366323-1202.4323663228
408319635311595.6228912578039.37710874333
409301186313721.915977896-12535.9159778958
410300381351443.810774479-51062.8107744788
411318765346629.303858245-27864.3038582453
412286146503734.387549589-217588.387549589
413306844308504.314732846-1660.31473284628
414307705417408.505620498-109703.505620498
415312448378871.501494072-66423.501494072
416299715361634.121492757-61919.121492757
417373399213171.009507244160227.990492756
418299446316461.457838241-17015.4578382412
419325586344632.110420888-19046.1104208882
420291221338039.1938138-46818.1938138002
421261173348529.28064543-87356.2806454303
422255027344497.052623647-89470.0526236467
423-78375547694.489631191-626069.489631191
424-58143258624.423721553-316767.423721553
425227033288981.310743318-61948.3107433183
426235098443590.561339795-208492.561339795
42721267262279.727724171-241012.727724171
428238675383401.098800024-144726.098800024
429197687318853.99638722-121166.99638722
430418341265990.197047171152350.802952829
431-29770672548.7558979675-370254.755897967


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
913.92833764380778e-861.96416882190389e-86
1017.9402903855259e-923.97014519276295e-92
1111.74208604088221e-948.71043020441103e-95
1211.38274342958369e-1056.91371714791844e-106
1312.4489569931926e-1201.2244784965963e-120
1413.57720897299916e-1291.78860448649958e-129
1511.42652836229420e-1327.13264181147102e-133
1612.81312699785176e-1431.40656349892588e-143
1718.84725154669706e-1484.42362577334853e-148
1811.49639738546693e-1497.48198692733464e-150
1913.04628553497769e-1551.52314276748885e-155
2016.4959425538994e-1553.2479712769497e-155
2114.10829470805878e-1592.05414735402939e-159
2211.39063052021122e-1616.95315260105609e-162
2311.04723017877244e-1625.23615089386218e-163
2416.33840705783634e-1633.16920352891817e-163
2511.27048585632758e-1626.35242928163791e-163
2611.95961922902115e-1649.79809614510577e-165
2711.17359963400072e-1675.86799817000362e-168
2819.01065542800652e-1704.50532771400326e-170
2911.83476575941589e-1829.17382879707947e-183
3011.40518216936148e-1847.0259108468074e-185
3113.35945039652713e-1881.67972519826357e-188
3211.03415139656370e-1895.17075698281852e-190
3315.41673588024249e-1962.70836794012125e-196
3412.34589563788282e-1971.17294781894141e-197
3511.13054926493714e-1975.6527463246857e-198
3612.42128394666956e-1971.21064197333478e-197
3711.79295746874765e-2048.96478734373825e-205
3812.21354424462682e-2091.10677212231341e-209
3911.27677148309472e-2086.38385741547359e-209
4014.13845490643011e-2092.06922745321505e-209
4111.02531976733007e-2085.12659883665033e-209
4211.99133053214703e-2089.95665266073516e-209
4314.28917590770659e-2092.14458795385330e-209
4412.47312744567342e-2081.23656372283671e-208
4517.94350156728692e-2083.97175078364346e-208
4613.09518759971819e-2071.54759379985910e-207
4712.24946700599668e-2061.12473350299834e-206
4819.1880832071344e-2064.5940416035672e-206
4913.33063409294381e-2051.66531704647191e-205
5019.45654825591099e-2064.72827412795549e-206
5111.35795577225046e-2066.7897788612523e-207
5218.64376872547243e-2064.32188436273621e-206
5313.85181575694514e-2051.92590787847257e-205
5414.09246276531137e-2042.04623138265569e-204
5518.49543691754968e-2074.24771845877484e-207
5616.14482363870022e-2073.07241181935011e-207
5714.07678096509545e-2112.03839048254772e-211
5811.22919064623945e-2116.14595323119723e-212
5917.84221651519247e-2113.92110825759623e-211
6012.66236318044885e-2111.33118159022443e-211
6112.67289035616056e-2121.33644517808028e-212
6215.68903875654248e-2122.84451937827124e-212
6314.34462305324307e-2112.17231152662154e-211
6411.04355652697154e-2105.21778263485772e-211
6514.10300227066732e-2102.05150113533366e-210
6611.9229847853893e-2109.6149239269465e-211
6713.73583766899653e-2111.86791883449826e-211
6814.24755709075417e-2102.12377854537709e-210
6913.21674578521973e-2091.60837289260986e-209
7011.92292033921933e-2089.61460169609663e-209
7117.49586818392028e-2083.74793409196014e-208
7211.91994672506663e-2099.59973362533314e-210
7312.19257505909155e-2091.09628752954578e-209
7411.56689888182765e-2087.83449440913824e-209
7516.52326861651986e-2083.26163430825993e-208
7612.36897880092984e-2071.18448940046492e-207
7715.07772655061764e-2072.53886327530882e-207
7819.81538327245062e-2074.90769163622531e-207
7917.87103879481566e-2063.93551939740783e-206
8014.15404253470847e-2052.07702126735423e-205
8113.18050061446333e-2041.59025030723167e-204
8212.82882190668189e-2041.41441095334094e-204
8312.17222379092401e-2041.08611189546200e-204
8411.60165498505340e-2038.00827492526699e-204
8511.50296333137017e-2027.51481665685084e-203
8612.54678697779517e-2031.27339348889758e-203
8711.84528092230104e-2039.22640461150518e-204
8811.05118463601964e-2025.25592318009818e-203
8913.33244811237218e-2021.66622405618609e-202
9012.67388767329152e-2011.33694383664576e-201
9112.67214640140513e-2001.33607320070256e-200
9211.67545265067358e-1998.3772632533679e-200
9312.69408192890308e-2001.34704096445154e-200
9411.58380011190924e-1997.9190005595462e-200
9512.22216224262787e-2001.11108112131394e-200
9617.11429813632541e-2013.55714906816271e-201
9717.08676731848236e-2003.54338365924118e-200
9814.43736185881832e-1992.21868092940916e-199
9911.42696218889655e-1987.13481094448276e-199
10011.47026707243081e-1977.35133536215403e-198
10111.27979733938474e-1966.39898669692372e-197
10212.26493655111794e-1971.13246827555897e-197
10318.53578631477438e-1974.26789315738719e-197
10417.15905085321681e-1973.57952542660841e-197
10514.17777861375277e-1962.08888930687639e-196
10615.9384635728842e-1962.9692317864421e-196
10711.40975593034611e-1967.04877965173057e-197
10818.48537848853372e-1984.24268924426686e-198
10911.8675747525243e-1979.3378737626215e-198
11017.6531001465505e-1973.82655007327525e-197
11118.89445567307167e-1974.44722783653583e-197
11212.89208145250939e-1971.44604072625470e-197
11311.08578432015326e-1995.4289216007663e-200
11415.26990203707759e-1992.63495101853880e-199
11511.54451885505309e-1987.72259427526545e-199
11613.20614508882994e-1981.60307254441497e-198
11711.42660034654516e-1977.13300173272579e-198
11815.06990682949379e-1972.53495341474690e-197
11914.25458814306041e-1982.12729407153021e-198
12013.62987762187384e-1971.81493881093692e-197
12119.976852013312e-1974.988426006656e-197
12219.43263951720591e-1964.71631975860296e-196
12313.55134161372767e-1951.77567080686383e-195
12416.58501514630926e-1953.29250757315463e-195
12516.50245974529164e-1943.25122987264582e-194
12613.58392362142127e-1941.79196181071063e-194
12713.70806538827007e-1931.85403269413503e-193
12813.81015525100698e-1921.90507762550349e-192
12913.59994921617231e-1911.79997460808615e-191
13013.66313301757659e-1901.83156650878830e-190
13113.70214428100902e-1891.85107214050451e-189
13211.32966694815004e-1896.64833474075022e-190
13311.34476547358893e-1886.72382736794465e-189
13411.35395898902157e-1876.76979494510786e-188
13511.35442157300033e-1866.77210786500165e-187
13611.26422755259293e-1856.32113776296466e-186
13711.24882191654446e-1846.24410958272228e-185
13811.22908681988255e-1836.14543409941277e-184
13911.20312445093327e-1826.01562225466634e-183
14011.17136133765855e-1815.85680668829273e-182
14111.08462049021750e-1805.42310245108751e-181
14211.04474418850228e-1795.22372094251138e-180
14316.805478444344e-1793.402739222172e-179
14416.48910407129793e-1783.24455203564897e-178
14515.40475545020676e-1772.70237772510338e-177
14614.19196954598255e-1762.09598477299127e-176
14713.93875667972086e-1751.96937833986043e-175
14813.68420094769592e-1741.84210047384796e-174
14913.4253824297296e-1731.7126912148648e-173
15013.17086487691644e-1721.58543243845822e-172
15112.80237843586985e-1711.40118921793493e-171
15211.83895342020723e-1709.19476710103614e-171
15311.67608810549513e-1698.38044052747567e-170
15411.50893175701072e-1687.54465878505362e-169
15511.36255515087576e-1676.81277575437882e-168
15611.22291656986638e-1666.11458284933188e-167
15711.0919461337667e-1655.4597306688335e-166
15819.70564784747863e-1654.85282392373932e-165
15917.15710414942629e-1643.57855207471314e-164
16016.29581148953424e-1633.14790574476712e-163
16115.5099789259996e-1622.7549894629998e-162
16214.79774488040169e-1612.39887244020085e-161
16314.15641027765883e-1602.07820513882941e-160
16413.29873124339131e-1591.64936562169566e-159
16512.83048450888632e-1581.41524225444316e-158
16612.41577449010899e-1571.20788724505450e-157
16712.05147083472390e-1561.02573541736195e-156
16813.19761958519746e-1581.59880979259873e-158
16912.75068868644368e-1571.37534434322184e-157
17012.35442383177266e-1561.17721191588633e-156
17112.00521286770107e-1551.00260643385054e-155
17211.70796805799595e-1548.53984028997974e-155
17311.44029933043072e-1537.2014966521536e-154
17411.20386937176107e-1526.01934685880535e-153
17511.00517879479987e-1515.02589397399933e-152
17618.35232143936744e-1514.17616071968372e-151
17716.90524301616076e-1503.45262150808038e-150
17815.52265949235672e-1492.76132974617836e-149
17914.52179844345638e-1482.26089922172819e-148
18013.68417215047653e-1471.84208607523827e-147
18111.9692562537163e-1469.8462812685815e-147
18211.55445939980696e-1457.77229699903482e-146
18317.39886001034615e-1453.69943000517308e-145
18413.16339722505527e-1441.58169861252763e-144
18512.46881841026097e-1431.23440920513048e-143
18611.85812752355570e-1429.29063761777848e-143
18711.06114657499695e-1415.30573287498473e-142
18818.38435278970664e-1414.19217639485332e-141
18914.849314125984e-1402.424657062992e-140
19013.79923229016808e-1391.89961614508404e-139
19112.64295809611855e-1381.32147904805927e-138
19212.05116087895546e-1371.02558043947773e-137
19311.55277205659068e-1367.7638602829534e-137
19411.19350134434188e-1355.96750672170939e-136
19519.13310457855377e-1354.56655228927689e-135
19616.82827879973957e-1343.41413939986978e-134
19714.66167498612605e-1332.33083749306303e-133
19813.45844496776881e-1321.72922248388441e-132
19912.55723618731007e-1311.27861809365503e-131
20018.33268571773197e-1314.16634285886598e-131
20116.1351469212388e-1303.0675734606194e-130
20214.5010967776851e-1292.25054838884255e-129
20313.29025415777247e-1281.64512707888623e-128
20412.21159266857078e-1271.10579633428539e-127
20516.13575850540707e-1273.06787925270354e-127
20614.44629170065137e-1262.22314585032568e-126
20713.07386087145307e-1251.53693043572653e-125
20812.21298789364214e-1241.10649394682107e-124
20911.85155854867826e-1249.25779274339132e-125
21011.33685484882348e-1236.68427424411738e-124
21119.67499540897386e-1234.83749770448693e-123
21216.9686081301489e-1223.48430406507445e-122
21314.52372402654699e-1212.26186201327349e-121
21413.18990256392325e-1201.59495128196163e-120
21512.27037149971955e-1191.13518574985978e-119
21611.60521914088664e-1188.02609570443321e-119
21711.12831977285345e-1175.64159886426724e-118
21817.58899486544364e-1173.79449743272182e-117
21915.28965301909934e-1162.64482650954967e-116
22011.89971327182432e-1159.4985663591216e-116
22111.21558203552742e-1146.07791017763712e-115
22218.37983312478827e-1144.18991656239414e-114
22315.74721888386754e-1132.87360944193377e-113
22413.92423722311378e-1121.96211861155689e-112
22512.66541216429557e-1111.33270608214779e-111
22611.77431729403270e-1108.87158647016348e-111
22711.19424227519114e-1095.97121137595572e-110
22817.99966283747656e-1093.99983141873828e-109
22914.93072830694004e-1082.46536415347002e-108
23013.27423817028928e-1071.63711908514464e-107
23112.13414364888881e-1061.06707182444441e-106
23211.40414271001635e-1057.02071355008174e-106
23319.1941088124647e-1054.59705440623235e-105
23415.7419594237587e-1042.87097971187935e-104
23513.72391038182637e-1031.86195519091318e-103
23612.40448221491318e-1021.20224110745659e-102
23711.54443011882989e-1017.72215059414947e-102
23819.77509818225767e-1014.88754909112883e-101
23916.21817987986435e-1003.10908993993217e-100
24013.93641321774186e-991.96820660887093e-99
24112.4798803214675e-981.23994016073375e-98
24211.52167061719146e-977.6083530859573e-98
24319.49358032720646e-974.74679016360323e-97
24415.82300108132824e-962.91150054066412e-96
24513.59029242873426e-951.79514621436713e-95
24612.20397277640215e-941.10198638820108e-94
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36015.51461469333704e-212.75730734666852e-21
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36711.60391821114003e-178.01959105570014e-18
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3720.9999999999999983.50169380758913e-151.75084690379456e-15
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3770.9999999999997375.26376846402418e-132.63188423201209e-13
3780.9999999999992961.40863935595136e-127.0431967797568e-13
3790.9999999999981083.78499966539734e-121.89249983269867e-12
3800.9999999999949761.00488793155531e-115.02443965777653e-12
3810.9999999999868232.63543987456599e-111.31771993728300e-11
3820.9999999999654976.90057078287371e-113.45028539143685e-11
3830.9999999999454521.09095245481645e-105.45476227408226e-11
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3870.9999999982355443.52891245574466e-091.76445622787233e-09
3880.999999996047977.90405959140408e-093.95202979570204e-09
3890.9999999904957041.90085916786411e-089.50429583932057e-09
3900.999999977539674.49206603206462e-082.24603301603231e-08
3910.9999999483337361.03332527936927e-075.16662639684636e-08
3920.999999880443422.39113160308261e-071.19556580154131e-07
3930.9999997217727545.56454492998326e-072.78227246499163e-07
3940.9999994481187011.10376259744676e-065.51881298723379e-07
3950.9999989889295272.02214094585824e-061.01107047292912e-06
3960.9999977695600364.46087992878343e-062.23043996439172e-06
3970.9999959507713888.09845722335407e-064.04922861167704e-06
3980.9999915883374811.68233250379186e-058.41166251895932e-06
3990.9999819929860863.60140278279749e-051.80070139139875e-05
4000.9999622261447877.55477104252767e-053.77738552126383e-05
4010.9999221609365550.0001556781268898687.78390634449341e-05
4020.9998525437029960.0002949125940074610.000147456297003731
4030.9997201319686340.0005597360627324530.000279868031366226
4040.9994491934083840.001101613183232300.000550806591616149
4050.998947619832030.002104760335940260.00105238016797013
4060.9980163293596060.003967341280788260.00198367064039413
4070.9964359616400430.007128076719914360.00356403835995718
4080.9942112143712020.01157757125759600.00578878562879799
4090.9902445419662060.01951091606758880.0097554580337944
4100.9830383310660230.03392333786795370.0169616689339768
4110.9715885698201560.05682286035968880.0284114301798444
4120.9566296104784560.08674077904308810.0433703895215441
4130.9306207648120050.1387584703759900.0693792351879951
4140.8933875106405560.2132249787188880.106612489359444
4150.8425037945085140.3149924109829720.157496205491486
4160.7738484282860080.4523031434279840.226151571713992
4170.91081513913510.1783697217298020.0891848608649008
4180.8508712743517180.2982574512965630.149128725648282
4190.7709301133691970.4581397732616070.229069886630803
4200.6587238687716440.6825522624567110.341276131228356
4210.5139630533789180.9720738932421640.486036946621082
4220.3521062745046280.7042125490092570.647893725495372


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3990.963768115942029NOK
5% type I error level4020.971014492753623NOK
10% type I error level4040.97584541062802NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/102h421291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/102h421291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/1wg7r1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/1wg7r1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/2wg7r1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/2wg7r1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/367ob1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/367ob1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/467ob1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/467ob1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/567ob1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/567ob1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/6hh5e1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/6hh5e1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/7sq4h1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/7sq4h1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/8sq4h1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/8sq4h1291381635.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/9sq4h1291381635.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/03/t1291381686k4kbm50lq76dczt/9sq4h1291381635.ps (open in new window)


 
Parameters (Session):
par1 = 6 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 6 ; 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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