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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, 18 Nov 2008 03:10:52 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/18/t1227003087kovvp9jjfd400l6.htm/, Retrieved Tue, 18 Nov 2008 10:11:39 +0000
 
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/2008/Nov/18/t1227003087kovvp9jjfd400l6.htm/},
    year = {2008},
}
@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 = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1687 0 1508 0 1507 0 1385 0 1632 0 1511 0 1559 0 1630 0 1579 0 1653 0 2152 0 2148 0 1752 0 1765 0 1717 0 1558 0 1575 0 1520 0 1805 0 1800 0 1719 0 2008 0 2242 0 2478 0 2030 0 1655 0 1693 0 1623 0 1805 0 1746 0 1795 0 1926 0 1619 0 1992 0 2233 0 2192 0 2080 0 1768 0 1835 0 1569 0 1976 0 1853 0 1965 0 1689 0 1778 0 1976 0 2397 0 2654 0 2097 0 1963 0 1677 0 1941 0 2003 0 1813 0 2012 0 1912 0 2084 0 2080 0 2118 0 2150 0 1608 0 1503 0 1548 0 1382 0 1731 0 1798 0 1779 0 1887 0 2004 0 2077 0 2092 0 2051 0 1577 0 1356 0 1652 0 1382 0 1519 0 1421 0 1442 0 1543 0 1656 0 1561 0 1905 0 2199 0 1473 0 1655 0 1407 0 1395 0 1530 0 1309 0 1526 0 1327 0 1627 0 1748 0 1958 0 2274 0 1648 0 1401 0 1411 0 1403 0 1394 0 1520 0 1528 0 1643 0 1515 0 1685 0 2000 0 2215 0 1956 0 1462 0 1563 0 1459 0 1446 0 1622 0 1657 0 1638 0 1643 0 1683 0 2050 0 2262 0 1813 0 1445 0 1762 0 1461 0 1556 0 1431 0 1427 0 1554 0 1645 0 1653 0 2016 0 2207 0 1665 0 1361 0 1506 0 1360 0 1453 0 1522 0 1460 0 1552 0 1548 0 1827 0 1737 0 1941 0 1474 0 1458 0 1542 0 1404 0 1522 0 1385 0 1641 0 1510 0 1681 0 1938 0 1868 0 1726 0 1456 0 1445 0 1456 0 1365 0 1487 0 1558 0 1488 0 1684 0 1594 0 1850 0 1998 0 2079 0 1494 0 1057 1 1218 1 1168 1 1236 1 1076 1 1174 1 1139 1 1427 1 1487 1 1483 1 1513 1 1357 1 1165 1 1282 1 1110 1 1297 1 1185 1 1222 1 1284 1 1444 1 1575 1 1737 1 1763 1
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time16 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
y[t] = + 2165.22639318886 -395.811145510835d[t] -442.550696594425M1[t] -617.812500000002M2[t] -567.25M3[t] -680.4375M4[t] -543.125000000001M5[t] -598.874999999998M6[t] -523.250000000001M7[t] -508.375M8[t] -455.5625M9[t] -316.187500000000M10[t] -116.625000000000M11[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)2165.2263931888643.63188149.624900
d-395.81114551083538.605577-10.252700
M1-442.55069659442561.373686-7.210800
M2-617.81250000000261.326238-10.074200
M3-567.2561.326238-9.249700
M4-680.437561.326238-11.095400
M5-543.12500000000161.326238-8.856300
M6-598.87499999999861.326238-9.765400
M7-523.25000000000161.326238-8.532200
M8-508.37561.326238-8.289700
M9-455.562561.326238-7.428500
M10-316.18750000000061.326238-5.15581e-060
M11-116.62500000000061.326238-1.90170.0588150.029407


Multiple Linear Regression - Regression Statistics
Multiple R0.814751285561214
R-squared0.663819657323651
Adjusted R-squared0.641282427647024
F-TEST (value)29.4543591580865
F-TEST (DF numerator)12
F-TEST (DF denominator)179
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation173.456794605829
Sum Squared Residuals5385619.46749226


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
116871722.67569659441-35.6756965944053
215081547.41389318886-39.413893188857
315071597.97639318886-90.9763931888592
413851484.78889318885-99.7888931888466
516321622.101393188869.8986068111442
615111566.35139318886-55.3513931888552
715591641.97639318885-82.9763931888532
816301656.85139318886-26.8513931888614
915791709.66389318885-130.663893188851
1016531849.03889318885-196.038893188855
1121522048.60139318886103.398606811145
1221482165.22639318885-17.226393188854
1317521722.6756965944329.3243034055713
1417651547.41389318885217.586106811146
1517171597.97639318885119.023606811146
1615581484.7888931888573.211106811145
1715751622.10139318885-47.1013931888544
1815201566.35139318885-46.3513931888545
1918051641.97639318885163.023606811145
2018001656.85139318885143.148606811146
2117191709.663893188859.33610681114532
2220081849.03889318885158.961106811145
2322422048.60139318885193.398606811146
2424782165.22639318885312.773606811145
2520301722.67569659443307.324303405571
2616551547.41389318885107.586106811146
2716931597.9763931888595.0236068111458
2816231484.78889318885138.211106811145
2918051622.10139318885182.898606811146
3017461566.35139318885179.648606811145
3117951641.97639318885153.023606811145
3219261656.85139318885269.148606811146
3316191709.66389318885-90.6638931888547
3419921849.03889318885142.961106811145
3522332048.60139318885184.398606811146
3621922165.2263931888526.7736068111454
3720801722.67569659443357.324303405571
3817681547.41389318885220.586106811146
3918351597.97639318885237.023606811146
4015691484.7888931888584.211106811145
4119761622.10139318885353.898606811146
4218531566.35139318885286.648606811145
4319651641.97639318885323.023606811145
4416891656.8513931888532.148606811146
4517781709.6638931888568.3361068111453
4619761849.03889318885126.961106811145
4723972048.60139318885348.398606811146
4826542165.22639318885488.773606811145
4920971722.67569659443374.324303405571
5019631547.41389318885415.586106811145
5116771597.9763931888579.0236068111458
5219411484.78889318886456.211106811145
5320031622.10139318885380.898606811146
5418131566.35139318885246.648606811145
5520121641.97639318885370.023606811145
5619121656.85139318885255.148606811146
5720841709.66389318885374.336106811145
5820801849.03889318885230.961106811145
5921182048.6013931888569.3986068111455
6021502165.22639318885-15.2263931888546
6116081722.67569659443-114.675696594429
6215031547.41389318885-44.4138931888543
6315481597.97639318885-49.9763931888542
6413821484.78889318885-102.788893188855
6517311622.10139318885108.898606811146
6617981566.35139318885231.648606811145
6717791641.97639318885137.023606811145
6818871656.85139318885230.148606811146
6920041709.66389318885294.336106811145
7020771849.03889318885227.961106811145
7120922048.6013931888543.3986068111455
7220512165.22639318885-114.226393188855
7315771722.67569659443-145.675696594429
7413561547.41389318885-191.413893188854
7516521597.9763931888554.0236068111458
7613821484.78889318885-102.788893188855
7715191622.10139318885-103.101393188854
7814211566.35139318885-145.351393188855
7914421641.97639318885-199.976393188855
8015431656.85139318885-113.851393188854
8116561709.66389318885-53.6638931888547
8215611849.03889318885-288.038893188855
8319052048.60139318885-143.601393188855
8421992165.2263931888533.7736068111454
8514731722.67569659443-249.675696594429
8616551547.41389318885107.586106811146
8714071597.97639318885-190.976393188854
8813951484.78889318885-89.788893188855
8915301622.10139318885-92.1013931888544
9013091566.35139318885-257.351393188855
9115261641.97639318885-115.976393188855
9213271656.85139318885-329.851393188854
9316271709.66389318885-82.6638931888547
9417481849.03889318885-101.038893188855
9519582048.60139318885-90.6013931888545
9622742165.22639318885108.773606811145
9716481722.67569659443-74.6756965944287
9814011547.41389318885-146.413893188854
9914111597.97639318885-186.976393188854
10014031484.78889318885-81.788893188855
10113941622.10139318885-228.101393188854
10215201566.35139318885-46.3513931888545
10315281641.97639318885-113.976393188855
10416431656.85139318885-13.851393188854
10515151709.66389318885-194.663893188855
10616851849.03889318885-164.038893188855
10720002048.60139318885-48.6013931888545
10822152165.2263931888549.7736068111454
10919561722.67569659443233.324303405571
11014621547.41389318885-85.4138931888543
11115631597.97639318885-34.9763931888542
11214591484.78889318885-25.7888931888550
11314461622.10139318885-176.101393188854
11416221566.3513931888555.6486068111455
11516571641.9763931888515.0236068111454
11616381656.85139318885-18.851393188854
11716431709.66389318885-66.6638931888547
11816831849.03889318885-166.038893188855
11920502048.601393188851.39860681114553
12022622165.2263931888596.7736068111454
12118131722.6756965944390.3243034055712
12214451547.41389318885-102.413893188854
12317621597.97639318885164.023606811146
12414611484.78889318885-23.7888931888550
12515561622.10139318885-66.1013931888544
12614311566.35139318885-135.351393188855
12714271641.97639318885-214.976393188855
12815541656.85139318885-102.851393188854
12916451709.66389318885-64.6638931888547
13016531849.03889318885-196.038893188855
13120162048.60139318885-32.6013931888545
13222072165.2263931888541.7736068111454
13316651722.67569659443-57.6756965944287
13413611547.41389318885-186.413893188854
13515061597.97639318885-91.9763931888542
13613601484.78889318885-124.788893188855
13714531622.10139318885-169.101393188854
13815221566.35139318885-44.3513931888545
13914601641.97639318885-181.976393188855
14015521656.85139318885-104.851393188854
14115481709.66389318885-161.663893188855
14218271849.03889318885-22.0388931888545
14317372048.60139318885-311.601393188855
14419412165.22639318885-224.226393188855
14514741722.67569659443-248.675696594429
14614581547.41389318885-89.4138931888543
14715421597.97639318885-55.9763931888542
14814041484.78889318885-80.788893188855
14915221622.10139318885-100.101393188854
15013851566.35139318885-181.351393188855
15116411641.97639318885-0.9763931888546
15215101656.85139318885-146.851393188854
15316811709.66389318885-28.6638931888547
15419381849.0388931888588.9611068111455
15518682048.60139318885-180.601393188855
15617262165.22639318885-439.226393188855
15714561722.67569659443-266.675696594429
15814451547.41389318885-102.413893188854
15914561597.97639318885-141.976393188854
16013651484.78889318885-119.788893188855
16114871622.10139318885-135.101393188854
16215581566.35139318885-8.3513931888545
16314881641.97639318885-153.976393188855
16416841656.8513931888527.148606811146
16515941709.66389318885-115.663893188855
16618501849.038893188850.9611068111455
16719982048.60139318885-50.6013931888545
16820792165.22639318885-86.2263931888546
16914941722.67569659443-228.675696594429
17010571151.60274767802-94.6027476780183
17112181202.1652476780215.8347523219817
17211681088.9777476780279.022252321981
17312361226.290247678029.70975232198158
17410761170.54024767802-94.5402476780185
17511741246.16524767802-72.1652476780186
17611391261.04024767802-122.040247678018
17714271313.85274767802113.147252321981
17814871453.2277476780233.7722523219814
17914831652.79024767802-169.790247678018
18015131769.41524767802-256.415247678019
18113571326.8645510835930.1354489164072
18211651151.6027476780213.3972523219817
18312821202.1652476780279.8347523219817
18411101088.9777476780221.0222523219809
18512971226.2902476780270.7097523219816
18611851170.5402476780214.4597523219815
18712221246.16524767802-24.1652476780187
18812841261.0402476780222.9597523219819
18914441313.85274767802130.147252321981
19015751453.22774767802121.772252321981
19117371652.7902476780284.2097523219815
19217631769.41524767802-6.41524767801867


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.4774123925937360.9548247851874730.522587607406264
170.3177830613741790.6355661227483580.682216938625821
180.1918850330176080.3837700660352150.808114966982392
190.219496442452130.438992884904260.78050355754787
200.1828713287849740.3657426575699470.817128671215026
210.1388506413979020.2777012827958030.861149358602098
220.2470668210919270.4941336421838540.752933178908073
230.1865730770935170.3731461541870330.813426922906483
240.2681743220394330.5363486440788670.731825677960567
250.3753173479730120.7506346959460240.624682652026988
260.2984712257880200.5969424515760410.70152877421198
270.2399252673916360.4798505347832720.760074732608364
280.2130450390493630.4260900780987270.786954960950637
290.2137688746654890.4275377493309780.786231125334511
300.2297752313907650.4595504627815310.770224768609235
310.1947715355403670.3895430710807330.805228464459633
320.2077651117228950.4155302234457910.792234888277105
330.1621565160742570.3243130321485150.837843483925743
340.1481164301044300.2962328602088590.85188356989557
350.1178312959736230.2356625919472460.882168704026377
360.09738211722199170.1947642344439830.902617882778008
370.1414009615478070.2828019230956140.858599038452193
380.1297822915516910.2595645831033810.87021770844831
390.1397728276513450.2795456553026900.860227172348655
400.1105854094843160.2211708189686310.889414590515685
410.1841247186689660.3682494373379320.815875281331034
420.2348993285677120.4697986571354230.765100671432288
430.2916501478873060.5833002957746130.708349852112694
440.2552543762765750.5105087525531490.744745623723425
450.2319339781760510.4638679563521020.768066021823949
460.2039096313316780.4078192626633560.796090368668322
470.2431477080700400.4862954161400810.756852291929960
480.473887762165810.947775524331620.52611223783419
490.5691985323093710.8616029353812580.430801467690629
500.7264188828149550.547162234370090.273581117185045
510.6883967611186170.6232064777627660.311603238881383
520.8882423937637220.2235152124725560.111757606236278
530.9448774632618280.1102450734763440.0551225367381722
540.9546545717721840.09069085645563120.0453454282278156
550.981115207137360.03776958572528140.0188847928626407
560.9865139644489280.02697207110214390.0134860355510720
570.9978479988944410.004304002211117370.00215200110555868
580.9985628936079760.002874212784048820.00143710639202441
590.9985002905584210.002999418883158080.00149970944157904
600.9985432203954620.002913559209076210.00145677960453811
610.9990717312162770.001856537567446680.000928268783723342
620.9991151039029790.001769792194042620.000884896097021311
630.9988719053312270.002256189337546440.00112809466877322
640.9989103460697690.002179307860462730.00108965393023137
650.9989306229093290.002138754181342430.00106937709067122
660.9993975059603050.001204988079390.000602494039695
670.9995047596873250.0009904806253494490.000495240312674724
680.9997607135953660.0004785728092682090.000239286404634104
690.9999484555580240.0001030888839515535.15444419757764e-05
700.9999799755985484.00488029040693e-052.00244014520346e-05
710.9999803059758693.93880482627085e-051.96940241313543e-05
720.9999839540974833.20918050348279e-051.60459025174140e-05
730.9999887792284692.24415430626064e-051.12207715313032e-05
740.999994095788111.18084237801413e-055.90421189007064e-06
750.9999921392217381.57215565242678e-057.8607782621339e-06
760.9999907574149911.84851700178040e-059.24258500890202e-06
770.9999917059601141.65880797721136e-058.29403988605678e-06
780.9999931962960761.36074078485785e-056.80370392428923e-06
790.9999967089921266.58201574797166e-063.29100787398583e-06
800.999996782748756.43450250216893e-063.21725125108447e-06
810.9999953790095749.24198085107973e-064.62099042553986e-06
820.9999989147619072.17047618646408e-061.08523809323204e-06
830.999999055368061.88926387964174e-069.4463193982087e-07
840.9999988296198942.34076021144639e-061.17038010572320e-06
850.9999995137226139.7255477329988e-074.8627738664994e-07
860.9999996539047166.92190568997731e-073.46095284498866e-07
870.999999722268035.5546393885066e-072.7773196942533e-07
880.9999995861537358.27692529861566e-074.13846264930783e-07
890.9999994841506181.03169876404525e-065.15849382022623e-07
900.9999997829307224.34138555732368e-072.17069277866184e-07
910.9999997341194975.31761004889164e-072.65880502444582e-07
920.9999999593390588.13218832371426e-084.06609416185713e-08
930.9999999348798061.30240387583734e-076.51201937918671e-08
940.9999999010283021.97943395314047e-079.89716976570233e-08
950.9999998612210932.77557813291379e-071.38778906645690e-07
960.9999999140799731.71840054584607e-078.59200272923037e-08
970.999999860121822.79756359989457e-071.39878179994729e-07
980.9999998250211583.49957683513652e-071.74978841756826e-07
990.9999998469509363.06098128076187e-071.53049064038094e-07
1000.9999997471545825.05690835816319e-072.52845417908160e-07
1010.999999812583293.7483341941049e-071.87416709705245e-07
1020.9999996851519436.29696114916211e-073.14848057458106e-07
1030.999999548876739.02246538632805e-074.51123269316402e-07
1040.999999292225961.41554807902718e-067.0777403951359e-07
1050.9999993645267471.27094650632298e-066.3547325316149e-07
1060.9999992972496571.40550068602918e-067.02750343014592e-07
1070.999998958728012.08254397902858e-061.04127198951429e-06
1080.9999991521463351.69570732985605e-068.47853664928023e-07
1090.9999999198513551.60297289800619e-078.01486449003093e-08
1100.9999998710871182.57825763589014e-071.28912881794507e-07
1110.9999997606059254.78788149181416e-072.39394074590708e-07
1120.9999995839660988.32067803672855e-074.16033901836428e-07
1130.9999994948233761.01035324743262e-065.0517662371631e-07
1140.9999994802675611.03946487774175e-065.19732438870876e-07
1150.9999994524008361.09519832770823e-065.47599163854117e-07
1160.9999991628744191.67425116273504e-068.37125581367521e-07
1170.9999985308737672.93825246625430e-061.46912623312715e-06
1180.9999984927537093.01449258219802e-061.50724629109901e-06
1190.9999983229212913.35415741711385e-061.67707870855692e-06
1200.9999996178671167.64265768332042e-073.82132884166021e-07
1210.9999998933733432.13253314532940e-071.06626657266470e-07
1220.999999818611413.62777181927527e-071.81388590963763e-07
1230.9999999493565521.01286896749012e-075.0643448374506e-08
1240.9999999120661831.75867634100664e-078.7933817050332e-08
1250.9999998422740743.15451851057457e-071.57725925528729e-07
1260.9999997331275695.33744862044504e-072.66872431022252e-07
1270.9999996892012636.21597472934647e-073.10798736467324e-07
1280.99999943877581.12244840081945e-065.61224200409725e-07
1290.9999989356780242.12864395257080e-061.06432197628540e-06
1300.999999427726231.14454753850936e-065.72273769254682e-07
1310.9999993909970021.21800599684692e-066.09002998423458e-07
1320.9999999357444851.28511029699837e-076.42555148499187e-08
1330.9999999456898831.08620234260407e-075.43101171302033e-08
1340.9999999155595621.68880875030271e-078.44404375151355e-08
1350.999999827304643.45390721431426e-071.72695360715713e-07
1360.999999681112796.37774418162373e-073.18887209081187e-07
1370.9999995163213779.67357246883755e-074.83678623441878e-07
1380.9999992181697841.56366043213988e-067.81830216069941e-07
1390.9999987851041472.42979170547042e-061.21489585273521e-06
1400.999997645868014.70826397889355e-062.35413198944678e-06
1410.9999975123879174.97522416654345e-062.48761208327172e-06
1420.9999950610824989.87783500307573e-064.93891750153786e-06
1430.9999977378293514.52434129751273e-062.26217064875636e-06
1440.9999964692147257.06157054924965e-063.53078527462482e-06
1450.9999948623953031.02752093948037e-055.13760469740187e-06
1460.9999902717740881.94564518248318e-059.7282259124159e-06
1470.999980945438123.81091237617349e-051.90545618808674e-05
1480.99996251312627.49737476012236e-053.74868738006118e-05
1490.9999284328706930.0001431342586141197.15671293070596e-05
1500.9998940027453560.0002119945092869740.000105997254643487
1510.9998940207980520.0002119584038961480.000105979201948074
1520.999817241528260.0003655169434797710.000182758471739886
1530.9996499702514620.000700059497075910.000350029748537955
1540.9995311834273330.0009376331453337170.000468816572666858
1550.9992521017508740.001495796498252030.000747898249126013
1560.9998484865948990.0003030268102022800.000151513405101140
1570.9998217739455420.0003564521089157640.000178226054457882
1580.9996466639037490.0007066721925024810.000353336096251241
1590.999472246590460.001055506819079270.000527753409539633
1600.9991619418563270.001676116287346330.000838058143673166
1610.998794430703550.002411138592899180.00120556929644959
1620.9981324186713650.00373516265726970.00186758132863485
1630.9965413176793270.006917364641346630.00345868232067332
1640.996430642396850.007138715206302260.00356935760315113
1650.996302913049990.007394173900021560.00369708695001078
1660.9926248205431520.01475035891369490.00737517945684745
1670.9869490046325480.02610199073490310.0130509953674515
1680.9909147209212230.01817055815755360.0090852790787768
1690.9822710463111070.03545790737778660.0177289536888933
1700.9718771603734020.05624567925319610.0281228396265981
1710.9497551587281750.1004896825436500.0502448412718248
1720.9122010401935920.1755979196128150.0877989598064076
1730.8524618585293440.2950762829413130.147538141470656
1740.7823573198125330.4352853603749330.217642680187467
1750.6569428186407690.6861143627184620.343057181359231
1760.5500728500896410.8998542998207170.449927149910359


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1090.677018633540373NOK
5% type I error level1150.714285714285714NOK
10% type I error level1170.726708074534162NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/18/t1227003087kovvp9jjfd400l6/105efd1227003034.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/18/t1227003087kovvp9jjfd400l6/8j7r51227003034.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/18/t1227003087kovvp9jjfd400l6/9b6zt1227003034.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/18/t1227003087kovvp9jjfd400l6/9b6zt1227003034.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




Copyright

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa


Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.


Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

  • personalize online software applications according to your needs
  • enforce strict security rules with respect to the data that you upload (e.g. statistical data)
  • manage user sessions of online applications
  • alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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