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csl1

*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, 25 Nov 2008 12:19:16 -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/25/t1227641686t20w8ld5ejs63v0.htm/, Retrieved Tue, 25 Nov 2008 19:34:46 +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/25/t1227641686t20w8ld5ejs63v0.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 time10 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
X[t] = + 2165.22639318886 -395.811145510836D[t] -442.550696594427M1[t] -617.8125M2[t] -567.25M3[t] -680.4375M4[t] -543.125M5[t] -598.875M6[t] -523.25M7[t] -508.375M8[t] -455.5625M9[t] -316.1875M10[t] -116.625M11[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-395.81114551083638.605577-10.252700
M1-442.55069659442761.373686-7.210800
M2-617.812561.326238-10.074200
M3-567.2561.326238-9.249700
M4-680.437561.326238-11.095400
M5-543.12561.326238-8.856300
M6-598.87561.326238-9.765400
M7-523.2561.326238-8.532200
M8-508.37561.326238-8.289700
M9-455.562561.326238-7.428500
M10-316.187561.326238-5.15581e-060
M11-116.62561.326238-1.90170.0588150.029407


Multiple Linear Regression - Regression Statistics
Multiple R0.814751285561214
R-squared0.66381965732365
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
116871722.67569659442-35.6756965944224
215081547.41389318885-39.4138931888546
315071597.97639318885-90.9763931888542
413851484.78889318885-99.788893188855
516321622.101393188859.89860681114526
615111566.35139318885-55.3513931888549
715591641.97639318885-82.9763931888545
816301656.85139318885-26.8513931888544
915791709.66389318885-130.663893188855
1016531849.03889318885-196.038893188855
1121522048.60139318885103.398606811145
1221482165.22639318885-17.2263931888546
1317521722.6756965944329.3243034055724
1417651547.41389318885217.586106811145
1517171597.97639318885119.023606811145
1615581484.7888931888573.2111068111455
1715751622.10139318885-47.1013931888545
1815201566.35139318885-46.3513931888545
1918051641.97639318885163.023606811146
2018001656.85139318885143.148606811145
2117191709.663893188859.33610681114551
2220081849.03889318885158.961106811146
2322422048.60139318885193.398606811146
2424782165.22639318885312.773606811146
2520301722.67569659443307.324303405572
2616551547.41389318885107.586106811146
2716931597.9763931888595.0236068111455
2816231484.78889318885138.211106811146
2918051622.10139318885182.898606811145
3017461566.35139318885179.648606811145
3117951641.97639318885153.023606811146
3219261656.85139318885269.148606811145
3316191709.66389318885-90.6638931888545
3419921849.03889318885142.961106811146
3522332048.60139318885184.398606811146
3621922165.2263931888526.7736068111456
3720801722.67569659443357.324303405572
3817681547.41389318885220.586106811145
3918351597.97639318885237.023606811145
4015691484.7888931888584.2111068111455
4119761622.10139318885353.898606811146
4218531566.35139318885286.648606811146
4319651641.97639318885323.023606811145
4416891656.8513931888532.1486068111455
4517781709.6638931888568.3361068111455
4619761849.03889318885126.961106811146
4723972048.60139318885348.398606811146
4826542165.22639318885488.773606811146
4920971722.67569659443374.324303405572
5019631547.41389318885415.586106811145
5116771597.9763931888579.0236068111455
5219411484.78889318885456.211106811146
5320031622.10139318885380.898606811146
5418131566.35139318885246.648606811146
5520121641.97639318885370.023606811145
5619121656.85139318885255.148606811145
5720841709.66389318885374.336106811146
5820801849.03889318885230.961106811146
5921182048.6013931888569.3986068111455
6021502165.22639318885-15.2263931888545
6116081722.67569659443-114.675696594428
6215031547.41389318885-44.4138931888545
6315481597.97639318885-49.9763931888545
6413821484.78889318885-102.788893188854
6517311622.10139318885108.898606811145
6617981566.35139318885231.648606811145
6717791641.97639318885137.023606811145
6818871656.85139318885230.148606811145
6920041709.66389318885294.336106811146
7020771849.03889318885227.961106811146
7120922048.6013931888543.3986068111455
7220512165.22639318885-114.226393188854
7315771722.67569659443-145.675696594428
7413561547.41389318885-191.413893188855
7516521597.9763931888554.0236068111455
7613821484.78889318885-102.788893188854
7715191622.10139318885-103.101393188855
7814211566.35139318885-145.351393188854
7914421641.97639318885-199.976393188854
8015431656.85139318885-113.851393188855
8116561709.66389318885-53.6638931888545
8215611849.03889318885-288.038893188855
8319052048.60139318885-143.601393188855
8421992165.2263931888533.7736068111456
8514731722.67569659443-249.675696594428
8616551547.41389318885107.586106811146
8714071597.97639318885-190.976393188854
8813951484.78889318885-89.7888931888545
8915301622.10139318885-92.1013931888545
9013091566.35139318885-257.351393188854
9115261641.97639318885-115.976393188855
9213271656.85139318885-329.851393188854
9316271709.66389318885-82.6638931888545
9417481849.03889318885-101.038893188854
9519582048.60139318885-90.6013931888546
9622742165.22639318885108.773606811146
9716481722.67569659443-74.6756965944276
9814011547.41389318885-146.413893188855
9914111597.97639318885-186.976393188854
10014031484.78889318885-81.7888931888545
10113941622.10139318885-228.101393188854
10215201566.35139318885-46.3513931888545
10315281641.97639318885-113.976393188855
10416431656.85139318885-13.8513931888545
10515151709.66389318885-194.663893188855
10616851849.03889318885-164.038893188855
10720002048.60139318885-48.6013931888545
10822152165.2263931888549.7736068111455
10919561722.67569659443233.324303405572
11014621547.41389318885-85.4138931888544
11115631597.97639318885-34.9763931888545
11214591484.78889318885-25.7888931888545
11314461622.10139318885-176.101393188854
11416221566.3513931888555.6486068111455
11516571641.9763931888515.0236068111455
11616381656.85139318885-18.8513931888545
11716431709.66389318885-66.6638931888545
11816831849.03889318885-166.038893188855
11920502048.601393188851.39860681114554
12022622165.2263931888596.7736068111456
12118131722.6756965944390.3243034055724
12214451547.41389318885-102.413893188854
12317621597.97639318885164.023606811145
12414611484.78889318885-23.7888931888545
12515561622.10139318885-66.1013931888545
12614311566.35139318885-135.351393188854
12714271641.97639318885-214.976393188854
12815541656.85139318885-102.851393188855
12916451709.66389318885-64.6638931888545
13016531849.03889318885-196.038893188855
13120162048.60139318885-32.6013931888545
13222072165.2263931888541.7736068111456
13316651722.67569659443-57.6756965944276
13413611547.41389318885-186.413893188855
13515061597.97639318885-91.9763931888545
13613601484.78889318885-124.788893188854
13714531622.10139318885-169.101393188854
13815221566.35139318885-44.3513931888545
13914601641.97639318885-181.976393188854
14015521656.85139318885-104.851393188855
14115481709.66389318885-161.663893188855
14218271849.03889318885-22.0388931888545
14317372048.60139318885-311.601393188855
14419412165.22639318885-224.226393188855
14514741722.67569659443-248.675696594428
14614581547.41389318885-89.4138931888544
14715421597.97639318885-55.9763931888545
14814041484.78889318885-80.7888931888545
14915221622.10139318885-100.101393188855
15013851566.35139318885-181.351393188854
15116411641.97639318885-0.976393188854502
15215101656.85139318885-146.851393188855
15316811709.66389318885-28.6638931888545
15419381849.0388931888588.9611068111455
15518682048.60139318885-180.601393188855
15617262165.22639318885-439.226393188855
15714561722.67569659443-266.675696594428
15814451547.41389318885-102.413893188854
15914561597.97639318885-141.976393188855
16013651484.78889318885-119.788893188854
16114871622.10139318885-135.101393188855
16215581566.35139318885-8.35139318885452
16314881641.97639318885-153.976393188855
16416841656.8513931888527.1486068111455
16515941709.66389318885-115.663893188855
16618501849.038893188850.961106811145528
16719982048.60139318885-50.6013931888545
16820792165.22639318885-86.2263931888545
16914941722.67569659443-228.675696594428
17010571151.60274767802-94.6027476780185
17112181202.1652476780215.8347523219813
17211681088.9777476780279.0222523219813
17312361226.290247678029.70975232198147
17410761170.54024767802-94.5402476780185
17511741246.16524767802-72.1652476780185
17611391261.04024767802-122.040247678018
17714271313.85274767802113.147252321981
17814871453.2277476780233.7722523219815
17914831652.79024767802-169.790247678019
18015131769.41524767802-256.415247678019
18113571326.8645510835930.1354489164084
18211651151.6027476780213.3972523219814
18312821202.1652476780279.8347523219813
18411101088.9777476780221.0222523219814
18512971226.2902476780270.7097523219815
18611851170.5402476780214.4597523219814
18712221246.16524767802-24.1652476780185
18812841261.0402476780222.9597523219815
18914441313.85274767802130.147252321981
19015751453.22774767802121.772252321981
19117371652.7902476780284.2097523219814
19217631769.41524767802-6.41524767801863


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.4774123925937370.9548247851874730.522587607406263
170.3177830613741790.6355661227483570.682216938625821
180.1918850330176070.3837700660352150.808114966982393
190.2194964424521290.4389928849042580.780503557547871
200.1828713287849740.3657426575699480.817128671215026
210.1388506413979020.2777012827958040.861149358602098
220.2470668210919270.4941336421838550.752933178908073
230.1865730770935160.3731461541870330.813426922906484
240.2681743220394350.536348644078870.731825677960565
250.3753173479730140.7506346959460290.624682652026986
260.2984712257880210.5969424515760420.701528774211979
270.2399252673916370.4798505347832740.760074732608363
280.2130450390493640.4260900780987290.786954960950636
290.2137688746654890.4275377493309780.786231125334511
300.2297752313907660.4595504627815330.770224768609234
310.1947715355403650.3895430710807310.805228464459635
320.2077651117228980.4155302234457960.792234888277102
330.1621565160742570.3243130321485130.837843483925743
340.1481164301044280.2962328602088570.851883569895572
350.1178312959736240.2356625919472480.882168704026376
360.0973821172219920.1947642344439840.902617882778008
370.1414009615478070.2828019230956150.858599038452193
380.1297822915516910.2595645831033820.87021770844831
390.1397728276513450.2795456553026900.860227172348655
400.1105854094843140.2211708189686280.889414590515686
410.1841247186689650.3682494373379310.815875281331035
420.2348993285677140.4697986571354280.765100671432286
430.2916501478873040.5833002957746070.708349852112696
440.2552543762765740.5105087525531480.744745623723426
450.2319339781760530.4638679563521060.768066021823947
460.2039096313316770.4078192626633540.796090368668323
470.2431477080700390.4862954161400780.756852291929961
480.4738877621658110.9477755243316210.526112237834189
490.5691985323093760.8616029353812490.430801467690624
500.726418882814950.54716223437010.27358111718505
510.6883967611186120.6232064777627760.311603238881388
520.8882423937637190.2235152124725620.111757606236281
530.944877463261830.1102450734763400.0551225367381702
540.9546545717721860.09069085645562880.0453454282278144
550.9811152071373580.03776958572528370.0188847928626418
560.9865139644489280.0269720711021440.013486035551072
570.9978479988944410.004304002211117360.00215200110555868
580.9985628936079760.002874212784048690.00143710639202435
590.998500290558420.002999418883158030.00149970944157901
600.9985432203954620.002913559209076350.00145677960453818
610.9990717312162770.001856537567446600.000928268783723299
620.9991151039029790.001769792194042590.000884896097021293
630.9988719053312270.002256189337546520.00112809466877326
640.9989103460697690.002179307860462710.00108965393023135
650.9989306229093290.00213875418134270.00106937709067135
660.9993975059603050.001204988079389960.000602494039694982
670.9995047596873250.0009904806253494790.000495240312674739
680.9997607135953660.0004785728092682330.000239286404634116
690.9999484555580240.0001030888839515505.15444419757752e-05
700.9999799755985484.00488029040694e-052.00244014520347e-05
710.9999803059758693.9388048262709e-051.96940241313545e-05
720.9999839540974833.20918050348268e-051.60459025174134e-05
730.9999887792284692.24415430626064e-051.12207715313032e-05
740.999994095788111.18084237801416e-055.9042118900708e-06
750.9999921392217381.57215565242674e-057.86077826213369e-06
760.9999907574149911.8485170017804e-059.242585008902e-06
770.9999917059601141.6588079772114e-058.294039886057e-06
780.9999931962960761.36074078485788e-056.8037039242894e-06
790.9999967089921266.58201574797168e-063.29100787398584e-06
800.9999967827487496.43450250216871e-063.21725125108435e-06
810.9999953790095749.24198085107995e-064.62099042553997e-06
820.9999989147619072.17047618646418e-061.08523809323209e-06
830.999999055368061.88926387964161e-069.44631939820804e-07
840.9999988296198942.34076021144642e-061.17038010572321e-06
850.9999995137226139.7255477329988e-074.8627738664994e-07
860.9999996539047156.92190568997736e-073.46095284498868e-07
870.999999722268035.5546393885066e-072.7773196942533e-07
880.9999995861537358.27692529861559e-074.13846264930779e-07
890.9999994841506181.03169876404527e-065.15849382022635e-07
900.9999997829307224.34138555732374e-072.17069277866187e-07
910.9999997341194985.31761004889151e-072.65880502444576e-07
920.9999999593390588.13218832371415e-084.06609416185708e-08
930.9999999348798061.30240387583724e-076.5120193791862e-08
940.9999999010283021.97943395314035e-079.89716976570177e-08
950.9999998612210932.77557813291402e-071.38778906645701e-07
960.9999999140799731.71840054584599e-078.59200272922997e-08
970.999999860121822.79756359989459e-071.39878179994729e-07
980.9999998250211583.49957683513671e-071.74978841756835e-07
990.9999998469509363.06098128076196e-071.53049064038098e-07
1000.9999997471545825.0569083581632e-072.5284541790816e-07
1010.999999812583293.7483341941048e-071.8741670970524e-07
1020.9999996851519436.29696114916214e-073.14848057458107e-07
1030.999999548876739.0224653863278e-074.5112326931639e-07
1040.999999292225961.41554807902720e-067.07774039513601e-07
1050.9999993645267471.27094650632294e-066.35473253161468e-07
1060.9999992972496571.40550068602919e-067.02750343014597e-07
1070.999998958728012.08254397902849e-061.04127198951424e-06
1080.9999991521463351.69570732985606e-068.47853664928028e-07
1090.9999999198513551.60297289800614e-078.01486449003072e-08
1100.9999998710871182.57825763589013e-071.28912881794506e-07
1110.9999997606059254.78788149181415e-072.39394074590708e-07
1120.9999995839660988.32067803672843e-074.16033901836421e-07
1130.9999994948233761.01035324743263e-065.05176623716316e-07
1140.9999994802675611.03946487774176e-065.1973243887088e-07
1150.9999994524008361.09519832770822e-065.4759916385411e-07
1160.9999991628744191.67425116273500e-068.37125581367501e-07
1170.9999985308737672.93825246625425e-061.46912623312712e-06
1180.9999984927537093.01449258219781e-061.50724629109890e-06
1190.9999983229212913.35415741711378e-061.67707870855689e-06
1200.9999996178671167.64265768331992e-073.82132884165996e-07
1210.9999998933733432.13253314532942e-071.06626657266471e-07
1220.999999818611413.62777181927492e-071.81388590963746e-07
1230.9999999493565521.01286896749015e-075.06434483745077e-08
1240.9999999120661831.7586763410066e-078.793381705033e-08
1250.9999998422740743.15451851057455e-071.57725925528728e-07
1260.9999997331275695.33744862044489e-072.66872431022244e-07
1270.9999996892012646.21597472934654e-073.10798736467327e-07
1280.99999943877581.12244840081939e-065.61224200409695e-07
1290.9999989356780242.12864395257073e-061.06432197628536e-06
1300.999999427726231.14454753850939e-065.72273769254693e-07
1310.9999993909970021.21800599684692e-066.09002998423462e-07
1320.9999999357444851.28511029699840e-076.42555148499201e-08
1330.9999999456898831.08620234260407e-075.43101171302035e-08
1340.9999999155595621.6888087503027e-078.4440437515135e-08
1350.999999827304643.45390721431444e-071.72695360715722e-07
1360.999999681112796.37774418162381e-073.18887209081191e-07
1370.9999995163213779.67357246883727e-074.83678623441864e-07
1380.9999992181697841.56366043213991e-067.81830216069957e-07
1390.9999987851041472.42979170547043e-061.21489585273522e-06
1400.999997645868014.70826397889382e-062.35413198944691e-06
1410.9999975123879174.97522416654354e-062.48761208327177e-06
1420.9999950610824989.87783500307583e-064.93891750153791e-06
1430.9999977378293514.52434129751268e-062.26217064875634e-06
1440.9999964692147257.06157054924961e-063.53078527462480e-06
1450.9999948623953031.02752093948036e-055.13760469740179e-06
1460.9999902717740881.94564518248321e-059.72822591241607e-06
1470.999980945438123.81091237617347e-051.90545618808673e-05
1480.99996251312627.49737476012257e-053.74868738006128e-05
1490.9999284328706930.0001431342586141217.15671293070605e-05
1500.9998940027453570.0002119945092869710.000105997254643485
1510.9998940207980520.0002119584038961510.000105979201948076
1520.999817241528260.0003655169434797720.000182758471739886
1530.9996499702514620.0007000594970758940.000350029748537947
1540.9995311834273330.0009376331453337070.000468816572666854
1550.9992521017508740.001495796498252000.000747898249125998
1560.9998484865948990.0003030268102022830.000151513405101141
1570.9998217739455420.000356452108915760.00017822605445788
1580.9996466639037490.0007066721925024920.000353336096251246
1590.999472246590460.001055506819079270.000527753409539634
1600.9991619418563270.001676116287346380.00083805814367319
1610.998794430703550.00241113859289920.0012055692964496
1620.9981324186713650.003735162657269710.00186758132863485
1630.9965413176793270.006917364641346640.00345868232067332
1640.9964306423968490.007138715206302330.00356935760315117
1650.996302913049990.007394173900021520.00369708695001076
1660.9926248205431520.01475035891369500.00737517945684748
1670.9869490046325480.02610199073490320.0130509953674516
1680.9909147209212230.01817055815755350.00908527907877673
1690.9822710463111070.03545790737778660.0177289536888933
1700.9718771603734020.0562456792531960.028122839626598
1710.9497551587281750.1004896825436500.0502448412718249
1720.9122010401935920.1755979196128150.0877989598064075
1730.8524618585293440.2950762829413120.147538141470656
1740.7823573198125330.4352853603749340.217642680187467
1750.6569428186407690.6861143627184620.343057181359231
1760.550072850089640.8998542998207190.449927149910359


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/25/t1227641686t20w8ld5ejs63v0/10dhrb1227640739.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/25/t1227641686t20w8ld5ejs63v0/96hmu1227640739.png (open in new window)
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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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