Multiple Regression

*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: Sun, 26 Dec 2010 20:57:10 +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/26/t1293396912lhfgwsjavsodzfq.htm/, Retrieved Sun, 26 Dec 2010 21:55:23 +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/26/t1293396912lhfgwsjavsodzfq.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:

Micha

Dataseries X:

» Textbox « » Textfile « » CSV «

549 3 0 1 564 3,1 -2 1 586 2,9 -4 1 604 2,4 -4 1 601 2,4 -7 1 545 2,7 -9 1 537 2,5 -13 1 552 2,1 -8 1 563 1,9 -13 1 575 0,8 -15 1 580 0,8 -15 1 575 0,3 -15 1 558 0 -10 1 564 -0,9 -12 1 581 -1 -11 1 597 -0,7 -11 1 587 -1,7 -17 1 536 -1 -18 1 524 -0,2 -19 1,09 537 0,7 -22 1,31 536 0,6 -24 1,66 533 1,9 -24 2 528 2,1 -20 2,31 516 2,7 -25 2,75 502 3,2 -22 3,42 506 4,8 -17 3,97 518 5,5 -9 4,25 534 5,4 -11 4,25 528 5,9 -13 4,18 478 5,8 -11 4 469 5,1 -9 4 490 4,1 -7 4 493 4,4 -3 4 508 3,6 -3 4 517 3,5 -6 4 514 3,1 -4 4 510 2,9 -8 4 527 2,2 -1 4 542 1,4 -2 4 565 1,2 -2 4 555 1,3 -1 4 499 1,3 1 3,9 511 1,3 2 3,75 526 1,8 2 3,75 532 1,8 -1 3,65 549 1,8 1 3,5 561 1,7 -1 3,5 557 2,1 -8 3,39 566 2 1 3,25 588 1,7 2 3,17 620 1,9 -2 3 626 2,3 -2 2,93 620 2,4 -2 2,75 573 2,5 -2 2,64 573 2,8 -6 2,5 574 2,6 -4 2,5 580 2,2 -5 2,45 590 2,8 -2 2,25 593 2,8 -1 2,25 597 2,8 -5 2,21 595 2,3 -9 2 612 2,2 -8 2 628 3 -14 2 629 2,9 -10 2 621 2,7 -11 2 569 2,7 -11 2 567 2,3 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 Input view raw input (R code) Raw Output view raw output of R engine Computing time 8 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Werkl[t] = + 615.257401139034 + 6.80817051072085HICP[t] + 0.0432285362072156cons[t] -33.3276162244645Rente[t] -5.64521901200417M1[t] + 12.9632301608716M2[t] + 27.8067716518888M3[t] + 37.1454696521715M4[t] + 25.3435520808326M5[t] -30.8186628281114M6[t] -33.0060980257521M7[t] -22.0416154598599M8[t] -15.5437481467340M9[t] -5.62544687503914M10[t] + 0.369926092587064M11[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 615.257401139034 13.575416 45.3214 0 0 HICP 6.80817051072085 2.482549 2.7424 0.007067 0.003533 cons 0.0432285362072156 0.369761 0.1169 0.907134 0.453567 Rente -33.3276162244645 3.167876 -10.5205 0 0 M1 -5.64521901200417 13.302233 -0.4244 0.672074 0.336037 M2 12.9632301608716 13.302795 0.9745 0.331849 0.165924 M3 27.8067716518888 13.334452 2.0853 0.039232 0.019616 M4 37.1454696521715 13.350454 2.7823 0.006302 0.003151 M5 25.3435520808326 13.315991 1.9032 0.059487 0.029744 M6 -30.8186628281114 13.358727 -2.307 0.022829 0.011414 M7 -33.0060980257521 13.321871 -2.4776 0.014668 0.007334 M8 -22.0416154598599 13.343882 -1.6518 0.101277 0.050638 M9 -15.5437481467340 13.333038 -1.1658 0.246084 0.123042 M10 -5.62544687503914 13.351494 -0.4213 0.67429 0.337145 M11 0.369926092587064 13.351827 0.0277 0.977944 0.488972 Multiple Linear Regression - Regression Statistics Multiple R 0.816721146478923 R-squared 0.667033431105846 Adjusted R-squared 0.626847810722069 F-TEST (value) 16.5988088459405 F-TEST (DF numerator) 14 F-TEST (DF denominator) 116 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 30.4129915979267 Sum Squared Residuals 107294.206720525 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 549 596.70907743473 -47.7090774347295 2 564 615.911886586261 -51.9118865862613 3 586 629.30733690272 -43.3073369027198 4 604 635.241949647642 -31.2419496476421 5 601 623.310346467682 -22.3103464676816 6 545 569.104125639539 -24.1041256395393 7 537 565.382142194926 -28.3821421949258 8 552 573.839499237566 -21.8394992375656 9 563 578.759589767511 -15.7595897675112 10 575 581.102446404999 -6.10244640499874 11 580 587.097819372625 -7.09781937262497 12 575 583.323808024677 -8.32380802467739 13 558 575.852280540493 -17.8522805404931 14 564 588.246919181306 -24.2469191813057 15 581 602.452872157458 -21.4528721574579 16 597 613.834021310957 -16.8340213109569 17 587 594.964562011654 -7.96456201165395 18 536 543.524837924007 -7.52483792400724 19 524 543.741225138534 -19.7412251385342 20 537 553.371299986071 -16.3712999860713 21 536 547.437227497148 -11.4372274971481 22 533 554.874760916462 -21.8747609164622 23 528 552.073121101477 -24.0731211014774 24 516 540.907803495522 -24.9078034955224 25 502 516.466852477109 -14.4668524771090 26 506 527.854328224719 -21.8543282247187 27 518 538.477684820048 -20.4776848200482 28 534 547.049108696844 -13.0491086968443 29 528 540.897752444164 -12.8977524441641 30 478 490.140148476966 -12.1401484769659 31 469 483.273450994235 -14.2734509942351 32 490 487.516220121821 2.48377987817916 33 493 496.229452732992 -3.22945273299185 34 508 500.70121759611 7.29878240388992 35 517 505.886087904043 11.1139120959575 36 514 502.879350679582 11.1206493204184 37 510 495.699583420604 14.3004165793956 38 527 509.844912989426 17.1550870105739 39 542 519.198689535659 22.8013104643407 40 565 527.175753433798 37.8242465662021 41 555 516.097881449738 38.9021185502617 42 499 463.354885235655 35.6451147643449 43 511 466.209821007891 44.7901789921087 44 526 480.578388829144 45.4216111708560 45 532 490.279332156095 41.7206678439053 46 549 505.283232933874 43.7167670661263 47 561 510.511331778013 50.4886682219867 48 557 516.228111920955 40.7718880790448 49 566 514.956998955169 51.043001044831 50 588 534.232434808993 53.7675651910071 51 620 555.930391015484 64.0696089845157 52 626 570.325290355768 55.6747096442322 53 620 565.203160755905 54.7968392440953 54 573 513.387800682724 59.6121993172762 55 573 517.735768764896 55.2642312351044 56 574 527.425074301058 46.5749256989420 57 580 532.822825684912 47.1771743150884 58 590 553.621238116554 36.3787618834464 59 593 559.659839620387 33.3401603796130 60 597 560.45010403195 36.5498959680504 61 595 558.226685026894 36.7733149731063 62 612 576.197545684905 35.8024543150954 63 628 596.228252367255 31.7717476327448 64 629 605.059047461295 23.9409525387053 65 621 591.852267251604 29.1477327483955 66 569 535.69005234266 33.3099476573396 67 567 530.779348940731 36.2206510592686 68 573 542.684019774939 30.3159802250611 69 584 552.034840900975 31.9651590990252 70 589 558.505828381102 30.4941716188979 71 591 562.32906458689 28.6709354131097 72 595 561.278321443231 33.7216785567688 73 594 558.313142099308 35.6868579006918 74 611 579.68808801268 31.3119119873205 75 613 588.577190188877 24.4228098111233 76 611 599.277522291304 11.7224777086964 77 594 588.069964698622 5.93003530137755 78 543 531.399846883435 11.6001531165649 79 537 531.676308672840 5.32369132716047 80 544 537.961528953642 6.03847104635847 81 555 539.73690544547 15.2630945545300 82 561 551.103297891724 9.89670210827646 83 562 558.37384788908 3.62615211092053 84 555 559.916687341087 -4.91668734108702 85 547 554.952285380155 -7.95228538015494 86 565 570.448409522877 -5.44840952287743 87 578 587.766687529183 -9.76668752918301 88 580 596.16519726115 -16.1651972611503 89 569 582.915188515253 -13.9151885152529 90 507 524.230714643556 -17.2307146435561 91 501 504.670559185904 -3.67055918590432 92 509 519.633486985815 -10.6334869858146 93 510 525.524007836411 -15.5240078364109 94 517 528.312111493177 -11.3121114931769 95 519 531.757130401344 -12.7571304013436 96 512 528.778488273589 -16.7784882735894 97 509 508.613502814484 0.386497185515915 98 519 528.626814625711 -9.62681462571126 99 523 542.789539065656 -19.7895390656563 100 525 552.809054117011 -27.8090541170111 101 517 539.731959515943 -22.7319595159426 102 456 481.570521989989 -25.5705219899894 103 455 483.511217634988 -28.5112176349885 104 461 495.794105766818 -34.7941057668176 105 470 508.505783612007 -38.5057836120067 106 475 518.380856347494 -43.3808563474944 107 476 524.970589293778 -48.9705892937783 108 471 520.213161141308 -49.2131611413081 109 471 508.108156393663 -37.1081563936626 110 503 515.572394921632 -12.5723949216321 111 513 521.516489231871 -8.51648923187136 112 510 519.782300220162 -9.78230022016174 113 484 509.862471784623 -25.8624717846234 114 431 455.061890977824 -24.0618909778235 115 436 450.845834997091 -14.8458349970905 116 443 454.782988702680 -11.7829887026795 117 448 456.68805080313 -8.68805080312973 118 460 468.692031764248 -8.69203176424809 119 467 476.265181515055 -9.26518151505454 120 460 478.024163648098 -18.0241636480982 121 464 477.101435457391 -13.1014354573914 122 485 497.37626544149 -12.3762654414904 123 501 520.754867185788 -19.7548671857878 124 521 535.28075520407 -14.2807552040695 125 488 511.094445104812 -23.0944451048115 126 439 468.535175203644 -29.5351752036440 127 442 474.174322467964 -32.1743224679637 128 457 492.413387340448 -35.413387340448 129 462 504.98198356335 -42.9819835633503 130 481 517.422978154257 -36.4229781542568 131 493 518.075986537309 -25.0759865373086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.00994705101950592 0.0198941020390118 0.990052948980494 19 0.00160287655145939 0.00320575310291878 0.99839712344854 20 0.000258673688611695 0.000517347377223389 0.999741326311388 21 0.000111628063948844 0.000223256127897687 0.999888371936051 22 1.75423850796910e-05 3.50847701593819e-05 0.99998245761492 23 3.34397760895665e-06 6.6879552179133e-06 0.99999665602239 24 1.00969441555952e-06 2.01938883111904e-06 0.999998990305584 25 6.56872933293935e-05 0.000131374586658787 0.99993431270667 26 5.38985167249932e-05 0.000107797033449986 0.999946101483275 27 1.54299893932485e-05 3.0859978786497e-05 0.999984570010607 28 4.17410085653644e-06 8.34820171307288e-06 0.999995825899143 29 1.11001765800863e-06 2.22003531601727e-06 0.999998889982342 30 3.15879542261611e-07 6.31759084523222e-07 0.999999684120458 31 9.95566828827405e-08 1.99113365765481e-07 0.999999900443317 32 2.35291501384831e-08 4.70583002769662e-08 0.99999997647085 33 8.237999721536e-09 1.64759994430720e-08 0.999999991762 34 1.86433916495203e-09 3.72867832990407e-09 0.99999999813566 35 6.0393950744425e-10 1.2078790148885e-09 0.99999999939606 36 1.57469082189825e-10 3.1493816437965e-10 0.99999999984253 37 3.14637962169766e-10 6.29275924339533e-10 0.999999999685362 38 3.40514633626478e-10 6.81029267252956e-10 0.999999999659485 39 1.80250517668283e-10 3.60501035336567e-10 0.99999999981975 40 2.0182888379494e-10 4.0365776758988e-10 0.999999999798171 41 1.02675895381747e-10 2.05351790763494e-10 0.999999999897324 42 4.58078035905893e-11 9.16156071811786e-11 0.999999999954192 43 7.73790184908663e-11 1.54758036981733e-10 0.999999999922621 44 1.10076505366340e-10 2.20153010732680e-10 0.999999999889923 45 1.30987970525167e-10 2.61975941050333e-10 0.999999999869012 46 2.16133166667766e-10 4.32266333335531e-10 0.999999999783867 47 1.66979807146322e-09 3.33959614292645e-09 0.999999998330202 48 2.09403358222569e-08 4.18806716445138e-08 0.999999979059664 49 9.34117366891892e-07 1.86823473378378e-06 0.999999065882633 50 4.9721112399898e-05 9.9442224799796e-05 0.9999502788876 51 0.00872978572404898 0.0174595714480980 0.99127021427595 52 0.0584448948272125 0.116889789654425 0.941555105172788 53 0.157686769524034 0.315373539048069 0.842313230475966 54 0.378163314940699 0.756326629881398 0.621836685059301 55 0.63535668207793 0.729286635844141 0.364643317922070 56 0.739336560651229 0.521326878697543 0.260663439348772 57 0.837769735761115 0.32446052847777 0.162230264238885 58 0.845886387182725 0.30822722563455 0.154113612817275 59 0.8343518168016 0.3312963663968 0.1656481831984 60 0.849149000893598 0.301701998212804 0.150850999106402 61 0.903005271644587 0.193989456710827 0.0969947283554134 62 0.941603407725083 0.116793184549834 0.0583965922749172 63 0.971017129115022 0.0579657417699556 0.0289828708849778 64 0.972413837571662 0.0551723248566765 0.0275861624283383 65 0.973827197748539 0.0523456045029226 0.0261728022514613 66 0.978749398835006 0.0425012023299885 0.0212506011649943 67 0.984714797501686 0.0305704049966286 0.0152852024983143 68 0.985098297093865 0.0298034058122705 0.0149017029061352 69 0.985300758848147 0.0293984823037052 0.0146992411518526 70 0.986890025804757 0.0262199483904850 0.0131099741952425 71 0.98913934253471 0.0217213149305780 0.0108606574652890 72 0.994329852805148 0.0113402943897039 0.00567014719485194 73 0.997077413325703 0.00584517334859402 0.00292258667429701 74 0.998031610399332 0.00393677920133596 0.00196838960066798 75 0.998286415291403 0.00342716941719467 0.00171358470859734 76 0.997903835061326 0.00419232987734797 0.00209616493867399 77 0.997516329050476 0.00496734189904703 0.00248367094952352 78 0.998089157419685 0.00382168516063037 0.00191084258031518 79 0.997912093649382 0.00417581270123549 0.00208790635061774 80 0.998145325005612 0.00370934998877578 0.00185467499438789 81 0.999235614615836 0.00152877076832877 0.000764385384164384 82 0.999673262976378 0.00065347404724291 0.000326737023621455 83 0.999826625863105 0.00034674827378903 0.000173374136894515 84 0.99989834702378 0.000203305952438836 0.000101652976219418 85 0.999877927822521 0.000244144354956962 0.000122072177478481 86 0.99979885431535 0.000402291369301511 0.000201145684650756 87 0.999755988493745 0.00048802301251006 0.00024401150625503 88 0.99960151311478 0.00079697377044133 0.000398486885220665 89 0.99962213936288 0.000755721274240968 0.000377860637120484 90 0.999687435739414 0.00062512852117231 0.000312564260586155 91 0.999811580821916 0.000376838356168829 0.000188419178084414 92 0.999911218641545 0.000177562716909429 8.87813584547144e-05 93 0.999952694092514 9.46118149728983e-05 4.73059074864492e-05 94 0.999988695687683 2.26086246346682e-05 1.13043123173341e-05 95 0.999998662548807 2.67490238673583e-06 1.33745119336792e-06 96 0.99999996209988 7.58002404585737e-08 3.79001202292868e-08 97 0.999999999431247 1.13750560888758e-09 5.68752804443788e-10 98 0.999999999174059 1.65188264349067e-09 8.25941321745335e-10 99 0.99999999695109 6.09781974361808e-09 3.04890987180904e-09 100 0.999999994561247 1.0877506602907e-08 5.4387533014535e-09 101 0.9999999997103 5.79400290739179e-10 2.89700145369589e-10 102 0.99999999911327 1.77346043610738e-09 8.8673021805369e-10 103 0.999999996896843 6.20631419256396e-09 3.10315709628198e-09 104 0.999999985112366 2.97752683400988e-08 1.48876341700494e-08 105 0.999999987235415 2.55291691892619e-08 1.27645845946309e-08 106 0.999999928535057 1.42929885703324e-07 7.14649428516622e-08 107 0.999999707704672 5.84590656394576e-07 2.92295328197288e-07 108 0.999998451737078 3.09652584485626e-06 1.54826292242813e-06 109 0.999997969611205 4.06077758956211e-06 2.03038879478105e-06 110 0.999986275202395 2.74495952100095e-05 1.37247976050048e-05 111 0.999935199494775 0.000129601010450058 6.4800505225029e-05 112 0.999913798088038 0.000172403823923008 8.62019119615042e-05 113 0.998915079862835 0.00216984027432896 0.00108492013716448 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 73 0.760416666666667 NOK 5% type I error level 82 0.854166666666667 NOK 10% type I error level 85 0.885416666666667 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/10barh1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/10barh1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/1witq1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/1witq1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/2witq1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/2witq1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/3witq1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/3witq1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/4p9at1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/4p9at1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/5p9at1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/5p9at1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/6p9at1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/6p9at1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/70i9v1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/70i9v1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/8barh1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/8barh1293397020.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/9barh1293397020.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/26/t1293396912lhfgwsjavsodzfq/9barh1293397020.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

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.

FreeStatistics.org is powered by