Multiple Regression with monthly dummy, linear trend & history

*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, 19 Dec 2010 11:09:13 +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/19/t12927573032zqfadyfjqoqjz8.htm/, Retrieved Sun, 19 Dec 2010 12:15:15 +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/19/t12927573032zqfadyfjqoqjz8.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

185705 0 194519 198112 206010 180173 0 185705 194519 198112 176142 0 180173 185705 194519 203401 0 176142 180173 185705 221902 0 203401 176142 180173 197378 0 221902 203401 176142 185001 0 197378 221902 203401 176356 0 185001 197378 221902 180449 0 176356 185001 197378 180144 0 180449 176356 185001 173666 0 180144 180449 176356 165688 0 173666 180144 180449 161570 0 165688 173666 180144 156145 0 161570 165688 173666 153730 0 156145 161570 165688 182698 0 153730 156145 161570 200765 0 182698 153730 156145 176512 0 200765 182698 153730 166618 0 176512 200765 182698 158644 0 166618 176512 200765 159585 0 158644 166618 176512 163095 0 159585 158644 166618 159044 0 163095 159585 158644 155511 0 159044 163095 159585 153745 0 155511 159044 163095 150569 0 153745 155511 159044 150605 0 150569 153745 155511 179612 0 150605 150569 153745 194690 0 179612 150605 150569 189917 0 194690 179612 150605 184128 0 189917 194690 179612 175335 0 184128 189917 194690 179566 0 175335 184128 189917 1 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Werkloosheid[t] = + 284.896369125289 + 1060.52423815882Dummy_crisis[t] + 1.02699351092810past_1[t] + 0.155831521445659past_2[t] -0.205239464638224past_3[t] + 1263.58435127132M1[t] + 178.280372103877M2[t] + 6888.79005240301M3[t] + 37094.0396228534M4[t] + 11132.9463352077M5[t] -18376.0718371182M6[t] -5228.27257574756M7[t] + 236.519978481622M8[t] + 10697.3178260887M9[t] + 5169.33729366704M10[t] -430.547119867729M11[t] -2.12042340352418t + 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) 284.896369125289 3608.983774 0.0789 0.937208 0.468604 Dummy_crisis 1060.52423815882 1438.843887 0.7371 0.462485 0.231243 past_1 1.02699351092810 0.08855 11.5979 0 0 past_2 0.155831521445659 0.126996 1.2271 0.222143 0.111072 past_3 -0.205239464638224 0.088547 -2.3179 0.022108 0.011054 M1 1263.58435127132 1931.359554 0.6542 0.514175 0.257087 M2 178.280372103877 1935.223666 0.0921 0.926749 0.463375 M3 6888.79005240301 1934.380818 3.5612 0.000526 0.000263 M4 37094.0396228534 2018.910425 18.3733 0 0 M5 11132.9463352077 3700.08096 3.0088 0.003182 0.001591 M6 -18376.0718371182 3566.193741 -5.1529 1e-06 0 M7 -5228.27257574756 2373.865222 -2.2024 0.029499 0.014749 M8 236.519978481622 2418.839544 0.0978 0.922264 0.461132 M9 10697.3178260887 2106.046502 5.0793 1e-06 1e-06 M10 5169.33729366704 2178.911645 2.3724 0.019222 0.009611 M11 -430.547119867729 2007.994763 -0.2144 0.830577 0.415289 t -2.12042340352418 14.680244 -0.1444 0.885389 0.442694 Multiple Linear Regression - Regression Statistics Multiple R 0.986914685206737 R-squared 0.974000595876712 Adjusted R-squared 0.970618559567992 F-TEST (value) 287.992353413032 F-TEST (DF numerator) 16 F-TEST (DF denominator) 123 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4556.99410942278 Sum Squared Residuals 2554242023.53761 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 185705 189906.823315737 -4201.82331573672 2 180173 180828.556743004 -655.556743004448 3 176142 181219.544263869 -5077.54426386897 4 203401 208229.783233049 -4828.78323304861 5 221902 210768.613491820 11133.3865081804 6 197378 205333.013566815 -7955.01356681463 7 185001 190581.119954474 -5580.11995447396 8 176356 175713.945833337 642.054166662494 9 180449 180398.830245423 50.1697545774773 10 180144 180265.299080756 -121.299080755628 11 173666 176762.174812059 -3096.17481205877 12 165688 169650.163801926 -3962.16380192562 13 161570 161771.394940399 -201.394940398751 14 156145 156541.128633659 -396.128633658824 15 153730 158673.76433734 -4943.76433734005 16 182698 186396.494267033 -3698.49426703306 17 200765 190920.31955192 9844.68044807997 18 176512 184973.653538468 -8461.6535384676 19 166618 170081.690042214 -3463.69004221429 20 158644 157895.845078677 748.15492132296 21 159585 163601.151909427 -4016.15190942741 22 163095 159825.490558508 3269.50944149149 23 159044 159611.449897633 -567.449897633386 24 155511 156233.364185378 -722.364185377562 25 153745 152514.79602488 1230.20397512012 26 150569 149894.573387992 674.426612008183 27 150605 153791.143815874 -3186.14381587361 28 179612 183898.776711754 -4286.77671175358 29 194690 188383.014246659 6306.98575334132 30 189917 178869.700130550 11047.2998694497 31 184128 183509.785470454 618.214529545693 32 175335 179188.807666842 -3853.80766684196 33 179566 180694.630436524 -1128.63043652406 34 181140 179327.643718155 1812.35628184532 35 177876 177806.120447218 69.8795527823011 36 175041 174259.350963884 781.64903611626 37 169292 171777.607284931 -2485.60728493119 38 166070 165014.116437315 1055.88356268468 39 166972 168099.511067459 -1127.51106745888 40 206348 199906.82088147 6441.17911852988 41 215706 215184.345244134 521.654755866055 42 202108 201234.70791501 873.292084989844 43 195411 193792.091209471 1618.90879052915 44 193111 188337.359858908 4773.64014109151 45 195198 198181.194749006 -2983.19474900637 46 198770 195810.505445845 2959.49455415466 47 194163 194674.192583867 -511.192583867205 48 190420 190499.555607390 -79.5556073895916 49 189733 186465.951636866 3267.04836313436 50 186029 185035.243521104 993.756478895732 51 191531 188600.80387443 2930.19612557009 52 232571 224018.250875375 8552.74912462508 53 243477 241820.442860829 1656.55713917128 54 227247 228775.793600971 -1528.79360097138 55 217859 218529.838700709 -670.838700709201 56 208679 209583.608556534 -904.608556534398 57 213188 212482.575738165 705.424261835487 58 216234 212079.443250267 4154.55674973334 59 213586 212192.403263193 1393.59673680729 60 209465 209450.589210989 14.4107890109594 61 204045 205442.011602246 -1397.01160224602 62 200237 198689.574772929 1547.42522707077 63 203666 201488.357727749 2177.6422722507 64 241476 235732.039088443 5743.96091155728 65 260307 249915.348193964 10391.6518060357 66 243324 244931.748104138 -1607.74810413768 67 244460 235810.355368385 8649.64463161505 68 233575 235928.341040311 -2353.34104031093 69 237217 238870.800534375 -1653.80053437533 70 235243 235151.631802585 91.3681974146975 71 230354 230323.911748767 30.0882512328984 72 227184 224676.273616758 2507.72638324229 73 221678 222325.450509831 -647.450509831471 74 217142 216092.829655724 1049.17034427606 75 219452 217935.377092873 1516.62290712692 76 256446 250934.057961184 5511.94203881558 77 265845 264254.379219548 1590.62078045239 78 248624 249686.680774078 -1062.68077407771 79 241114 239018.536075593 2095.46392440658 80 229245 232155.866580399 -2910.86658039874 81 231805 232789.292117875 -984.29211787463 82 219277 229580.07860142 -10303.0786014200 83 219313 213946.814960266 5366.18503973356 84 212610 211934.543092979 675.456907021002 85 214771 208888.919464855 5882.08053514453 86 211142 208968.900730423 2173.09926957711 87 211457 213662.802585475 -2205.80258547452 88 240048 243180.399614054 -3132.39961405426 89 240636 247373.858320378 -6737.8583203777 90 230580 222857.320507366 7722.67949263427 91 208795 219899.180000579 -11104.1800005786 92 197922 201301.075910971 -3379.07591097084 93 194596 199262.351252561 -4666.35125256148 94 194581 193093.255483855 1487.74451614546 95 185686 189189.118802935 -3503.11880293547 96 178106 181162.727206259 -3056.72720625931 97 172608 173256.537530003 -648.537530002586 98 167302 167167.104909748 134.895090252149 99 168053 169125.220034708 -1072.22003470848 100 202300 200401.185832253 1898.81416774735 101 202388 210815.448961934 -8427.44896193402 102 182516 186577.313072172 -4061.31307217238 103 173476 172299.454089398 1176.54591060160 104 166444 165363.359814378 1080.64018562222 105 171297 171270.020557157 26.9794428430532 106 169701 171483.476611390 -1782.47661138953 107 164182 166441.884419922 -2259.88441992176 108 161914 159957.599699457 1956.40030054276 109 159612 158357.370363244 1254.62963675588 110 151001 155685.097613216 -4684.09761321628 111 158114 153656.804690942 4457.19530905835 112 186530 191356.058935808 -4826.05893580753 113 187069 197451.639473334 -10382.6394733338 114 174330 171462.290581423 2867.70941857730 115 169362 165777.007646576 3584.99235342371 116 166827 164041.814191975 2785.18580802508 117 178037 173737.43760746 4299.56239254 118 186413 180344.530662597 6068.46933740323 119 189226 185611.776871456 3614.22312854406 120 191563 187933.646739195 3629.35326080478 121 188906 190314.462816119 -1408.46281611885 122 186005 186285.156306603 -280.156306603116 123 195309 189120.548406956 6188.45159304432 124 223532 228972.079193507 -5440.07919350746 125 226899 234038.959503828 -7139.95950382777 126 214126 210474.19311016 3651.80688984001 127 206903 205234.295155266 1668.70484473448 128 204442 200597.515855795 3844.48414420475 129 220375 210024.714852027 10350.2851479733 130 214320 221956.644784623 -7636.64478462309 131 212588 213124.152192684 -536.152192683516 132 205816 207560.185875786 -1744.18587578599 133 202196 202839.674510889 -643.674510889282 134 195722 197334.717288282 -1612.71728828201 135 198563 198220.122102326 342.877897674109 136 229139 231075.053406071 -1936.05340607067 137 229527 238284.630931654 -8757.63093165386 138 211868 213353.585098850 -1485.58509884976 139 203555 202148.646286880 1406.35371311974 140 195770 196242.459611872 -472.459611872152 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.0118314024130387 0.0236628048260773 0.988168597586961 21 0.0144070242892608 0.0288140485785216 0.98559297571074 22 0.00480219126431148 0.00960438252862296 0.995197808735689 23 0.00304416806444331 0.00608833612888663 0.996955831935557 24 0.0110093835349611 0.0220187670699223 0.988990616465039 25 0.00628299265284086 0.0125659853056817 0.99371700734716 26 0.0024017198587421 0.0048034397174842 0.997598280141258 27 0.000965638251422117 0.00193127650284423 0.999034361748578 28 0.000675482755622986 0.00135096551124597 0.999324517244377 29 0.00234161193623796 0.00468322387247591 0.997658388063762 30 0.197280173998781 0.394560347997562 0.802719826001219 31 0.246545444616407 0.493090889232813 0.753454555383593 32 0.210605014335107 0.421210028670213 0.789394985664894 33 0.292044980391802 0.584089960783604 0.707955019608198 34 0.322455061823257 0.644910123646514 0.677544938176743 35 0.267736338810588 0.535472677621175 0.732263661189412 36 0.211897585168325 0.423795170336651 0.788102414831675 37 0.21890279481817 0.43780558963634 0.78109720518183 38 0.178383961098914 0.356767922197829 0.821616038901085 39 0.148186046811472 0.296372093622943 0.851813953188528 40 0.219647862169788 0.439295724339575 0.780352137830212 41 0.328986811754895 0.657973623509789 0.671013188245105 42 0.276361079063907 0.552722158127814 0.723638920936093 43 0.228791535860146 0.457583071720293 0.771208464139854 44 0.216051787355045 0.432103574710090 0.783948212644955 45 0.201309662714015 0.402619325428029 0.798690337285985 46 0.159712474992599 0.319424949985199 0.8402875250074 47 0.137489078296875 0.274978156593749 0.862510921703125 48 0.113632500822117 0.227265001644234 0.886367499177883 49 0.0870949000536296 0.174189800107259 0.91290509994637 50 0.0684366712089638 0.136873342417928 0.931563328791036 51 0.0636844780434999 0.127368956087000 0.9363155219565 52 0.109855383163520 0.219710766327041 0.89014461683648 53 0.10532749691632 0.21065499383264 0.89467250308368 54 0.0936398677775118 0.187279735555024 0.906360132222488 55 0.0962747534996425 0.192549506999285 0.903725246500358 56 0.097066145973153 0.194132291946306 0.902933854026847 57 0.0789755092086173 0.157951018417235 0.921024490791383 58 0.0634981783524886 0.126996356704977 0.936501821647511 59 0.04794661495221 0.09589322990442 0.95205338504779 60 0.0383721191104891 0.0767442382209782 0.96162788088951 61 0.0380370519051514 0.0760741038103029 0.961962948094849 62 0.0301548528102262 0.0603097056204523 0.969845147189774 63 0.0228182801509923 0.0456365603019846 0.977181719849008 64 0.0200918614177322 0.0401837228354643 0.979908138582268 65 0.072383563187125 0.14476712637425 0.927616436812875 66 0.0595000912433205 0.119000182486641 0.94049990875668 67 0.113072107156647 0.226144214313294 0.886927892843353 68 0.101262943304151 0.202525886608303 0.898737056695849 69 0.0917101177663875 0.183420235532775 0.908289882233613 70 0.098244018671414 0.196488037342828 0.901755981328586 71 0.0823578154018821 0.164715630803764 0.917642184598118 72 0.0638959751826677 0.127791950365335 0.936104024817332 73 0.0550025911238398 0.110005182247680 0.94499740887616 74 0.0443068981071552 0.0886137962143105 0.955693101892845 75 0.0330146462259915 0.0660292924519831 0.966985353774009 76 0.0406589487847434 0.0813178975694868 0.959341051215257 77 0.117801065376138 0.235602130752277 0.882198934623862 78 0.100026500250686 0.200053000501372 0.899973499749314 79 0.0898610475428564 0.179722095085713 0.910138952457144 80 0.089483065225241 0.178966130450482 0.910516934774759 81 0.0770669003597292 0.154133800719458 0.922933099640271 82 0.361362861878443 0.722725723756885 0.638637138121557 83 0.358883523222391 0.717767046444783 0.641116476777609 84 0.319812476284620 0.639624952569241 0.68018752371538 85 0.362687990169907 0.725375980339814 0.637312009830093 86 0.385262819390117 0.770525638780234 0.614737180609883 87 0.354753324021879 0.709506648043757 0.645246675978121 88 0.376894646348894 0.753789292697788 0.623105353651106 89 0.635450121193039 0.729099757613921 0.364549878806960 90 0.893505314211304 0.212989371577392 0.106494685788696 91 0.953084741461332 0.0938305170773352 0.0469152585386676 92 0.951988983999537 0.0960220320009265 0.0480110160004633 93 0.967002520069058 0.065994959861885 0.0329974799309425 94 0.960184544657025 0.0796309106859505 0.0398154553429753 95 0.950744174034316 0.0985116519313677 0.0492558259656839 96 0.948913321162743 0.102173357674515 0.0510866788372573 97 0.929490825670792 0.141018348658417 0.0705091743292084 98 0.911960613345831 0.176078773308338 0.088039386654169 99 0.90742466638789 0.185150667224220 0.0925753336121102 100 0.941703969085734 0.116592061828533 0.0582960309142664 101 0.955301839170284 0.0893963216594324 0.0446981608297162 102 0.950625321978948 0.098749356042103 0.0493746780210515 103 0.931078077323845 0.137843845352310 0.0689219226761548 104 0.90584501136946 0.188309977261082 0.094154988630541 105 0.917732230628748 0.164535538742504 0.082267769371252 106 0.884320639332782 0.231358721334436 0.115679360667218 107 0.862362102190396 0.275275795619207 0.137637897809604 108 0.814566519685554 0.370866960628893 0.185433480314446 109 0.778529189722074 0.442941620555851 0.221470810277926 110 0.745821317644211 0.508357364711578 0.254178682355789 111 0.681543889367299 0.636912221265401 0.318456110632701 112 0.628574905912574 0.742850188174853 0.371425094087426 113 0.657779442709773 0.684441114580455 0.342220557290227 114 0.626795612224824 0.746408775550352 0.373204387775176 115 0.575909718947993 0.848180562104014 0.424090281052007 116 0.537916579857253 0.924166840285494 0.462083420142747 117 0.96578114945105 0.0684377010979015 0.0342188505489508 118 0.929161656216012 0.141676687567976 0.070838343783988 119 0.851736117944853 0.296527764110293 0.148263882055147 120 0.879969813595024 0.240060372809953 0.120030186404976 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 6 0.0594059405940594 NOK 5% type I error level 12 0.118811881188119 NOK 10% type I error level 27 0.267326732673267 NOK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/10mj0h1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/10mj0h1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/1xi3n1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/1xi3n1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/28r3q1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/28r3q1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/38r3q1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/38r3q1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/48r3q1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/48r3q1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/501kb1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/501kb1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/601kb1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/601kb1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/7bajw1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/7bajw1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/8bajw1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/8bajw1292756941.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/9mj0h1292756941.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/19/t12927573032zqfadyfjqoqjz8/9mj0h1292756941.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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Software written by Ed van Stee & Patrick Wessa

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