*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: Wed, 15 Dec 2010 19:10:17 +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/15/t1292440157coib27v6fm69xgr.htm/, Retrieved Wed, 15 Dec 2010 20:09:20 +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/15/t1292440157coib27v6fm69xgr.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 «

4 0 5 5 0 4 6 0 5 6 0 6 6 0 6 7 0 6 8 0 7 7 0 8 8 0 7 7 0 8 8 0 7 8 0 8 9 0 8 9 0 9 8 0 9 9 0 8 9 0 9 10 0 9 11 0 10 12 0 11 13 0 12 13 0 13 13 0 13 14 0 13 14 0 14 15 0 14 15 0 15 16 0 15 16 0 16 17 0 16 18 0 17 19 0 18 20 0 19 22 0 20 20 0 22 22 0 20 25 0 22 24 0 25 25 0 24 28 0 25 26 0 28 27 0 26 26 0 27 25 0 26 27 0 25 28 0 27 30 0 28 31 0 30 32 0 31 34 0 32 34 0 34 33 0 34 32 0 33 34 0 32 36 0 34 37 0 36 40 0 37 38 0 40 38 0 38 36 0 38 40 0 36 40 0 40 42 0 40 44 0 42 45 0 44 47 0 45 49 0 47 47 0 49 49 0 47 52 0 49 50 0 52 50 0 50 57 0 50 58 0 57 58 0 58 58 0 58 61 0 58 61 0 61 64 0 61 68 0 64 40 0 68 34 0 40 46 0 34 36 0 46 34 0 36 45 0 34 55 0 45 50 0 55 56 0 50 72 0 56 76 0 72 78 0 76 77 0 78 90 0 77 88 0 90 97 0 88 93 0 97 84 0 93 67 0 84 72 0 67 75 0 72 71 0 75 75 0 71 90 0 75 78 0 90 73 0 78 62 0 73 65 0 62 61 0 65 58 0 61 33 0 58 39 0 33 56 0 39 79 0 56 82 0 79 79 0 82 73 0 79 87 0 7 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation CO2-uitstoot[t] = + 0.0424296098248327 -5.07184841354021`Kyoto-protocol`[t] + 0.851676438315116`Y-1`[t] + 0.112139788243898t + 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) 0.0424296098248327 0.938534 0.0452 0.963994 0.481997 `Kyoto-protocol` -5.07184841354021 3.214778 -1.5777 0.11649 0.058245 `Y-1` 0.851676438315116 0.040007 21.2884 0 0 t 0.112139788243898 0.031721 3.5352 0.000524 0.000262 Multiple Linear Regression - Regression Statistics Multiple R 0.988522052468713 R-squared 0.977175848216957 Adjusted R-squared 0.976775424501465 F-TEST (value) 2440.3545804382 F-TEST (DF numerator) 3 F-TEST (DF denominator) 171 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.00814902705278 Sum Squared Residuals 6172.73315904807 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4 4.41295158964428 -0.412951589644282 2 5 3.67341493957306 1.32658506042694 3 6 4.63723116613199 1.36276883386801 4 6 5.6010473926911 0.398952607308896 5 6 5.713187180935 0.286812819064998 6 7 5.8253269691789 1.1746730308211 7 8 6.78914319573792 1.21085680426208 8 7 7.75295942229693 -0.752959422296928 9 8 7.01342277222571 0.986577227774287 10 7 7.97723899878472 -0.977238998784724 11 8 7.23770234871351 0.762297651286491 12 8 8.20151857527252 -0.20151857527252 13 9 8.31365836351642 0.686341636483582 14 9 9.27747459007544 -0.277474590075435 15 8 9.38961437831933 -1.38961437831933 16 9 8.65007772824811 0.349922271751888 17 9 9.61389395480713 -0.613893954807129 18 10 9.72603374305103 0.273966256948972 19 11 10.68984996961 0.310150030389961 20 12 11.6536661961691 0.346333803830944 21 13 12.6174824227281 0.382517577271932 22 13 13.5812986492871 -0.581298649287079 23 13 13.693438437531 -0.693438437530977 24 14 13.8055782257749 0.194421774225125 25 14 14.7693944523339 -0.769394452333892 26 15 14.8815342405778 0.11846575942221 27 15 15.8453504671368 -0.845350467136801 28 16 15.9574902553807 0.0425097446193007 29 16 16.9213064819397 -0.921306481939717 30 17 17.0334462701836 -0.0334462701836146 31 18 17.9972624967426 0.00273750325737411 32 19 18.9610787233016 0.0389212766983568 33 20 19.9248949498607 0.0751050501393455 34 22 20.8887111764197 1.11128882358033 35 20 22.7042038412938 -2.7042038412938 36 22 21.1129907529075 0.887009247092532 37 25 22.9284834177816 2.07151658221841 38 24 25.5956525209708 -1.59565252097084 39 25 24.8561158708996 0.143884129100383 40 28 25.8199320974586 2.18006790254137 41 26 28.4871012006479 -2.48710120064788 42 27 26.8958881122615 0.104111887738456 43 26 27.8597043388206 -1.85970433882056 44 25 27.1201676887493 -2.12016768874934 45 27 26.3806310386781 0.619368961321879 46 28 28.1961237035522 -0.196123703552249 47 30 29.1599399301113 0.840060069888737 48 31 30.9754325949854 0.0245674050146054 49 32 31.9392488215444 0.0607511784555911 50 34 32.9030650481034 1.09693495189658 51 34 34.7185577129775 -0.718557712977551 52 33 34.8306975012215 -1.83069750122145 53 32 34.0911608511502 -2.09116085115023 54 34 33.351624201079 0.648375798920985 55 36 35.1671168659531 0.832883134046858 56 37 36.9826095308273 0.0173904691727267 57 40 37.9464257573863 2.05357424261371 58 38 40.6135948605755 -2.61359486057553 59 38 39.0223817721892 -1.0223817721892 60 36 39.1345215604331 -3.1345215604331 61 40 37.5433084720468 2.45669152795324 62 40 41.0621540135511 -1.06215401355113 63 42 41.174293801795 0.825706198204974 64 44 42.9897864666692 1.01021353333084 65 45 44.8052791315433 0.194720868456715 66 47 45.7690953581023 1.2309046418977 67 49 47.5845880229764 1.41541197702357 68 47 49.4000806878506 -2.40008068785056 69 49 47.8088675994642 1.19113240053578 70 52 49.6243602643384 2.37563973566165 71 50 52.2915293675276 -2.2915293675276 72 50 50.7003162791413 -0.700316279141265 73 57 50.8124560673852 6.18754393261484 74 58 56.8863309238349 1.11366907616513 75 58 57.8501471503939 0.149852849606112 76 58 57.9622869386378 0.037713061362214 77 61 58.0744267268817 2.92557327311832 78 61 60.7415958300709 0.25840416992907 79 64 60.8537356183148 3.14626438168517 80 68 63.5209047215041 4.47909527849593 81 40 67.0397502630084 -27.0397502630084 82 34 43.3049497784291 -9.30494977842909 83 46 38.3070309367823 7.69296906321771 84 36 48.6392879848076 -12.6392879848076 85 34 40.2346633899003 -6.23466338990031 86 45 38.643450301514 6.35654969848602 87 55 48.1240309112242 6.87596908877585 88 50 56.7529350826192 -6.75293508261921 89 56 52.6066926792875 3.39330732071247 90 72 57.8288910974221 14.1711089025779 91 76 71.5678538987079 4.43214610129213 92 78 75.0866994402122 2.91330055978776 93 77 76.9021921050864 0.0978078949136302 94 90 76.1626554550152 13.8373445449848 95 88 87.3465889413555 0.653411058644447 96 97 85.7553758529692 11.2446241470308 97 93 93.5326035860492 -0.532603586049171 98 84 90.2380376210326 -6.2380376210326 99 67 82.6850894644405 -15.6850894644405 100 72 68.3187298013274 3.68127019867262 101 75 72.6892517811469 2.31074821885314 102 71 75.3564208843361 -4.35642088433611 103 75 72.0618549193195 2.93814508068047 104 90 75.5807004608239 14.4192995391761 105 78 88.4679868237945 -10.4679868237945 106 73 78.360009352257 -5.36000935225705 107 62 74.2137669489254 -12.2137669489254 108 65 64.957465915703 0.0425340842970153 109 61 67.6246350188922 -6.62463501889223 110 58 64.3300690538757 -6.33006905387566 111 33 61.8871795271742 -28.8871795271742 112 39 40.7074083575402 -1.70740835754021 113 56 45.9296067756748 10.0703932243252 114 79 60.5202460152757 18.4797539847243 115 82 80.2209438847672 1.77905611523276 116 79 82.8881129879565 -3.88811298795648 117 73 80.445223461255 -7.44522346125504 118 87 75.4473046196082 11.5526953803918 119 85 87.4829145442638 -2.48291454426376 120 83 85.8917014558774 -2.89170145587743 121 82 84.300488367491 -2.30048836749109 122 83 83.5609517174199 -0.560951717419872 123 92 84.5247679439789 7.47523205602111 124 95 92.3019956770588 2.69800432294116 125 97 94.969164780248 2.03083521975192 126 87 96.7846574451222 -9.7846574451222 127 84 88.380032850215 -4.38003285021494 128 84 85.9371433235135 -1.93714332351349 129 89 86.0492831117574 2.95071688824261 130 103 90.4198050915769 12.5801949084231 131 106 102.455415016232 3.5445849837676 132 109 105.122584119422 3.87741588057836 133 106 107.789753222611 -1.78975322261089 134 105 105.346863695909 -0.346863695909438 135 115 104.607327045838 10.3926729541618 136 120 113.236231217233 6.76376878276672 137 124 117.606753197053 6.39324680294725 138 121 121.125598738557 -0.125598738557119 139 131 118.682709211856 12.3172907881443 140 139 127.311613383251 11.6883866167493 141 133 134.237164678016 -1.23716467801554 142 119 129.239245836369 -10.2392458363687 143 123 117.427915488201 5.57208451179897 144 120 120.946761029705 -0.946761029705388 145 128 118.503871503004 9.49612849699606 146 134 125.429422797769 8.57057720223125 147 126 130.651621215903 -4.65162121590336 148 115 123.950349497626 -8.95034949762632 149 106 114.694048464404 -8.69404846440395 150 99 107.141100307812 -8.1411003078118 151 100 101.29150502785 -1.29150502784989 152 99 102.255321254409 -3.25532125440891 153 99 101.515784604338 -2.51578460433769 154 100 101.627924392582 -1.62792439258158 155 100 102.591740619141 -2.5917406191406 156 108 102.703880407385 5.2961195926155 157 109 109.629431702149 -0.629431702149322 158 115 110.593247928708 4.40675207129167 159 114 115.815446346843 -1.81544634684293 160 108 115.075909696772 -7.07590969677171 161 113 110.077990855125 2.92200914487509 162 118 114.448512834944 3.55148716505561 163 122 118.819034814764 3.18096518523613 164 118 122.337880356268 -4.33788035626822 165 121 119.043314391252 1.95668560874834 166 118 121.710483494441 -3.7104834944409 167 121 119.267593967739 1.73240603226054 168 121 121.934763070929 -0.934763070928698 169 112 122.046902859173 -10.0469028591726 170 119 114.49395470258 4.50604529741954 171 116 120.56782955903 -4.56782955903017 172 110 113.053091618789 -3.05309161878851 173 111 108.055172777142 2.94482722285829 174 106 109.018989003701 -3.01898900370073 175 108 104.872746600369 3.12725339963095 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.000821830096984814 0.00164366019396963 0.999178169903015 8 0.00015881240238148 0.00031762480476296 0.999841187597619 9 1.89381812833468e-05 3.78763625666936e-05 0.999981061818717 10 1.25029840413732e-05 2.50059680827465e-05 0.99998749701596 11 1.84311609912246e-06 3.68623219824493e-06 0.999998156883901 12 2.61305492100515e-07 5.22610984201029e-07 0.999999738694508 13 2.74277774161488e-08 5.48555548322977e-08 0.999999972572223 14 2.69047186175295e-09 5.3809437235059e-09 0.999999997309528 15 1.60805828469912e-09 3.21611656939825e-09 0.999999998391942 16 1.94899343336464e-10 3.89798686672927e-10 0.9999999998051 17 2.62446243821172e-11 5.24892487642345e-11 0.999999999973755 18 2.84860917108138e-12 5.69721834216275e-12 0.999999999997151 19 6.36555091011624e-13 1.27311018202325e-12 0.999999999999363 20 3.02005667864535e-13 6.0401133572907e-13 0.999999999999698 21 1.40187875012143e-13 2.80375750024285e-13 0.99999999999986 22 1.68689201221631e-14 3.37378402443261e-14 0.999999999999983 23 1.84447719755587e-15 3.68895439511173e-15 0.999999999999998 24 3.44143229705924e-16 6.88286459411848e-16 1 25 3.66480563605496e-17 7.32961127210993e-17 1 26 6.47997226914037e-18 1.29599445382807e-17 1 27 6.75611243594189e-19 1.35122248718838e-18 1 28 1.14109064245456e-19 2.28218128490911e-19 1 29 1.16873117847802e-20 2.33746235695604e-20 1 30 1.8976619747484e-21 3.7953239494968e-21 1 31 3.5764135842975e-22 7.15282716859501e-22 1 32 6.97321815696626e-23 1.39464363139325e-22 1 33 1.26083974038722e-23 2.52167948077443e-23 1 34 1.30932598127292e-23 2.61865196254583e-23 1 35 4.72260564544272e-23 9.44521129088543e-23 1 36 3.004223867798e-23 6.008447735596e-23 1 37 2.31857484277915e-22 4.63714968555829e-22 1 38 5.93207523129173e-23 1.18641504625835e-22 1 39 1.04775510905661e-23 2.09551021811322e-23 1 40 3.49294976565681e-23 6.98589953131362e-23 1 41 3.74962883141827e-23 7.49925766283653e-23 1 42 6.58143025440552e-24 1.3162860508811e-23 1 43 1.98840660346123e-24 3.97681320692245e-24 1 44 8.0312891360986e-25 1.60625782721972e-24 1 45 2.05070097964059e-25 4.10140195928119e-25 1 46 3.29663622456245e-26 6.59327244912491e-26 1 47 1.2236440463811e-26 2.4472880927622e-26 1 48 2.23575485062035e-27 4.4715097012407e-27 1 49 4.06616126379041e-28 8.13232252758083e-28 1 50 1.90042443054267e-28 3.80084886108533e-28 1 51 2.83037081359115e-29 5.66074162718229e-29 1 52 7.97215989765368e-30 1.59443197953074e-29 1 53 2.88199067026211e-30 5.76398134052422e-30 1 54 7.74781271394615e-31 1.54956254278923e-30 1 55 2.66635827197622e-31 5.33271654395244e-31 1 56 4.62128078595882e-32 9.24256157191764e-32 1 57 9.609146446249e-32 1.9218292892498e-31 1 58 6.60939933288359e-32 1.32187986657672e-31 1 59 1.0663829875254e-32 2.13276597505081e-32 1 60 1.48968014096096e-32 2.97936028192192e-32 1 61 4.17964485263909e-32 8.35928970527819e-32 1 62 6.93844759399843e-33 1.38768951879969e-32 1 63 2.30414968229917e-33 4.60829936459834e-33 1 64 9.562560655017e-34 1.9125121310034e-33 1 65 1.9784863007931e-34 3.9569726015862e-34 1 66 9.00723732863456e-35 1.80144746572691e-34 1 67 4.05898437398682e-35 8.11796874797364e-35 1 68 2.12986405116737e-35 4.25972810233474e-35 1 69 7.64952371243945e-36 1.52990474248789e-35 1 70 9.87062331323163e-36 1.97412466264633e-35 1 71 5.15001381625357e-36 1.03000276325071e-35 1 72 8.75528514131646e-37 1.75105702826329e-36 1 73 3.26478515277502e-33 6.52957030555004e-33 1 74 7.3723787803947e-34 1.47447575607894e-33 1 75 1.37357277782799e-34 2.74714555565598e-34 1 76 2.54226909029318e-35 5.08453818058635e-35 1 77 1.986772713324e-35 3.97354542664799e-35 1 78 3.72785255470529e-36 7.45570510941057e-36 1 79 2.60733228306951e-36 5.21466456613901e-36 1 80 4.79835521986541e-36 9.59671043973082e-36 1 81 1.23645448073457e-12 2.47290896146915e-12 0.999999999998764 82 3.02848740339667e-11 6.05697480679334e-11 0.999999999969715 83 4.36450099723679e-11 8.72900199447358e-11 0.999999999956355 84 2.50094734700134e-09 5.00189469400268e-09 0.999999997499053 85 3.49549242900941e-09 6.99098485801882e-09 0.999999996504508 86 4.4890849855576e-09 8.97816997111519e-09 0.999999995510915 87 6.5905389121441e-09 1.31810778242882e-08 0.99999999340946 88 8.76420499810168e-09 1.75284099962034e-08 0.999999991235795 89 5.92332718001453e-09 1.18466543600291e-08 0.999999994076673 90 2.49453054110895e-07 4.98906108221789e-07 0.999999750546946 91 2.57214653132561e-07 5.14429306265122e-07 0.999999742785347 92 1.93234261643068e-07 3.86468523286135e-07 0.999999806765738 93 1.09331359105048e-07 2.18662718210097e-07 0.99999989066864 94 2.10292939376098e-06 4.20585878752197e-06 0.999997897070606 95 1.23481951248022e-06 2.46963902496044e-06 0.999998765180487 96 4.7468425184947e-06 9.4936850369894e-06 0.999995253157482 97 3.02067981358668e-06 6.04135962717336e-06 0.999996979320186 98 3.59036848804231e-06 7.18073697608463e-06 0.999996409631512 99 6.92941639184309e-05 0.000138588327836862 0.999930705836082 100 5.18668087591253e-05 0.000103733617518251 0.99994813319124 101 3.5006111633665e-05 7.001222326733e-05 0.999964993888366 102 2.82973731601422e-05 5.65947463202843e-05 0.99997170262684 103 1.96306152402374e-05 3.92612304804747e-05 0.99998036938476 104 0.000173120347064532 0.000346240694129065 0.999826879652935 105 0.000368306559231494 0.000736613118462987 0.999631693440769 106 0.000337006246275215 0.00067401249255043 0.999662993753725 107 0.00113918098385467 0.00227836196770934 0.998860819016145 108 0.000783138582303656 0.00156627716460731 0.999216861417696 109 0.00087461214687718 0.00174922429375436 0.999125387853123 110 0.000942394221271306 0.00188478844254261 0.999057605778729 111 0.284299354324875 0.568598708649751 0.715700645675125 112 0.276625271282974 0.553250542565948 0.723374728717026 113 0.314747284251795 0.629494568503589 0.685252715748205 114 0.630194027223841 0.739611945552318 0.369805972776159 115 0.587980135883651 0.824039728232699 0.412019864116349 116 0.573296443952387 0.853407112095227 0.426703556047613 117 0.627160291930589 0.745679416138823 0.372839708069411 118 0.712336053655483 0.575327892689033 0.287663946344517 119 0.68808728048002 0.623825439039961 0.311912719519981 120 0.669395922941208 0.661208154117585 0.330604077058793 121 0.647631219903236 0.704737560193527 0.352368780096764 122 0.613634511202948 0.772730977594105 0.386365488797052 123 0.611234236700441 0.777531526599118 0.388765763299559 124 0.568247051526733 0.863505896946534 0.431752948473267 125 0.522737504483039 0.954524991033922 0.477262495516961 126 0.664549594845406 0.670900810309188 0.335450405154594 127 0.695703183899056 0.608593632201889 0.304296816100944 128 0.706314038058669 0.587371923882663 0.293685961941331 129 0.67754918775698 0.644901624486041 0.322450812243021 130 0.732031956787203 0.535936086425595 0.267968043212797 131 0.693492478463205 0.613015043073589 0.306507521536795 132 0.652682212157672 0.694635575684657 0.347317787842328 133 0.638803222772066 0.722393554455869 0.361196777227934 134 0.61569087882769 0.768618242344619 0.38430912117231 135 0.641689626026312 0.716620747947375 0.358310373973688 136 0.622041892700936 0.755916214598128 0.377958107299064 137 0.603270604828269 0.793458790343462 0.396729395171731 138 0.552752725846341 0.894494548307318 0.447247274153659 139 0.691901387119879 0.616197225760242 0.308098612880121 140 0.843868459220197 0.312263081559606 0.156131540779803 141 0.810529971629029 0.378940056741943 0.189470028370972 142 0.86354977301988 0.272900453960241 0.136450226980121 143 0.867816766658281 0.264366466683438 0.132183233341719 144 0.832471940514479 0.335056118971042 0.167528059485521 145 0.928850423489508 0.142299153020985 0.0711495765104925 146 0.994525395061937 0.0109492098761263 0.00547460493806317 147 0.996685309926874 0.00662938014625175 0.00331469007312587 148 0.996006618167644 0.00798676366471176 0.00399338183235588 149 0.993959128147841 0.0120817437043174 0.00604087185215872 150 0.99373196456831 0.0125360708633784 0.0062680354316892 151 0.989708396815223 0.0205832063695547 0.0102916031847773 152 0.98661071373103 0.0267785725379416 0.0133892862689708 153 0.984279659740465 0.0314406805190704 0.0157203402595352 154 0.983145099521974 0.0337098009560515 0.0168549004780257 155 0.991672748444822 0.0166545031103564 0.00832725155517822 156 0.986205614156722 0.0275887716865552 0.0137943858432776 157 0.982892427863044 0.0342151442739117 0.0171075721369558 158 0.971658927031494 0.0566821459370128 0.0283410729685064 159 0.953605074197544 0.0927898516049129 0.0463949258024564 160 0.98992733169202 0.0201453366159616 0.0100726683079808 161 0.995750784976338 0.00849843004732419 0.0042492150236621 162 0.997126342613266 0.00574731477346882 0.00287365738673441 163 0.992675292291918 0.0146494154161643 0.00732470770808216 164 0.98862056469719 0.0227588706056177 0.0113794353028089 165 0.97399225475507 0.0520154904898615 0.0260077452449308 166 0.96077710921596 0.0784457815680814 0.0392228907840407 167 0.90893680146789 0.182126397064218 0.0910631985321092 168 0.86567771012253 0.268644579754941 0.134322289877471 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 108 0.666666666666667 NOK 5% type I error level 121 0.746913580246914 NOK 10% type I error level 125 0.771604938271605 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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