Workshop 8 Regression Analysis of Time Series

*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: Sat, 27 Nov 2010 10:26:04 +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/Nov/27/t12908537073v177t2hu0fme6d.htm/, Retrieved Sat, 27 Nov 2010 11:28:29 +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/Nov/27/t12908537073v177t2hu0fme6d.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 «

0 24 0 25 0 17 0 18 0 18 0 16 1 20 1 16 1 18 1 17 1 23 1 30 1 23 1 18 1 15 1 12 1 21 1 15 1 20 1 31 1 27 1 34 1 21 1 31 1 19 1 16 1 20 1 21 1 22 1 17 1 24 1 25 1 26 1 25 1 17 1 32 1 33 1 13 1 32 1 25 1 29 1 22 1 18 1 17 1 20 1 15 1 20 1 33 1 29 1 23 1 26 1 18 1 20 1 11 1 28 1 26 1 22 1 17 1 12 1 14 1 17 1 21 1 19 1 18 1 10 1 29 1 31 1 19 1 9 1 20 1 28 1 19 1 30 1 29 1 26 1 23 1 13 1 21 1 19 1 28 1 23 1 18 1 21 1 20 1 23 1 21 1 21 1 15 1 28 1 19 1 26 1 10 1 16 1 22 1 19 1 31 1 31 1 29 1 19 1 22 1 23 1 15 1 20 1 18 1 23 1 25 1 21 1 24 1 25 1 17 1 13 1 28 1 21 1 25 1 9 1 16 1 19 1 17 1 25 1 20 1 29 1 14 1 22 1 15 1 19 1 20 1 15 1 20 1 18 1 33 1 22 1 16 1 17 1 16 1 21 1 26 1 18 1 18 1 17 1 22 1 30 1 30 1 24 1 21 1 21 1 29 1 31 1 20 1 16 1 22 1 20 1 28 1 38 1 22 1 20 1 17 1 28 1 22 1 31

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 7 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Concernovermistakes[t] = + 21.995337995338 + 1.40151515151515Month[t] + 1.35395854145854M1[t] -2.64955877455878M2[t] -1.22450466200466M3[t] -3.47943722943723M4[t] -3.71372377622378M5[t] -4.33262570762571M6[t] -3.13625957375957M7[t] -2.4474691974692M8[t] -1.45098651348651M9[t] -0.992965367965368M10[t] -2.68879037629038M11[t] + 0.00351731601731602t + 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) 21.995337995338 2.899528 7.5858 0 0 Month 1.40151515151515 2.571152 0.5451 0.586528 0.293264 M1 1.35395854145854 2.209902 0.6127 0.541049 0.270524 M2 -2.64955877455878 2.209966 -1.1989 0.232517 0.116259 M3 -1.22450466200466 2.21008 -0.5541 0.580395 0.290198 M4 -3.47943722943723 2.251334 -1.5455 0.124405 0.062203 M5 -3.71372377622378 2.251272 -1.6496 0.101187 0.050594 M6 -4.33262570762571 2.251259 -1.9245 0.056246 0.028123 M7 -3.13625957375957 2.244117 -1.3975 0.164384 0.082192 M8 -2.4474691974692 2.243896 -1.0907 0.277204 0.138602 M9 -1.45098651348651 2.243725 -0.6467 0.518857 0.259429 M10 -0.992965367965368 2.243603 -0.4426 0.658732 0.329366 M11 -2.68879037629038 2.243529 -1.1985 0.232691 0.116346 t 0.00351731601731602 0.010483 0.3355 0.737719 0.36886 Multiple Linear Regression - Regression Statistics Multiple R 0.288504216420314 R-squared 0.0832346828922996 Adjusted R-squared 0.001041930324023 F-TEST (value) 1.01267666906711 F-TEST (DF numerator) 13 F-TEST (DF denominator) 145 p-value 0.442297652472542 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.71983678896478 Sum Squared Residuals 4743.89726939727 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.3528138528138 0.64718614718616 2 25 19.3528138528139 5.64718614718614 3 17 20.7813852813853 -3.78138528138528 4 18 18.52997002997 -0.529970029970031 5 18 18.2992007992008 -0.299200799200804 6 16 17.6838161838162 -1.68381618381619 7 20 20.2852147852148 -0.285214785214788 8 16 20.9775224775225 -4.97752247752248 9 18 21.9775224775225 -3.97752247752247 10 17 22.4390609390609 -5.43906093906094 11 23 20.7467532467532 2.25324675324675 12 30 23.4390609390609 6.56093906093906 13 23 24.7965367965368 -1.7965367965368 14 18 20.7965367965368 -2.7965367965368 15 15 22.2251082251082 -7.22510822510823 16 12 19.973692973693 -7.97369297369297 17 21 19.7429237429237 1.25707625707626 18 15 19.1275391275391 -4.12753912753913 19 20 20.3274225774226 -0.327422577422577 20 31 21.0197302697303 9.98026973026973 21 27 22.0197302697303 4.98026973026973 22 34 22.4812687312687 11.5187312687313 23 21 20.788961038961 0.211038961038961 24 31 23.4812687312687 7.51873126873127 25 19 24.8387445887446 -5.83874458874459 26 16 20.8387445887446 -4.83874458874459 27 20 22.267316017316 -2.26731601731602 28 21 20.0159007659008 0.984099234099234 29 22 19.7851315351315 2.21486846486846 30 17 19.1697469197469 -2.16974691974692 31 24 20.3696303696304 3.63036963036963 32 25 21.0619380619381 3.93806193806194 33 26 22.0619380619381 3.93806193806194 34 25 22.5234765234765 2.47652347652348 35 17 20.8311688311688 -3.83116883116883 36 32 23.5234765234765 8.47652347652348 37 33 24.8809523809524 8.11904761904762 38 13 20.8809523809524 -7.88095238095239 39 32 22.3095238095238 9.69047619047619 40 25 20.0581085581086 4.94189144189144 41 29 19.8273393273393 9.17266067266068 42 22 19.2119547119547 2.78804528804529 43 18 20.4118381618382 -2.41183816183816 44 17 21.1041458541459 -4.10414585414585 45 20 22.1041458541459 -2.10414585414585 46 15 22.5656843156843 -7.56568431568432 47 20 20.8733766233766 -0.873376623376624 48 33 23.5656843156843 9.43431568431568 49 29 24.9231601731602 4.07683982683982 50 23 20.9231601731602 2.07683982683983 51 26 22.3517316017316 3.6482683982684 52 18 20.1003163503164 -2.10031635031635 53 20 19.8695471195471 0.13045288045288 54 11 19.2541625041625 -8.2541625041625 55 28 20.454045954046 7.54595404595405 56 26 21.1463536463536 4.85364635364635 57 22 22.1463536463536 -0.146353646353647 58 17 22.6078921078921 -5.60789210789211 59 12 20.9155844155844 -8.91558441558442 60 14 23.6078921078921 -9.60789210789211 61 17 24.965367965368 -7.96536796536797 62 21 20.965367965368 0.0346320346320345 63 19 22.3939393939394 -3.39393939393939 64 18 20.1425241425241 -2.14252414252414 65 10 19.9117549117549 -9.9117549117549 66 29 19.2963702963703 9.7036297036297 67 31 20.4962537462537 10.5037462537463 68 19 21.1885614385614 -2.18856143856144 69 9 22.1885614385614 -13.1885614385614 70 20 22.6500999000999 -2.6500999000999 71 28 20.9577922077922 7.0422077922078 72 19 23.6500999000999 -4.6500999000999 73 30 25.0075757575758 4.99242424242424 74 29 21.0075757575758 7.99242424242424 75 26 22.4361471861472 3.56385281385281 76 23 20.1847319347319 2.81526806526806 77 13 19.9539627039627 -6.9539627039627 78 21 19.3385780885781 1.66142191142191 79 19 20.5384615384615 -1.53846153846154 80 28 21.2307692307692 6.76923076923077 81 23 22.2307692307692 0.769230769230769 82 18 22.6923076923077 -4.69230769230769 83 21 21 -5.43117525779457e-17 84 20 23.6923076923077 -3.69230769230769 85 23 25.0497835497836 -2.04978354978355 86 21 21.0497835497835 -0.0497835497835497 87 21 22.478354978355 -1.47835497835498 88 15 20.2269397269397 -5.22693972693973 89 28 19.9961704961705 8.0038295038295 90 19 19.3807858807859 -0.380785880785881 91 26 20.5806693306693 5.41933066933067 92 10 21.272977022977 -11.272977022977 93 16 22.272977022977 -6.27297702297702 94 22 22.7345154845155 -0.734515484515485 95 19 21.0422077922078 -2.04220779220779 96 31 23.7345154845155 7.26548451548451 97 31 25.0919913419913 5.90800865800866 98 29 21.0919913419913 7.90800865800866 99 19 22.5205627705628 -3.52056277056277 100 22 20.2691475191475 1.73085248085248 101 23 20.0383782883783 2.96162171162171 102 15 19.4229936729937 -4.42299367299367 103 20 20.6228771228771 -0.622877122877123 104 18 21.3151848151848 -3.31518481518482 105 23 22.3151848151848 0.684815184815185 106 25 22.7767232767233 2.22327672327672 107 21 21.0844155844156 -0.0844155844155845 108 24 23.7767232767233 0.223276723276723 109 25 25.1341991341991 -0.134199134199135 110 17 21.1341991341991 -4.13419913419913 111 13 22.5627705627706 -9.56277056277056 112 28 20.3113553113553 7.68864468864469 113 21 20.0805860805861 0.91941391941392 114 25 19.4652014652015 5.53479853479854 115 9 20.6650849150849 -11.6650849150849 116 16 21.3573926073926 -5.35739260739261 117 19 22.3573926073926 -3.35739260739261 118 17 22.8189310689311 -5.81893106893107 119 25 21.1266233766234 3.87337662337663 120 20 23.8189310689311 -3.81893106893107 121 29 25.1764069264069 3.82359307359307 122 14 21.1764069264069 -7.17640692640693 123 22 22.6049783549784 -0.604978354978355 124 15 20.3535631035631 -5.3535631035631 125 19 20.1227938727939 -1.12279387279387 126 20 19.5074092574093 0.492590742590742 127 15 20.7072927072927 -5.70729270729271 128 20 21.3996003996004 -1.3996003996004 129 18 22.3996003996004 -4.3996003996004 130 33 22.8611388611389 10.1388611388611 131 22 21.1688311688312 0.831168831168831 132 16 23.8611388611389 -7.86113886113886 133 17 25.2186147186147 -8.21861471861472 134 16 21.2186147186147 -5.21861471861472 135 21 22.6471861471861 -1.64718614718615 136 26 20.3957708957709 5.6042291042291 137 18 20.1650016650017 -2.16500166500167 138 18 19.549617049617 -1.54961704961705 139 17 20.7495004995005 -3.7495004995005 140 22 21.4418081918082 0.558191808191808 141 30 22.4418081918082 7.5581918081918 142 30 22.9033466533467 7.09665334665335 143 24 21.211038961039 2.78896103896104 144 21 23.9033466533467 -2.90334665334665 145 21 25.2608225108225 -4.26082251082251 146 29 21.2608225108225 7.73917748917749 147 31 22.6893939393939 8.31060606060606 148 20 20.4379786879787 -0.437978687978688 149 16 20.2072094572095 -4.20720945720946 150 22 19.5918248418248 2.40817515817516 151 20 20.7917082917083 -0.791708291708292 152 28 21.484015984016 6.51598401598402 153 38 22.484015984016 15.515984015984 154 22 22.9455544455544 -0.945554445554446 155 20 21.2532467532468 -1.25324675324675 156 17 23.9455544455544 -6.94555444555444 157 28 25.3030303030303 2.6969696969697 158 22 21.3030303030303 0.696969696969697 159 31 22.7316017316017 8.26839826839827 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.186018245597383 0.372036491194766 0.813981754402617 18 0.0871965062102043 0.174393012420409 0.912803493789796 19 0.0355563794863127 0.0711127589726255 0.964443620513687 20 0.14682813559267 0.293656271185341 0.85317186440733 21 0.085210864009095 0.17042172801819 0.914789135990905 22 0.111005306867716 0.222010613735432 0.888994693132284 23 0.198881959077544 0.397763918155088 0.801118040922456 24 0.184910538779579 0.369821077559157 0.815089461220421 25 0.24764662066856 0.49529324133712 0.75235337933144 26 0.280449515854607 0.560899031709213 0.719550484145393 27 0.217821319767851 0.435642639535703 0.782178680232149 28 0.17494415839584 0.349888316791681 0.82505584160416 29 0.125938773715723 0.251877547431446 0.874061226284277 30 0.0894230722895998 0.1788461445792 0.9105769277104 31 0.0643144472637689 0.128628894527538 0.935685552736231 32 0.0516832168581026 0.103366433716205 0.948316783141897 33 0.0357299117193272 0.0714598234386545 0.964270088280673 34 0.0311984262040937 0.0623968524081874 0.968801573795906 35 0.044919271689992 0.089838543379984 0.955080728310008 36 0.0362867212116559 0.0725734424233118 0.963713278788344 37 0.0516055594394931 0.103211118878986 0.948394440560507 38 0.0889468954655244 0.177893790931049 0.911053104534476 39 0.176743474006825 0.35348694801365 0.823256525993175 40 0.156589791502145 0.31317958300429 0.843410208497855 41 0.158716555885576 0.317433111771152 0.841283444114424 42 0.126660498348342 0.253320996696685 0.873339501651658 43 0.155236009913409 0.310472019826819 0.84476399008659 44 0.230857181527133 0.461714363054266 0.769142818472867 45 0.233179534966863 0.466359069933725 0.766820465033137 46 0.356837199447941 0.713674398895881 0.643162800552059 47 0.309232222690182 0.618464445380364 0.690767777309818 48 0.321300914400207 0.642601828800413 0.678699085599793 49 0.286292647787165 0.572585295574329 0.713707352212835 50 0.247420875825799 0.494841751651599 0.7525791241742 51 0.216646878193444 0.433293756386888 0.783353121806556 52 0.188135712363596 0.376271424727191 0.811864287636404 53 0.171207377920909 0.342414755841818 0.828792622079091 54 0.207618742651455 0.415237485302911 0.792381257348544 55 0.21997439388624 0.439948787772481 0.78002560611376 56 0.200120143745262 0.400240287490524 0.799879856254738 57 0.171574870031624 0.343149740063247 0.828425129968376 58 0.183107767218234 0.366215534436468 0.816892232781766 59 0.238536082883487 0.477072165766973 0.761463917116513 60 0.472239165721288 0.944478331442576 0.527760834278712 61 0.510104345831749 0.979791308336503 0.489895654168251 62 0.462378926274308 0.924757852548616 0.537621073725692 63 0.422650205563764 0.845300411127528 0.577349794436236 64 0.376324287268961 0.752648574537921 0.623675712731039 65 0.470269939124361 0.940539878248723 0.529730060875639 66 0.599819244168103 0.800361511663794 0.400180755831897 67 0.707193787174976 0.585612425650048 0.292806212825024 68 0.672472457940178 0.655055084119645 0.327527542059822 69 0.816442070232577 0.367115859534845 0.183557929767423 70 0.786331637341229 0.427336725317542 0.213668362658771 71 0.81787052437534 0.364258951249321 0.182129475624661 72 0.814804087063487 0.370391825873025 0.185195912936513 73 0.813766314253921 0.372467371492157 0.186233685746079 74 0.852412164728547 0.295175670542906 0.147587835271453 75 0.838778868144973 0.322442263710055 0.161221131855027 76 0.817808803326274 0.364382393347452 0.182191196673726 77 0.824391633209693 0.351216733580614 0.175608366790307 78 0.795752173958979 0.408495652082043 0.204247826041021 79 0.770892061565009 0.458215876869981 0.229107938434991 80 0.804835125162985 0.39032974967403 0.195164874837015 81 0.771694544327323 0.456610911345354 0.228305455672677 82 0.752926712349396 0.494146575301208 0.247073287650604 83 0.712592638462758 0.574814723074483 0.287407361537242 84 0.689662501955171 0.620674996089658 0.310337498044829 85 0.6465874253648 0.706825149270401 0.353412574635201 86 0.60076183692244 0.79847632615512 0.39923816307756 87 0.552448608346904 0.895102783306193 0.447551391653096 88 0.536091274300361 0.927817451399278 0.463908725699639 89 0.60251954379202 0.79496091241596 0.39748045620798 90 0.553556383964299 0.892887232071403 0.446443616035701 91 0.610928835334718 0.778142329330565 0.389071164665282 92 0.701056376288969 0.597887247422063 0.298943623711031 93 0.710059397890488 0.579881204219024 0.289940602109512 94 0.669332396960966 0.661335206078069 0.330667603039034 95 0.625504603458845 0.748990793082311 0.374495396541155 96 0.724772941352192 0.550454117295617 0.275227058647808 97 0.760579220737819 0.478841558524362 0.239420779262181 98 0.844832340115653 0.310335319768693 0.155167659884347 99 0.816300972913863 0.367398054172274 0.183699027086137 100 0.785820189823091 0.428359620353818 0.214179810176909 101 0.786965171018474 0.426069657963051 0.213034828981526 102 0.761415260144725 0.47716947971055 0.238584739855275 103 0.769935924738837 0.460128150522327 0.230064075261163 104 0.731124767503707 0.537750464992585 0.268875232496293 105 0.688008161639485 0.623983676721029 0.311991838360515 106 0.65140953162603 0.697180936747941 0.348590468373971 107 0.60181931372742 0.79636137254516 0.39818068627258 108 0.634958372140219 0.730083255719562 0.365041627859781 109 0.611472555133294 0.777054889733411 0.388527444866706 110 0.567233800668374 0.865532398663252 0.432766199331626 111 0.636132269379813 0.727735461240374 0.363867730620187 112 0.730728249134147 0.538543501731706 0.269271750865853 113 0.72971658933161 0.54056682133678 0.27028341066839 114 0.776021807021449 0.447956385957103 0.223978192978551 115 0.797347917393948 0.405304165212104 0.202652082606052 116 0.768649336354943 0.462701327290114 0.231350663645057 117 0.757497437827841 0.485005124344318 0.242502562172159 118 0.782468206890621 0.435063586218757 0.217531793109379 119 0.780304698484758 0.439390603030485 0.219695301515242 120 0.771786512645749 0.456426974708502 0.228213487354251 121 0.86125170885184 0.277496582296321 0.13874829114816 122 0.842581844891156 0.314836310217688 0.157418155108844 123 0.799985468136654 0.400029063726691 0.200014531863345 124 0.779205079248669 0.441589841502663 0.220794920751331 125 0.754803708784304 0.490392582431391 0.245196291215696 126 0.710301171609216 0.579397656781569 0.289698828390784 127 0.652143204950105 0.695713590099789 0.347856795049894 128 0.583959173519173 0.832081652961654 0.416040826480827 129 0.770170177431137 0.459659645137725 0.229829822568863 130 0.861160993906304 0.277678012187392 0.138839006093696 131 0.824618292418221 0.350763415163558 0.175381707581779 132 0.775192619666197 0.449614760667607 0.224807380333803 133 0.742933253799374 0.514133492401252 0.257066746200626 134 0.757388024431814 0.485223951136372 0.242611975568186 135 0.836470666407129 0.327058667185742 0.163529333592871 136 0.822722785065846 0.354554429868308 0.177277214934154 137 0.751127561136396 0.497744877727207 0.248872438863604 138 0.676297219755388 0.647405560489225 0.323702780244612 139 0.579103675929108 0.841792648141784 0.420896324070892 140 0.545079109696102 0.909841780607796 0.454920890303898 141 0.660976805407795 0.678046389184409 0.339023194592205 142 0.605059311031694 0.789881377936613 0.394940688968306 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 5 0.0396825396825397 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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