*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 23 Nov 2010 14:16:38 +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/23/t12905217519monfm5oc1a3kfo.htm/, Retrieved Tue, 23 Nov 2010 15:16:13 +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/23/t12905217519monfm5oc1a3kfo.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 «

9 5.5 6 5.33 12 9 3.5 4 5.56 11 9 8.5 4 3.78 14 9 5 4 4.00 12 9 6 4.5 4.00 21 9 6 3.5 3.56 12 9 5.5 2 4.44 22 9 5.5 5.5 3.56 11 9 6 3.5 4.00 10 9 6.5 3.5 3.78 13 9 7 6 5.11 10 9 8 5 6.67 8 9 5.5 5 5.11 15 9 5 4 4.00 14 9 5.5 4 3.33 10 9 7.5 2 2.67 14 9 4.5 4.5 4.67 14 9 5.5 4 3.33 11 9 8.5 3.5 4.44 10 9 8.5 5.5 6.89 13 9 5.5 4.5 6.00 7 9 9 5.5 7.56 14 9 7 6.5 4.67 12 9 5 4 6.89 14 9 5.5 4 4.22 11 9 7.5 4.5 3.56 9 9 7.5 3 4.44 11 9 6.5 4.5 4.67 15 9 8 4.5 4.89 14 9 6.5 3 3.78 13 9 4.5 3 5.33 9 9 9 8 5.56 15 9 9 2.5 5.78 10 9 6 3.5 5.56 11 9 8.5 4.5 3.78 13 9 4.5 3 7.11 8 9 4.5 3 7.33 20 9 6 2.5 2.89 12 9 9 6 7.11 10 9 6 3.5 5.56 10 9 9 5 6.44 9 9 7 4.5 4.89 14 9 7.5 4 4.00 8 9 8 2.5 3.78 14 9 5 4 4.44 11 9 5.5 4 3.33 13 9 7 5 4.44 9 9 4.5 3 7.33 11 9 6 4 6.44 15 9 8.5 3.5 5.11 11 9 2.5 2 5.78 10 9 6 4 4.00 14 9 6 4 4.44 18 10 3 2 2.44 14 10 12 10 6.22 11 10 6 4 5.78 12 10 6 4 4.89 13 10 7 3 3.78 9 10 3.5 2 2.67 10 10 6.5 4 3.11 15 10 6 4.5 3.78 20 10 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 15 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Depression[t] = + 9.24355550579304 + 0.493286378792208Month[t] -0.00260207016403216Expect[t] -0.0557478262810441Criticism[t] -0.214965647664329Concerns[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) 9.24355550579304 3.305874 2.7961 0.005832 0.002916 Month 0.493286378792208 0.30908 1.596 0.112542 0.056271 Expect -0.00260207016403216 0.183669 -0.0142 0.988715 0.494357 Criticism -0.0557478262810441 0.232612 -0.2397 0.810912 0.405456 Concerns -0.214965647664329 0.210983 -1.0189 0.30986 0.15493 Multiple Linear Regression - Regression Statistics Multiple R 0.161389265252687 R-squared 0.0260464949388022 Adjusted R-squared 0.000749001300848984 F-TEST (value) 1.02960772761003 F-TEST (DF numerator) 4 F-TEST (DF denominator) 154 p-value 0.393886977846912 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.1442247281482 Sum Squared Residuals 1522.46696772919 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12 12.1885676692836 -0.18856766928365 2 11 12.2558253632109 -1.25582536321095 3 14 12.6254538652333 1.37454613476670 4 12 12.5872686683213 -0.587268668321265 5 21 12.5567926850167 8.44320731498328 6 12 12.7071253962701 -0.70712539627006 7 22 12.6028784008290 9.39712159917097 8 11 12.59693077879 -1.59693077878999 9 10 12.6125405112978 -2.61254051129776 10 13 12.6585319187019 0.341468081298109 11 10 12.2319570065237 -2.23195700652371 12 8 11.9497563522844 -3.94975635228437 13 15 12.2916079380508 2.7083920619492 14 14 12.5872686683213 1.41273133167873 15 10 12.7299946171743 -2.72999461717435 16 14 12.9781634568668 1.02183654313317 17 14 12.4166688063277 1.58333119367234 18 11 12.7299946171744 -1.72999461717435 19 10 12.5114504509154 -2.51145045091537 20 13 11.8732889615757 1.12671103842433 21 7 12.1281624247701 -5.12816242477007 22 14 11.7279609425586 2.27203905744144 23 12 12.2986679783555 -0.298667978355490 24 14 11.9660179465714 2.03398205342865 25 11 12.5386751907531 -1.53867519075310 26 9 12.6474744647430 -3.64747446474297 27 11 12.5419264342199 -1.54192643421992 28 15 12.4114646659996 2.58853533400041 29 14 12.3602691182674 1.63973088173261 30 13 12.6864058318424 0.313594168157587 31 9 12.3584132182908 -3.35841321829077 32 15 12.0185226721846 2.98147732781539 33 10 12.2778432742442 -2.27784327424420 34 11 12.2771941009414 -1.27719410094140 35 13 12.5975799520928 0.402420047907217 36 8 11.9757743654483 -3.97577436544826 37 20 11.9284819229621 8.0715180770379 38 12 12.9069002064862 -0.906900206486205 39 10 11.796821570867 -1.79682157086698 40 10 12.2771941009414 -2.2771941009414 41 9 11.9965963810831 -2.99659638108313 42 14 12.3628711884314 1.63712881156857 43 8 12.5807634929112 -4.58076349291119 44 14 12.7103766397369 1.28962336026311 45 11 12.4926837833490 -1.49268378334896 46 13 12.7299946171744 0.270005382825651 47 9 12.4317318167399 -3.43173181673985 48 11 11.9284819229621 -0.928481922962108 49 15 12.0601504178563 2.93984958214373 50 11 12.3674234669803 -1.36742346698027 51 10 12.3226306434509 -2.32263064345093 52 14 12.5846665981572 1.41533340184277 53 18 12.4900817131849 5.50991828681507 54 14 13.5326012503600 0.467398749640019 55 11 12.2506298604642 -1.25062986046417 56 12 12.6953141241069 -0.695314124106936 57 13 12.8866335505282 0.113366449471811 58 9 13.1783911755526 -4.17839117555261 59 10 13.4818581163152 -3.48185811631517 60 15 13.2679713682887 1.73202863171132 61 20 13.0973715062951 6.90262849370493 62 12 12.9883727842134 -0.98837278421337 63 12 13.0559323774398 -1.05593237743978 64 14 13.0552832041370 0.944716795863015 65 13 13.5455146042955 -0.545514604295531 66 11 12.6409616413161 -1.64096164131609 67 17 12.4580032902815 4.54199670971845 68 12 13.0293594993813 -1.02935949938127 69 13 13.5662341687232 -0.566234168723177 70 14 12.9846691270592 1.01533087294085 71 13 12.6286031522752 0.371396847724847 72 15 13.0624375528499 1.93756244715014 73 13 12.4722176792991 0.527782320700887 74 10 12.4620088467348 -2.46200884673482 75 11 12.7471588451419 -1.74715884514193 76 19 12.8393411080420 6.16065889195796 77 13 13.3710116370559 -0.371011637055876 78 17 12.9034500097098 4.09654999029021 79 13 13.0332626046273 -0.0332626046273221 80 9 12.6551760303337 -3.65517603033366 81 11 12.7822922466790 -1.78229224667898 82 10 13.0792540120315 -3.07925401203146 83 9 12.9326249579323 -3.93262495793233 84 12 12.9224161253680 -0.922416125368029 85 12 12.9281669877917 -0.928166987791667 86 13 12.9565957658268 0.0434042341732008 87 13 13.0188487675179 -0.0188487675179238 88 12 13.2258830661306 -1.22588306613059 89 15 12.4282816199634 2.57171838003657 90 22 13.0585344476038 8.94146555239619 91 13 12.6927120539429 0.307287946057096 92 15 13.5215437964011 1.47845620359894 93 13 13.2600627065894 -0.260062706589362 94 15 12.9384782715632 2.06152172843682 95 10 12.9762137432643 -2.97621374326426 96 11 12.3334972868993 -1.33349728689930 97 16 12.4262262718950 3.57377372810502 98 11 12.4341349335943 -1.43413493359429 99 11 13.0585344476038 -2.05853444760381 100 10 12.8853325154462 -2.88533251544617 101 10 12.7796901765149 -2.77969017651494 102 16 13.2777277871656 2.72227221283441 103 12 12.9185130201220 -0.91851302012198 104 11 13.0183020454224 -2.01830204542235 105 16 12.784894316843 3.21510568315699 106 19 12.8275293410967 6.17247065890333 107 11 12.9644019763189 -1.96440197631890 108 16 12.7349998041928 3.26500019580718 109 15 13.1483681007177 1.85163189928232 110 24 13.6742796245088 10.3257203754912 111 14 13.8377251377896 0.162274862210421 112 15 12.9773158250367 2.02268417496331 113 11 13.3474937376310 -2.34749373763103 114 15 13.1444649954716 1.85553500452836 115 12 13.9227530519768 -1.92275305197681 116 10 13.7481449450535 -3.74814494505351 117 14 13.5174417378454 0.482558262154581 118 13 13.6781827297549 -0.678182729754897 119 9 13.2041159269987 -4.20411592699873 120 15 13.5933542636595 1.4066457363405 121 15 13.1647240034129 1.83527599658714 122 14 13.7904326953034 0.209567304696573 123 11 13.2936961197348 -2.2936961197348 124 8 13.7788203764499 -5.77882037644989 125 11 13.5570249667241 -2.55702496672409 126 11 13.4701492953593 -2.47014929535927 127 8 13.8293640624029 -5.82936406240287 128 10 13.4779555058514 -3.47795550585136 129 11 13.5407633724371 -2.5407633724371 130 13 12.8567047841015 0.143295215898549 131 11 13.2949971548168 -2.29499715481682 132 20 13.6658242407140 6.33417575928604 133 10 13.7034545727314 -3.70345457273139 134 15 13.7812229985221 1.21877700147791 135 12 13.4272123718066 -1.42721237180655 136 14 13.1224443959620 0.877555604038027 137 23 13.6269871820227 9.3730128179773 138 14 13.5420644075191 0.457935592480886 139 16 13.5906578850873 2.40934211491272 140 11 13.2405503636178 -2.24055036361779 141 12 12.9733102685834 -0.973310268583418 142 10 12.9376301449508 -2.9376301449508 143 14 12.9352356656776 1.06476433432236 144 12 13.5173392866382 -1.51733928663820 145 12 13.3370854569749 -1.33708545697490 146 11 13.1037720368037 -2.10377203680375 147 12 12.9156095454411 -0.915609545441137 148 13 13.5058294189919 -0.505829418991885 149 11 13.6379503275734 -2.63795032757343 150 19 13.3215700328753 5.67842996712468 151 12 13.4500815927108 -1.45008159271084 152 17 13.0888114775988 3.91118852240122 153 9 12.6329564775144 -3.63295647751441 154 12 13.4330656854374 -1.43306568543741 155 19 13.3268766244106 5.67312337558939 156 18 13.6729785894268 4.32702141057317 157 15 13.0953166530089 1.90468334699114 158 14 13.3202689977933 0.679731002206694 159 11 12.7178900832935 -1.71789008329345 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.980771638345918 0.038456723308165 0.0192283616540825 9 0.987695177828852 0.0246096443422955 0.0123048221711478 10 0.977801610586647 0.0443967788267053 0.0221983894133526 11 0.963569994217362 0.0728600115652753 0.0364300057826377 12 0.959984339774789 0.0800313204504223 0.0400156602252111 13 0.954570021246807 0.0908599575063869 0.0454299787531934 14 0.928252451758952 0.143495096482095 0.0717475482410476 15 0.935662134448091 0.128675731103818 0.0643378655519088 16 0.915130911819663 0.169738176360673 0.0848690881803367 17 0.88139965530035 0.237200689399300 0.118600344699650 18 0.858228433835611 0.283543132328778 0.141771566164389 19 0.839059811245035 0.321880377509929 0.160940188754965 20 0.814140152849397 0.371719694301207 0.185859847150603 21 0.885371119833343 0.229257760333313 0.114628880166657 22 0.879051358789928 0.241897282420145 0.120948641210072 23 0.847587888176407 0.304824223647186 0.152412111823593 24 0.808767107634988 0.382465784730024 0.191232892365012 25 0.775853044839256 0.448293910321487 0.224146955160744 26 0.771037761993227 0.457924476013546 0.228962238006773 27 0.744105546995203 0.511788906009594 0.255894453004797 28 0.727251280167363 0.545497439665274 0.272748719832637 29 0.690239729564482 0.619520540871036 0.309760270435518 30 0.634353435874214 0.731293128251572 0.365646564125786 31 0.67944895967099 0.64110208065802 0.32055104032901 32 0.693070766984523 0.613858466030953 0.306929233015477 33 0.673004362116431 0.653991275767138 0.326995637883569 34 0.626587212002159 0.746825575995682 0.373412787997841 35 0.570813731911615 0.85837253617677 0.429186268088385 36 0.580083053146592 0.839833893706816 0.419916946853408 37 0.826786108696957 0.346427782606087 0.173213891303043 38 0.791459918639452 0.417080162721095 0.208540081360548 39 0.763164664940106 0.473670670119788 0.236835335059894 40 0.743317049199077 0.513365901601845 0.256682950800923 41 0.731840176988317 0.536319646023366 0.268159823011683 42 0.698858865101052 0.602282269797896 0.301141134898948 43 0.737177112766546 0.525645774466908 0.262822887233454 44 0.702369600046357 0.595260799907285 0.297630399953643 45 0.667659718987026 0.664680562025948 0.332340281012974 46 0.61960488966229 0.76079022067542 0.38039511033771 47 0.624159126521769 0.751681746956462 0.375840873478231 48 0.583152949339276 0.833694101321448 0.416847050660724 49 0.570332855874994 0.859334288250012 0.429667144125006 50 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0.204036086727975 0.897981956636013 103 0.0955648932696385 0.191129786539277 0.904435106730362 104 0.107462801011949 0.214925602023898 0.892537198988051 105 0.0941334797198085 0.188266959439617 0.905866520280192 106 0.128170935062321 0.256341870124641 0.87182906493768 107 0.127408540751861 0.254817081503721 0.87259145924814 108 0.110836560233572 0.221673120467144 0.889163439766428 109 0.095701034192265 0.19140206838453 0.904298965807735 110 0.416982750530948 0.833965501061896 0.583017249469052 111 0.369424630178137 0.738849260356275 0.630575369821863 112 0.340767655411976 0.681535310823953 0.659232344588024 113 0.318431028157304 0.636862056314607 0.681568971842696 114 0.283484521505919 0.566969043011839 0.71651547849408 115 0.255802707585252 0.511605415170505 0.744197292414748 116 0.284471943373689 0.568943886747379 0.71552805662631 117 0.241456159701519 0.482912319403038 0.758543840298481 118 0.204149716024803 0.408299432049606 0.795850283975197 119 0.232114698683129 0.464229397366258 0.767885301316871 120 0.205218556241390 0.410437112482781 0.79478144375861 121 0.210339272145149 0.420678544290298 0.78966072785485 122 0.172732564431027 0.345465128862054 0.827267435568973 123 0.154521300318496 0.309042600636992 0.845478699681504 124 0.214814867089528 0.429629734179056 0.785185132910472 125 0.19269944491365 0.3853988898273 0.80730055508635 126 0.192351875161353 0.384703750322707 0.807648124838647 127 0.350040814255519 0.700081628511038 0.649959185744481 128 0.370598971592270 0.741197943184541 0.62940102840773 129 0.396829366284867 0.793658732569733 0.603170633715133 130 0.378359717576874 0.756719435153747 0.621640282423126 131 0.351585209243346 0.703170418486693 0.648414790756654 132 0.439121550227745 0.87824310045549 0.560878449772255 133 0.56341002323029 0.873179953539421 0.436589976769711 134 0.503483738048521 0.993032523902959 0.496516261951479 135 0.468468029222388 0.936936058444776 0.531531970777612 136 0.402658586872526 0.805317173745052 0.597341413127474 137 0.76845811952334 0.46308376095332 0.23154188047666 138 0.709730843463606 0.580538313072787 0.290269156536394 139 0.653101299836226 0.693797400327547 0.346898700163773 140 0.610071883792312 0.779856232415376 0.389928116207688 141 0.546308465474531 0.907383069050938 0.453691534525469 142 0.492027083953054 0.984054167906108 0.507972916046946 143 0.418132524161946 0.836265048323891 0.581867475838054 144 0.337276773541877 0.674553547083753 0.662723226458123 145 0.330352711222166 0.660705422444332 0.669647288777834 146 0.248397216102347 0.496794432204693 0.751602783897653 147 0.175015640006478 0.350031280012955 0.824984359993522 148 0.120747282010672 0.241494564021345 0.879252717989327 149 0.225327650624310 0.450655301248619 0.77467234937569 150 0.250821764923187 0.501643529846374 0.749178235076813 151 0.257020965074454 0.514041930148907 0.742979034925546 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 3 0.0208333333333333 OK 10% type I error level 6 0.0416666666666667 OK

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/10vekg1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/10vekg1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/1ovnm1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/1ovnm1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/2ovnm1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/2ovnm1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/3z5mp1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/3z5mp1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/4z5mp1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/4z5mp1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/5z5mp1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/5z5mp1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/6re3a1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/6re3a1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/7re3a1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/7re3a1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/8knlv1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/8knlv1290521781.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/9knlv1290521781.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/23/t12905217519monfm5oc1a3kfo/9knlv1290521781.ps (open in new window)

Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Do not include Seasonal 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') }

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Software written by Ed van Stee & Patrick Wessa

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