Multiple Regression Analysis with Interaction

*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: Thu, 16 Dec 2010 14:56:54 +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/16/t1292511428opihn8hirgzir49.htm/, Retrieved Thu, 16 Dec 2010 15:57:11 +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/16/t1292511428opihn8hirgzir49.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 13 26 0 9 0 15 0 25 0 25 0 0 16 20 0 9 0 15 0 25 0 24 0 0 19 21 0 9 0 14 0 19 0 21 0 1 15 31 31 14 14 10 10 18 18 23 23 0 14 21 0 8 0 10 0 18 0 17 0 0 13 18 0 8 0 12 0 22 0 19 0 0 19 26 0 11 0 18 0 29 0 18 0 0 15 22 0 10 0 12 0 26 0 27 0 0 14 22 0 9 0 14 0 25 0 23 0 0 15 29 0 15 0 18 0 23 0 23 0 1 16 15 15 14 14 9 9 23 23 29 29 0 16 16 0 11 0 11 0 23 0 21 0 1 16 24 24 14 14 11 11 24 24 26 26 0 17 17 0 6 0 17 0 30 0 25 0 1 15 19 19 20 20 8 8 19 19 25 25 1 15 22 22 9 9 16 16 24 24 23 23 0 20 31 0 10 0 21 0 32 0 26 0 1 18 28 28 8 8 24 24 30 30 20 20 0 16 38 0 11 0 21 0 29 0 29 0 1 16 26 26 14 14 14 14 17 17 24 24 0 19 25 0 11 0 7 0 25 0 23 0 0 16 25 0 16 0 18 0 26 0 24 0 1 17 29 29 14 14 18 18 26 26 30 30 0 17 28 0 11 0 13 0 25 0 22 0 1 16 15 15 11 11 11 11 23 23 22 22 0 15 18 0 12 0 13 0 21 0 13 0 1 14 21 21 9 9 13 13 19 19 24 24 0 15 25 0 7 0 18 0 35 0 17 0 1 12 23 23 13 13 14 14 19 19 24 24 0 14 23 0 10 0 12 0 20 0 21 0 0 16 19 0 9 0 9 0 21 0 23 0 1 14 18 18 9 9 12 12 21 21 24 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 Learning[t] = + 13.5078628117885 -5.18203521944939Gender[t] -0.0012444168094538Concern[t] + 0.000772116482002167Concern_G[t] -0.216792193652821Doubts[t] -0.0504114143255668Doubts_G[t] + 0.0604243877511438Expectations[t] + 0.0863311703675794Expectations_G[t] + 0.0249723220996845Standards[t] + 0.0146764424024256Standards_G[t] + 0.11992279614248Organization[t] + 0.177189346574434Organization_G[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) 13.5078628117885 1.633788 8.2678 0 0 Gender -5.18203521944939 2.889215 -1.7936 0.075102 0.037551 Concern -0.0012444168094538 0.045505 -0.0273 0.978223 0.489112 Concern_G 0.000772116482002167 0.072392 0.0107 0.991506 0.495753 Doubts -0.216792193652821 0.087006 -2.4917 0.013916 0.006958 Doubts_G -0.0504114143255668 0.138545 -0.3639 0.716526 0.358263 Expectations 0.0604243877511438 0.068505 0.882 0.37931 0.189655 Expectations_G 0.0863311703675794 0.107957 0.7997 0.425291 0.212645 Standards 0.0249723220996845 0.056538 0.4417 0.659414 0.329707 Standards_G 0.0146764424024256 0.096957 0.1514 0.879908 0.439954 Organization 0.11992279614248 0.056605 2.1186 0.035944 0.017972 Organization_G 0.177189346574434 0.104356 1.6979 0.091808 0.045904 Multiple Linear Regression - Regression Statistics Multiple R 0.498534553974114 R-squared 0.248536701506169 Adjusted R-squared 0.18775658177505 F-TEST (value) 4.08911174584148 F-TEST (DF numerator) 11 F-TEST (DF denominator) 136 p-value 3.43259806045992e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.90452270012216 Sum Squared Residuals 493.300113278163 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13 16.0531220041886 -3.05312200418857 2 16 15.9406657089028 0.0593342910971947 3 19 15.3693945833167 3.63060541668334 4 15 13.5851483952049 1.41485160479509 5 14 14.8398257192953 -0.839825719295306 6 13 15.3041426259097 -2.30414262590966 7 19 15.0612404955377 3.93875950446226 8 15 15.9248522289048 -0.924852228904775 9 14 15.7578296913903 -1.75782969139028 10 15 14.6401185186124 0.359881481387614 11 16 15.4268663211374 0.573133678862553 12 16 14.8606484052036 1.1393515947964 13 16 14.8644390707792 1.1355609292208 14 17 16.9604087224328 0.039591277567177 15 15 12.3279562849625 2.6720437150375 16 15 16.0438430737689 -1.04384307376891 17 20 16.4873831038356 3.51261689616439 18 18 16.8288135035943 1.17118649640571 19 16 16.546731414645 -0.546731414645001 20 16 14.4319955075319 1.56800449246813 21 19 14.8975413393983 4.10245866060173 22 16 14.6231437546389 1.37685624536109 23 17 17.1571125758449 -0.157112575844878 24 17 15.1364316193343 1.86356838066571 25 16 14.4422032622917 1.55779673770834 26 15 13.752889140095 1.24711085990505 27 14 15.7029170199466 -1.70291701994656 28 15 15.9595648234141 -0.9595648234141 29 12 14.7799135454968 -2.77991354549683 30 14 15.0542371026423 -1.05423710264234 31 16 15.3595517146642 0.640448285335816 32 14 15.6368758918144 -1.63687589181441 33 10 12.8146808555192 -2.81468085551924 34 14 14.1653442799207 -0.165344279920668 35 16 16.3919005879631 -0.391900587963088 36 16 14.2683255840356 1.73167441596444 37 16 13.1721011370865 2.82789886291348 38 14 15.411477804569 -1.411477804569 39 20 18.8423355659075 1.15766443409246 40 14 14.8520369388871 -0.852036938887054 41 14 15.1508572331343 -1.15085723313427 42 11 14.6214740981898 -3.62147409818977 43 15 15.705479346406 -0.70547934640602 44 16 15.6287104213874 0.371289578612649 45 14 14.9763482467373 -0.97634824673731 46 16 14.4342291024677 1.56577089753228 47 14 14.8728994176262 -0.872899417626203 48 12 15.1297153084676 -3.1297153084676 49 16 15.0918911031355 0.908108896864501 50 9 11.9158537785387 -2.91585377853869 51 14 14.5857001682823 -0.585700168282283 52 16 15.6015222020432 0.398477797956813 53 16 15.1798509255626 0.820149074437405 54 15 14.6261208698299 0.373879130170114 55 16 15.0222668147175 0.977733185282478 56 12 13.2984595523681 -1.29845955236812 57 16 16.6765614542336 -0.67656145423362 58 16 16.0722750336477 -0.07227503364772 59 14 16.2646917060952 -2.2646917060952 60 16 13.2325416404131 2.76745835958686 61 17 16.8361671992221 0.163832800777918 62 18 14.8261156707186 3.1738843292814 63 18 16.1061398939031 1.89386010609686 64 12 14.7437248893534 -2.7437248893534 65 16 16.0534066283651 -0.0534066283651058 66 10 14.4966156603232 -4.49661566032317 67 14 13.292452360104 0.707547639896045 68 18 15.6149216824867 2.38507831751334 69 18 16.668436454512 1.33156354548796 70 16 15.6339572344787 0.366042765521279 71 16 15.6020987603879 0.397901239612105 72 16 14.7839126694337 1.2160873305663 73 13 14.3384345626706 -1.33843456267063 74 16 14.3928936470929 1.60710635290705 75 16 14.9473897889577 1.05261021104232 76 20 16.380984461519 3.61901553848102 77 16 15.3104272321948 0.68957276780518 78 15 10.9290781568249 4.07092184317509 79 15 15.4802570407779 -0.48025704077787 80 16 15.805894265004 0.194105734996024 81 14 14.3509339906632 -0.350933990663188 82 15 13.8047118546161 1.19528814538389 83 12 15.1105861331594 -3.11058613315945 84 17 16.1617266527635 0.838273347236485 85 16 15.3853065667351 0.614693433264925 86 15 13.6865999586281 1.31340004137194 87 13 14.6140518772852 -1.61405187728519 88 16 15.8849005509398 0.115099449060164 89 16 15.409999304267 0.590000695733015 90 16 16.1124909255941 -0.112490925594077 91 16 15.7908328019193 0.209167198080687 92 14 15.2020660515986 -1.20206605159858 93 16 14.4486170845089 1.5513829154911 94 16 15.3423470593078 0.657652940692245 95 20 16.2178822903068 3.78211770969323 96 15 16.104040623777 -1.10404062377701 97 16 14.4157973018649 1.58420269813505 98 13 13.452612607659 -0.452612607659024 99 17 15.8974299260681 1.10257007393194 100 16 14.2896430821777 1.71035691782226 101 12 13.6167381287677 -1.61673812876773 102 16 15.1667765307621 0.83322346923789 103 16 15.2917006634984 0.708299336501571 104 17 15.4482119187887 1.55178808121129 105 13 13.0159927941607 -0.0159927941606898 106 12 15.8202118554908 -3.82021185549084 107 18 16.1641144484612 1.83588555153881 108 14 14.2201676952428 -0.220167695242777 109 14 14.7562455420886 -0.756245542088608 110 13 14.265187487489 -1.26518748748898 111 16 15.4899918861172 0.510008113882762 112 13 13.3297013635071 -0.32970136350707 113 16 15.3045397536833 0.695460246316715 114 13 15.1193876849296 -2.11938768492958 115 16 15.8800287013318 0.119971298668177 116 15 14.9033110565 0.0966889434999663 117 16 15.4593989287941 0.540601071205911 118 15 14.8502854566158 0.149714543384221 119 17 15.7866410815481 1.21335891845187 120 15 15.9176792750186 -0.917679275018601 121 12 14.1741137132631 -2.17411371326315 122 16 14.207439401431 1.79256059856898 123 10 14.5235130169568 -4.52351301695684 124 16 14.8493169612494 1.15068303875062 125 14 14.3192684973494 -0.319268497349389 126 15 16.2180117772926 -1.2180117772926 127 13 14.3070819105776 -1.30708191057757 128 15 15.5381897230794 -0.538189723079434 129 11 14.1941775385563 -3.19417753855626 130 12 14.468898638148 -2.46889863814797 131 16 16.0331207011334 -0.0331207011333533 132 15 15.597652741249 -0.597652741248951 133 17 15.4224582878409 1.57754171215911 134 16 15.6484252428481 0.351574757151937 135 10 15.1378886559636 -5.13788865596359 136 18 14.2888450012249 3.7111549987751 137 13 14.2309861584759 -1.23098615847592 138 15 14.6392346135214 0.360765386478589 139 16 14.4422032622917 1.55779673770834 140 16 15.1537033570847 0.846296642915302 141 14 13.9797910456883 0.0202089543116723 142 10 13.7355128058378 -3.73551280583782 143 17 16.1617266527635 0.838273347236485 144 13 14.7976131981177 -1.79761319811766 145 15 15.9176792750186 -0.917679275018601 146 16 15.9416975058924 0.0583024941075791 147 12 15.5051601924463 -3.50516019244631 148 13 14.0706346238246 -1.07063462382465 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.940764351349273 0.118471297301455 0.0592356486507273 16 0.885160102594755 0.22967979481049 0.114839897405245 17 0.915293159722874 0.169413680554253 0.0847068402771263 18 0.86012852353987 0.27974295292026 0.13987147646013 19 0.790627912449379 0.418744175101242 0.209372087550621 20 0.718400794920581 0.563198410158837 0.281599205079419 21 0.91229195413127 0.17541609173746 0.0877080458687298 22 0.878336182144198 0.243327635711605 0.121663817855802 23 0.845617927629665 0.30876414474067 0.154382072370335 24 0.797865775431279 0.404268449137443 0.202134224568721 25 0.745666069728364 0.508667860543271 0.254333930271636 26 0.713077597089956 0.573844805820089 0.286922402910044 27 0.663770263896549 0.672459472206901 0.336229736103451 28 0.749494323068778 0.501011353862443 0.250505676931222 29 0.803661065544739 0.392677868910522 0.196338934455261 30 0.769213096108583 0.461573807782835 0.230786903891417 31 0.719180856796117 0.561638286407765 0.280819143203883 32 0.669743625116065 0.66051274976787 0.330256374883935 33 0.80035136246148 0.399297275077039 0.199648637538519 34 0.750815114760207 0.498369770479585 0.249184885239793 35 0.722410191120197 0.555179617759606 0.277589808879803 36 0.713948505141304 0.572102989717393 0.286051494858696 37 0.708265590351411 0.583468819297177 0.291734409648589 38 0.705725874911898 0.588548250176205 0.294274125088102 39 0.741326475022466 0.517347049955068 0.258673524977534 40 0.697434292040789 0.605131415918422 0.302565707959211 41 0.693947142713055 0.612105714573889 0.306052857286945 42 0.816206329375893 0.367587341248214 0.183793670624107 43 0.776686482155484 0.446627035689033 0.223313517844516 44 0.73770796011945 0.5245840797611 0.26229203988055 45 0.694351163796577 0.611297672406845 0.305648836203423 46 0.66326916905442 0.67346166189116 0.33673083094558 47 0.615987139139413 0.768025721721173 0.384012860860587 48 0.690204491730965 0.619591016538069 0.309795508269035 49 0.645298429674414 0.709403140651172 0.354701570325586 50 0.687680939133993 0.624638121732014 0.312319060866007 51 0.642045237245677 0.715909525508646 0.357954762754323 52 0.596291184790132 0.807417630419735 0.403708815209868 53 0.572692930104254 0.854614139791492 0.427307069895746 54 0.536828393318427 0.926343213363146 0.463171606681573 55 0.491699340511385 0.98339868102277 0.508300659488615 56 0.453758511341 0.907517022682 0.546241488659 57 0.412578682635696 0.825157365271391 0.587421317364304 58 0.363673487399464 0.727346974798928 0.636326512600536 59 0.399243307945347 0.798486615890694 0.600756692054653 60 0.431252267995283 0.862504535990567 0.568747732004717 61 0.400322305834153 0.800644611668306 0.599677694165847 62 0.486365344998992 0.972730689997984 0.513634655001008 63 0.49308404160997 0.98616808321994 0.50691595839003 64 0.568488438276266 0.863023123447468 0.431511561723734 65 0.520130796773443 0.959738406453113 0.479869203226557 66 0.760492416764896 0.479015166470209 0.239507583235104 67 0.729038750211491 0.541922499577018 0.270961249788509 68 0.761538611254267 0.476922777491466 0.238461388745733 69 0.749671204844566 0.500657590310868 0.250328795155434 70 0.710165468235253 0.579669063529495 0.289834531764747 71 0.667112875285065 0.665774249429869 0.332887124714935 72 0.63651434752553 0.72697130494894 0.36348565247447 73 0.62655093781793 0.746898124364139 0.373449062182069 74 0.637303312172601 0.725393375654797 0.362696687827399 75 0.603401016338492 0.793197967323016 0.396598983661508 76 0.730379254888467 0.539241490223067 0.269620745111533 77 0.693071040061628 0.613857919876744 0.306928959938372 78 0.813142258470968 0.373715483058064 0.186857741529032 79 0.779028185105177 0.441943629789647 0.220971814894823 80 0.739686159687674 0.520627680624651 0.260313840312326 81 0.715085849190743 0.569828301618514 0.284914150809257 82 0.691228345907234 0.617543308185532 0.308771654092766 83 0.77062745169024 0.458745096619519 0.229372548309759 84 0.740315425583688 0.519369148832623 0.259684574416312 85 0.70390178472057 0.592196430558861 0.296098215279431 86 0.696941555552919 0.606116888894162 0.303058444447081 87 0.68632532516837 0.627349349663259 0.313674674831629 88 0.638557052867866 0.722885894264267 0.361442947132134 89 0.592574782895407 0.814850434209187 0.407425217104593 90 0.543172825946577 0.913654348106847 0.456827174053423 91 0.505829880802484 0.988340238395032 0.494170119197516 92 0.509125379513411 0.981749240973178 0.490874620486589 93 0.508596710541837 0.982806578916325 0.491403289458163 94 0.459494607925028 0.918989215850057 0.540505392074972 95 0.616488173044977 0.767023653910045 0.383511826955023 96 0.576219019829409 0.847561960341182 0.423780980170591 97 0.590795058238922 0.818409883522156 0.409204941761078 98 0.537623740460648 0.924752519078705 0.462376259539353 99 0.508503353964899 0.982993292070203 0.491496646035101 100 0.485828944680629 0.971657889361259 0.514171055319371 101 0.46099190376794 0.92198380753588 0.53900809623206 102 0.423759084175802 0.847518168351603 0.576240915824198 103 0.395302761670189 0.790605523340377 0.604697238329811 104 0.410390464976636 0.820780929953271 0.589609535023364 105 0.374693027395262 0.749386054790524 0.625306972604738 106 0.543990503419065 0.912018993161869 0.456009496580935 107 0.514615728093597 0.970768543812805 0.485384271906403 108 0.516423169089585 0.96715366182083 0.483576830910415 109 0.459662025370599 0.919324050741198 0.540337974629401 110 0.411471553921506 0.822943107843011 0.588528446078494 111 0.356599679348363 0.713199358696726 0.643400320651637 112 0.325456322073787 0.650912644147575 0.674543677926213 113 0.284309327706858 0.568618655413716 0.715690672293142 114 0.276074040760982 0.552148081521965 0.723925959239018 115 0.223561814861245 0.44712362972249 0.776438185138755 116 0.193040781526091 0.386081563052182 0.80695921847391 117 0.197794401573767 0.395588803147535 0.802205598426233 118 0.174168394979082 0.348336789958164 0.825831605020918 119 0.157534200536058 0.315068401072115 0.842465799463942 120 0.123585389527961 0.247170779055923 0.876414610472039 121 0.112034701694866 0.224069403389731 0.887965298305134 122 0.1162659472918 0.232531894583599 0.8837340527082 123 0.160352491204447 0.320704982408894 0.839647508795553 124 0.117632163871819 0.235264327743638 0.882367836128181 125 0.0834828494264175 0.166965698852835 0.916517150573583 126 0.0565565319514779 0.113113063902956 0.943443468048522 127 0.0362592944898875 0.072518588979775 0.963740705510112 128 0.0214185330812032 0.0428370661624064 0.978581466918797 129 0.0169808611077899 0.0339617222155798 0.98301913889221 130 0.012519158782199 0.0250383175643981 0.9874808412178 131 0.00602224233810134 0.0120444846762027 0.993977757661899 132 0.00257565077121935 0.0051513015424387 0.99742434922878 133 0.00202657121462797 0.00405314242925594 0.997973428785372 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0168067226890756 NOK 5% type I error level 6 0.0504201680672269 NOK 10% type I error level 7 0.0588235294117647 OK

Charts produced by software:

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Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 2 ; 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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