W7 Multiple Regression

*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 16:18:28 +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/t1290530927jp0q0qp2plaugfk.htm/, Retrieved Tue, 23 Nov 2010 17:48:51 +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/t1290530927jp0q0qp2plaugfk.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:

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14 26 9 15 6 25 25 11 18 20 9 15 6 25 24 12 11 21 9 14 13 19 21 15 12 31 14 10 8 18 23 10 16 21 8 10 7 18 17 12 18 18 8 12 9 22 19 11 14 26 11 18 5 29 18 5 14 22 10 12 8 26 27 16 15 22 9 14 9 25 23 11 15 29 15 18 11 23 23 15 17 15 14 9 8 23 29 12 19 16 11 11 11 23 21 9 10 24 14 11 12 24 26 11 18 17 6 17 8 30 25 15 14 19 20 8 7 19 25 12 14 22 9 16 9 24 23 16 17 31 10 21 12 32 26 14 14 28 8 24 20 30 20 11 16 38 11 21 7 29 29 10 18 26 14 14 8 17 24 7 14 25 11 7 8 25 23 11 12 25 16 18 16 26 24 10 17 29 14 18 10 26 30 11 9 28 11 13 6 25 22 16 16 15 11 11 8 23 22 14 14 18 12 13 9 21 13 12 11 21 9 13 9 19 24 12 16 25 7 18 11 35 17 11 13 23 13 14 12 19 24 6 17 23 10 12 8 20 21 14 15 19 9 9 7 21 23 9 14 18 9 12 8 21 24 15 16 18 13 8 9 24 24 12 9 26 16 5 4 23 24 12 15 18 12 10 8 19 23 9 17 18 6 11 8 17 26 13 13 28 14 11 8 24 24 15 15 17 14 12 6 15 21 11 16 29 10 12 8 25 23 10 16 12 4 15 4 27 28 13 12 28 12 16 14 27 22 16 11 20 14 14 10 18 24 13 15 17 9 17 9 25 21 14 17 17 9 13 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 Happines[t] = + 15.9209864112048 -0.013923866821038Concern_over_Mistakes[t] -0.281152036524041Doubts_about_actions[t] + 0.110618369076942Parental_Expectations[t] -0.109305009852638Parental_Criticism[t] -0.00364126304979581Personal_Standards[t] + 0.0291377852193792Organization[t] + 0.0388082434030575Popularity[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) 15.9209864112048 1.884379 8.4489 0 0 Concern_over_Mistakes -0.013923866821038 0.042239 -0.3296 0.742171 0.371086 Doubts_about_actions -0.281152036524041 0.077754 -3.6159 0.00042 0.00021 Parental_Expectations 0.110618369076942 0.068768 1.6086 0.110011 0.055006 Parental_Criticism -0.109305009852638 0.087307 -1.252 0.212717 0.106358 Personal_Standards -0.00364126304979581 0.056468 -0.0645 0.948679 0.47434 Organization 0.0291377852193792 0.05507 0.5291 0.597587 0.298794 Popularity 0.0388082434030575 0.063735 0.6089 0.543598 0.271799 Multiple Linear Regression - Regression Statistics Multiple R 0.386071666193761 R-squared 0.149051331437627 Adjusted R-squared 0.105572202386995 F-TEST (value) 3.42811216995754 F-TEST (DF numerator) 7 F-TEST (DF denominator) 137 p-value 0.00207522201230936 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.24668769712789 Sum Squared Residuals 691.521968354336 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14 15.0963467538529 -1.09634675385292 2 18 15.1895604129629 2.81043958703713 3 11 14.3507420609462 -3.35074206094623 4 12 12.7776703995443 -0.777670399544335 5 16 14.6159160722414 1.38408392775856 6 18 14.6652166659897 3.33478333401032 7 14 14.5238237887352 -0.523823788735159 8 14 14.5691005820812 -0.569100582081221 9 15 14.6552332520635 0.344766747936502 10 15 13.2572329214863 1.7427670785137 11 17 13.1240707824774 3.87592921752259 12 19 13.4973977218603 5.50260227813974 13 10 12.6529098177204 -2.65290981772041 14 18 16.2047710416263 1.79522895837372 15 14 11.2781636481464 2.72183635185362 16 14 15.0741524702825 -1.07415247028246 17 17 14.8735292126495 2.12647078735047 18 14 14.6510509991446 -0.651050999144594 19 16 14.9845393288367 1.01546067116329 20 18 13.2061175280173 4.7938824719827 21 14 13.3861340048663 0.613865995133652 22 12 12.3094240820379 -0.309424082037925 23 17 13.685497701637 3.31450229836299 24 9 14.3915860703661 -5.39158607036607 25 16 14.0624156204739 1.93758437952612 26 14 13.518849684107 0.481150315892965 27 11 14.6483323567288 -3.64833235672881 28 16 15.1883898394367 0.811610160563277 29 13 13.0457303560912 -0.0457303560912498 30 17 14.3245810954366 2.67541890456343 31 15 14.2994715922402 0.700528407759752 32 14 14.7979328020772 -0.797932802077198 33 16 12.9941976504621 3.00580234953793 34 9 12.2576618114038 -3.2576618114038 35 15 13.4785352348131 1.52146476518694 36 17 15.5259946784042 1.47400532159579 37 13 13.1313917930203 -0.131391793020284 38 15 13.4039077550117 1.59609224498829 39 16 14.1258741760879 1.87412582391211 40 16 17.0733984080376 -1.07339840803763 41 12 13.5605665361522 -1.56056653615216 42 11 13.3002589066068 -2.3002589066068 43 15 15.1148568531699 -0.114856853169928 44 17 15.0694977660082 1.93050223399178 45 13 14.2591604366919 -1.2591604366919 46 16 13.0796560392148 2.92034396078516 47 14 14.1924199912982 -0.19241999129824 48 11 14.5137086665548 -3.51370866655479 49 12 13.1709852079733 -1.17098520797325 50 12 14.4920322716881 -2.49203227168814 51 15 14.3902486530509 0.609751346949128 52 16 14.9169003860484 1.08309961395158 53 15 14.6013405216979 0.398659478302115 54 12 14.778016135197 -2.77801613519699 55 12 14.1948086806033 -2.19480868060331 56 8 12.5724144628216 -4.57241446282164 57 13 15.4771432367284 -2.47714323672837 58 11 14.8735976589011 -3.87359765890109 59 14 14.8471572119599 -0.84715721195989 60 15 12.4076492354216 2.59235076457842 61 10 13.8676660065156 -3.86766600651559 62 11 14.3593220435923 -3.35932204359232 63 12 13.5860647837061 -1.58606478370605 64 15 12.9672029878257 2.03279701217429 65 15 14.6431491683095 0.356850831690526 66 14 13.7936248068377 0.206375193162318 67 16 12.9144880052754 3.08551199472465 68 15 14.7085352925772 0.291464707422847 69 15 15.1303522006806 -0.130352200680612 70 13 14.8321220081259 -1.83212200812593 71 17 14.8689156786679 2.13108432133206 72 13 13.6204306969395 -0.620430696939519 73 15 13.6745282537884 1.32547174621156 74 13 14.1724516845164 -1.17245168451637 75 15 13.8407924853543 1.15920751464569 76 16 14.2317279549076 1.76827204509238 77 15 14.4657106372158 0.534289362784213 78 16 13.7559090518628 2.24409094813721 79 15 14.1445144075995 0.85548559240053 80 14 14.609371577487 -0.609371577487046 81 15 12.6346948176438 2.36530518235619 82 7 12.7790383078128 -5.7790383078128 83 17 14.9437678807955 2.05623211920455 84 13 14.8216225873461 -1.82162258734606 85 15 13.9953106291211 1.00468937087888 86 14 13.3727814724166 0.627218527583415 87 13 13.8441634893288 -0.844163489328771 88 16 15.1892681467178 0.810731853282163 89 12 14.4598055165961 -2.45980551659606 90 14 15.3222001435219 -1.32220014352191 91 17 14.5121572339796 2.4878427660204 92 15 15.424062935526 -0.424062935525951 93 17 12.9281383483416 4.07186165165838 94 12 14.1517887686352 -2.15178876863525 95 16 15.1053025357502 0.89469746424976 96 11 13.9984294366401 -2.9984294366401 97 15 13.1687827672716 1.83121723272835 98 9 14.4761190005816 -5.47611900058161 99 16 14.6479336792415 1.35206632075855 100 10 12.6419332020375 -2.64193320203755 101 10 12.6448030323297 -2.6448030323297 102 15 14.8137415344717 0.186258465528322 103 11 13.9410765636774 -2.94107656367737 104 13 14.9392636340428 -1.93926363404275 105 14 13.1448841484294 0.855115851570617 106 18 15.095246112285 2.90475388771503 107 16 14.8861051567031 1.11389484329691 108 14 12.5300006232887 1.46999937671129 109 14 13.6301491993308 0.36985080066918 110 14 13.511008357087 0.488991642913018 111 14 14.6414485081166 -0.64144850811657 112 12 13.3031354408185 -1.30313544081853 113 14 14.3023032385033 -0.302303238503307 114 15 14.419371107915 0.580628892085044 115 15 14.9837036955696 0.0162963044303615 116 13 13.5802741281511 -0.580274128151066 117 17 14.7848048580796 2.21519514192041 118 17 15.2167737470621 1.78322625293795 119 19 15.0747921202689 3.92520787973105 120 15 14.0656672464009 0.934332753599117 121 13 14.206155408575 -1.20615540857503 122 9 13.0310330165383 -4.03103301653828 123 15 15.3011111008892 -0.301111100889229 124 15 14.5781218485289 0.42187815147114 125 16 14.7733997595337 1.22660024046626 126 11 13.5454397393461 -2.5454397393461 127 14 14.460077351731 -0.460077351730967 128 11 12.9143119088605 -1.9143119088605 129 15 13.4168188846048 1.58318111539521 130 13 13.4748061426351 -0.474806142635061 131 16 13.1038468423132 2.89615315768678 132 14 14.5661926367677 -0.566192636767732 133 15 14.7104686343731 0.289531365626855 134 16 13.5027637561166 2.49723624388342 135 16 14.9949461697315 1.00505383026852 136 11 12.43441005922 -1.43441005922005 137 13 13.582844883783 -0.582844883783041 138 16 14.0624156204739 1.93758437952612 139 12 14.0598038006965 -2.05980380069647 140 9 12.5158535472441 -3.51585354724407 141 13 12.8440310528125 0.155968947187459 142 13 14.8216225873461 -1.82162258734606 143 14 13.7736877721266 0.226312227873369 144 19 15.0747921202689 3.92520787973105 145 13 15.429041240669 -2.429041240669 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.687660604739566 0.624678790520867 0.312339395260434 12 0.736670574082993 0.526658851834015 0.263329425917007 13 0.715560089811292 0.568879820377415 0.284439910188708 14 0.625518294502254 0.748963410995491 0.374481705497746 15 0.69918942107153 0.60162115785694 0.30081057892847 16 0.636780086593086 0.726439826813828 0.363219913406914 17 0.800013882497385 0.39997223500523 0.199986117502615 18 0.729767751433727 0.540464497132546 0.270232248566273 19 0.730321267133287 0.539357465733425 0.269678732866713 20 0.73122387551769 0.537552248964619 0.268776124482309 21 0.70913945992032 0.58172108015936 0.29086054007968 22 0.677010843373905 0.64597831325219 0.322989156626095 23 0.654806766474528 0.690386467050944 0.345193233525472 24 0.750149072703607 0.499701854592785 0.249850927296393 25 0.700435652845717 0.599128694308567 0.299564347154283 26 0.643034737409251 0.713930525181499 0.356965262590749 27 0.849865519840906 0.300268960318189 0.150134480159094 28 0.819324371008848 0.361351257982304 0.180675628991152 29 0.82007973620547 0.359840527589059 0.17992026379453 30 0.858439980318043 0.283120039363914 0.141560019681957 31 0.823542599391906 0.352914801216188 0.176457400608094 32 0.792573165843801 0.414853668312397 0.207426834156199 33 0.79001437807273 0.419971243854539 0.209985621927269 34 0.825146005980575 0.349707988038851 0.174853994019425 35 0.794321944637917 0.411356110724165 0.205678055362082 36 0.758078734760369 0.483842530479262 0.241921265239631 37 0.722334346474365 0.55533130705127 0.277665653525635 38 0.687308004202748 0.625383991594505 0.312691995797252 39 0.692126235443061 0.615747529113879 0.307873764556939 40 0.741903040230579 0.516193919538842 0.258096959769421 41 0.70185628748605 0.5962874250279 0.29814371251395 42 0.736401906113106 0.527196187773788 0.263598093886894 43 0.693706228338176 0.612587543323647 0.306293771661824 44 0.670370802110427 0.659258395779147 0.329629197889573 45 0.629016079268052 0.741967841463895 0.370983920731948 46 0.654314197055495 0.69137160588901 0.345685802944505 47 0.620993993615137 0.758012012769726 0.379006006384863 48 0.766560169268696 0.466879661462608 0.233439830731304 49 0.748614701240024 0.502770597519952 0.251385298759976 50 0.760667312214331 0.478665375571337 0.239332687785669 51 0.744506561918953 0.510986876162093 0.255493438081047 52 0.721650899929824 0.556698200140351 0.278349100070176 53 0.677873755908971 0.644252488182058 0.322126244091029 54 0.69968079326599 0.60063841346802 0.30031920673401 55 0.686896027857835 0.62620794428433 0.313103972142165 56 0.834872173538976 0.330255652922047 0.165127826461024 57 0.85338059062467 0.29323881875066 0.14661940937533 58 0.898922660291806 0.202154679416388 0.101077339708194 59 0.87791757297402 0.244164854051959 0.122082427025979 60 0.888532216020168 0.222935567959665 0.111467783979832 61 0.922675921241445 0.154648157517109 0.0773240787585546 62 0.943209653847914 0.113580692304171 0.0567903461520856 63 0.934538067180548 0.130923865638904 0.065461932819452 64 0.932919752729093 0.134160494541814 0.0670802472709068 65 0.9159378477229 0.1681243045542 0.0840621522770998 66 0.895472554506903 0.209054890986195 0.104527445493097 67 0.916457601987395 0.16708479602521 0.083542398012605 68 0.900373110471257 0.199253779057486 0.099626889528743 69 0.87815820544661 0.243683589106779 0.12184179455339 70 0.872966587259513 0.254066825480974 0.127033412740487 71 0.869772880317907 0.260454239364186 0.130227119682093 72 0.844930796099827 0.310138407800346 0.155069203900173 73 0.825424149838767 0.349151700322466 0.174575850161233 74 0.801454288076265 0.39709142384747 0.198545711923735 75 0.777548271132975 0.44490345773405 0.222451728867025 76 0.766395958143537 0.467208083712927 0.233604041856463 77 0.727812613981133 0.544374772037733 0.272187386018867 78 0.727618622125718 0.544762755748563 0.272381377874282 79 0.691187730172619 0.617624539654763 0.308812269827381 80 0.64911180040529 0.70177639918942 0.35088819959471 81 0.665032734449154 0.669934531101692 0.334967265550846 82 0.858311972460985 0.283376055078031 0.141688027539015 83 0.85648135076677 0.287037298466461 0.14351864923323 84 0.852095515402077 0.295808969195847 0.147904484597923 85 0.826009412716907 0.347981174566185 0.173990587283093 86 0.80066459473378 0.398670810532442 0.199335405266221 87 0.769851541540045 0.46029691691991 0.230148458459955 88 0.733039422757056 0.533921154485889 0.266960577242944 89 0.744718892973081 0.510562214053837 0.255281107026919 90 0.729157630234725 0.54168473953055 0.270842369765275 91 0.75109566238711 0.497808675225781 0.248904337612891 92 0.710303186920724 0.579393626158552 0.289696813079276 93 0.835069771065239 0.329860457869522 0.164930228934761 94 0.841869476894811 0.316261046210377 0.158130523105189 95 0.809216406856083 0.381567186287835 0.190783593143917 96 0.832306293708812 0.335387412582377 0.167693706291188 97 0.832067995460359 0.335864009079282 0.167932004539641 98 0.946231982868052 0.107536034263896 0.0537680171319481 99 0.933922526285635 0.132154947428731 0.0660774737143654 100 0.934954016849165 0.130091966301669 0.0650459831508346 101 0.930549404821158 0.138901190357683 0.0694505951788417 102 0.909277298145856 0.181445403708288 0.090722701854144 103 0.937311877662291 0.125376244675418 0.0626881223377091 104 0.958718440780044 0.0825631184399127 0.0412815592199563 105 0.956325598430506 0.0873488031389876 0.0436744015694938 106 0.956970067232926 0.0860598655341474 0.0430299327670737 107 0.943864105760542 0.112271788478915 0.0561358942394577 108 0.946329150697836 0.107341698604328 0.0536708493021638 109 0.927462689842353 0.145074620315294 0.0725373101576469 110 0.924203127916062 0.151593744167876 0.075796872083938 111 0.905019538272783 0.189960923454433 0.0949804617272166 112 0.878444696847408 0.243110606305185 0.121555303152592 113 0.854439415361661 0.291121169276677 0.145560584638339 114 0.817191027262568 0.365617945474864 0.182808972737432 115 0.780206542518043 0.439586914963913 0.219793457481957 116 0.727447096116677 0.545105807766647 0.272552903883323 117 0.776714839774188 0.446570320451625 0.223285160225812 118 0.782460428572563 0.435079142854874 0.217539571427437 119 0.802917243833533 0.394165512332934 0.197082756166467 120 0.820385050773527 0.359229898452947 0.179614949226473 121 0.770839981799213 0.458320036401574 0.229160018200787 122 0.756249870026505 0.487500259946991 0.243750129973495 123 0.70284984221872 0.594300315562562 0.297150157781281 124 0.632706458360621 0.734587083278757 0.367293541639379 125 0.613079100782909 0.773841798434181 0.386920899217091 126 0.5338875943013 0.9322248113974 0.4661124056987 127 0.441643078719614 0.883286157439229 0.558356921280386 128 0.368069109633491 0.736138219266982 0.631930890366509 129 0.358325224686917 0.716650449373834 0.641674775313083 130 0.277094159387656 0.554188318775312 0.722905840612344 131 0.453894757607814 0.907789515215627 0.546105242392186 132 0.347645173148598 0.695290346297196 0.652354826851402 133 0.249968657397356 0.499937314794712 0.750031342602644 134 0.196067595777532 0.392135191555064 0.803932404222468 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 3 0.0241935483870968 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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