Paper: Multiple Linear Regression (monthly dummies)

*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, 09 Dec 2010 12:25:49 +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/09/t12918980941hp18jpw03n7cwz.htm/, Retrieved Thu, 09 Dec 2010 13:34:55 +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/09/t12918980941hp18jpw03n7cwz.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 «

24 14 11 12 24 26 10 25 11 7 8 25 23 14 17 6 17 8 30 25 18 18 12 10 8 19 23 15 18 8 12 9 22 19 18 16 10 12 7 22 29 11 20 10 11 4 25 25 17 16 11 11 11 23 21 19 18 16 12 7 17 22 7 17 11 13 7 21 25 12 23 13 14 12 19 24 13 30 12 16 10 19 18 15 23 8 11 10 15 22 14 18 12 10 8 16 15 14 15 11 11 8 23 22 16 12 4 15 4 27 28 16 21 9 9 9 22 20 12 15 8 11 8 14 12 12 20 8 17 7 22 24 13 31 14 17 11 23 20 16 27 15 11 9 23 21 9 21 9 14 13 19 21 11 31 14 10 8 18 23 12 19 11 11 8 20 28 11 16 8 15 9 23 24 14 20 9 15 6 25 24 18 21 9 13 9 19 24 11 22 9 16 9 24 23 14 17 9 13 6 22 23 17 25 16 18 16 26 24 12 26 11 18 5 29 18 14 25 8 12 7 32 25 14 17 9 17 9 25 21 15 32 16 9 6 29 26 11 33 11 9 6 28 22 15 13 16 12 5 17 22 14 32 12 18 12 28 22 11 25 12 12 7 29 23 12 29 14 18 10 26 30 17 22 9 14 9 25 23 15 18 10 15 8 14 17 9 17 9 16 5 25 23 16 20 10 10 8 26 23 13 15 12 11 8 20 25 15 20 14 14 10 18 24 11 33 14 9 6 32 24 10 29 10 12 8 25 23 16 23 14 17 7 25 21 13 26 16 5 4 23 2 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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation PS[t] = + 6.14877022785273 + 0.353909374463323CM[t] -0.340140308890912D[t] + 0.187547743317141PE[t] -0.0218597760694683PC[t] + 0.414511745648744O[t] -0.055790671462666`H `[t] + 1.91304219854686M1[t] + 3.20749012754116M2[t] + 2.29146189157973M3[t] + 1.04229613763446M4[t] + 1.11536866188866M5[t] + 2.25591011160927M6[t] + 0.866676009591269M7[t] + 2.79259992654015M8[t] + 0.816064160614426M9[t] + 0.182942017830659M10[t] + 0.206770309169597M11[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) 6.14877022785273 3.263652 1.884 0.061622 0.030811 CM 0.353909374463323 0.058762 6.0228 0 0 D -0.340140308890912 0.12035 -2.8263 0.005394 0.002697 PE 0.187547743317141 0.103963 1.804 0.073369 0.036685 PC -0.0218597760694683 0.130768 -0.1672 0.86748 0.43374 O 0.414511745648744 0.074323 5.5771 0 0 `H ` -0.055790671462666 0.132543 -0.4209 0.674451 0.337225 M1 1.91304219854686 1.33692 1.4309 0.154662 0.077331 M2 3.20749012754116 1.354492 2.368 0.01924 0.00962 M3 2.29146189157973 1.344833 1.7039 0.090602 0.045301 M4 1.04229613763446 1.36951 0.7611 0.447885 0.223942 M5 1.11536866188866 1.363755 0.8179 0.414814 0.207407 M6 2.25591011160927 1.363916 1.654 0.100353 0.050177 M7 0.866676009591269 1.360019 0.6373 0.524994 0.262497 M8 2.79259992654015 1.354753 2.0613 0.041108 0.020554 M9 0.816064160614426 1.335105 0.6112 0.542027 0.271014 M10 0.182942017830659 1.344702 0.136 0.891979 0.445989 M11 0.206770309169597 1.361999 0.1518 0.879551 0.439775 Multiple Linear Regression - Regression Statistics Multiple R 0.657416140227832 R-squared 0.43219598143206 Adjusted R-squared 0.3637373408955 F-TEST (value) 6.31324224443585 F-TEST (DF numerator) 17 F-TEST (DF denominator) 141 p-value 8.03553890094122e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.39580543571185 Sum Squared Residuals 1625.94073256663 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 24 23.8137796249422 0.186220375057788 2 25 24.3531080632850 0.646891936715029 3 30 24.7878446146897 5.21215538531025 4 19 19.8772607017328 -0.877260701732849 5 22 19.8387111751325 2.16128882486746 6 22 24.1705249670097 -2.17052496700972 7 25 22.0821689363653 2.9178310636347 8 23 20.3296682885634 2.67033171143661 9 17 18.7192363779055 -1.71923637790550 10 21 20.585036028063 0.414963971936982 11 19 21.6599863942585 -2.65998639425846 12 19 22.0908852371785 -3.09088523717846 13 15 23.6632219875176 -8.66322198751764 14 16 18.7821513979123 -2.78215139791227 15 23 20.1220839673848 2.87791603261521 16 27 23.5168728037248 3.48312719627516 17 22 20.7469115341049 1.25308846589509 18 14 17.1849983434503 -3.18499834345029 19 22 23.6308076260435 -1.63080762604348 20 23 25.4960347074826 -2.4960347074826 21 23 21.4872006729362 1.51279932706383 22 19 21.1350869194662 -2.13508691946615 23 18 23.1296481378974 -5.12964813789736 24 20 22.0122834048641 -2.01228340486415 25 23 22.7869306069099 0.213069393090103 26 25 24.9992923672243 0.000707632775675614 27 19 24.3870333911222 -5.38703339112219 28 24 23.4725364815549 0.527463518445079 29 22 21.1116262173615 0.888373782638507 30 26 24.1150665594054 1.88493344059460 31 29 22.4222490962516 6.57775090374837 32 32 26.7472607729094 5.25273922709065 33 25 20.7794912127753 4.22050878722474 34 29 23.9349463204706 5.06505367952938 35 28 24.1321758622818 3.8678241377182 36 17 15.7868101968747 1.21318980312527 37 28 26.9243317875929 1.07566821240705 38 29 25.0841475899746 3.91585241002544 39 26 28.5858122280069 -2.58581222800692 40 25 23.0416503234580 1.95834967654203 41 14 19.4160261152381 -5.41602611523811 42 25 22.8924613445657 2.10753865543434 43 26 21.2013212833235 4.79867871667654 44 20 21.5824076018632 -1.58240760186320 45 18 21.0227127084867 -3.02271270848667 46 32 24.1959034928809 7.80409650711906 47 25 23.934323425318 1.06567657468202 48 25 20.5414826495505 4.45851735044952 49 23 22.1176766849051 0.882323315094906 50 21 23.908273522058 -2.90827352205798 51 20 24.9063893658019 -4.90638936580193 52 15 15.8764028453032 -0.87640284530316 53 30 26.0255947343067 3.97440526569328 54 24 26.5557566659754 -2.55575666597541 55 26 23.8864918300167 2.1135081699833 56 24 22.9578244600350 1.04217553996505 57 22 20.8256286249576 1.17437137504239 58 14 14.1871184963506 -0.187118496350568 59 24 20.8905056273397 3.1094943726603 60 24 21.7094291759346 2.29057082406538 61 24 24.169688300541 -0.169688300540989 62 24 21.6640801942310 2.33591980576903 63 19 19.1169778063536 -0.116977806353572 64 31 27.1689712914661 3.83102870853388 65 22 26.4021944756145 -4.40219447561446 66 27 22.4219874013483 4.57801259865168 67 19 17.1048496095279 1.89515039047207 68 25 23.6920947830707 1.30790521692927 69 20 24.4773365505020 -4.47733655050204 70 21 20.2265489158174 0.773451084182563 71 27 26.4126917995004 0.587308200499596 72 23 23.1423493748509 -0.142349374850932 73 25 26.4659751165094 -1.46597511650937 74 20 23.9267728341495 -3.92677283414946 75 22 23.4983695363039 -1.49836953630393 76 23 22.8856125644766 0.114387435523365 77 25 24.3561623447288 0.643837655271192 78 25 24.5244836050379 0.475516394962088 79 17 23.0619840643732 -6.06198406437317 80 19 23.0605867841818 -4.06058678418185 81 25 23.1596966911531 1.8403033088469 82 19 21.7904476894089 -2.79044768940894 83 20 22.0052612871699 -2.00526128716993 84 26 21.1330307795191 4.86696922048086 85 23 21.1939394091234 1.80606059087655 86 27 26.3285365084981 0.671463491501924 87 17 21.7285482193295 -4.72854821932953 88 17 23.0255857841869 -6.02558578418692 89 17 19.5722677137679 -2.57226771376791 90 22 22.9247158231212 -0.924715823121187 91 21 22.8220553771362 -1.82205537713623 92 32 30.0162069426751 1.98379305732486 93 21 24.4486440456690 -3.44864404566895 94 21 23.2662700860218 -2.26627008602179 95 18 20.1513689601983 -2.15136896019830 96 18 20.0586416129406 -2.05864161294062 97 23 23.2628299258930 -0.26282992589297 98 19 22.2712196601799 -3.27121966017988 99 20 21.5972940494516 -1.59729404945163 100 21 21.5499573417065 -0.549957341706525 101 20 23.6147074741298 -3.61470747412985 102 17 19.9923647998927 -2.99236479989269 103 18 19.6029285633576 -1.60292856335762 104 19 21.9742713767137 -2.97427137671375 105 22 21.4912496252541 0.508750374745933 106 15 17.5735081371596 -2.57350813715963 107 14 17.2600761736985 -3.26007617369846 108 18 25.186978645569 -7.18697864556898 109 24 21.7852151560524 2.21478484394758 110 35 25.1124633303110 9.88753666968903 111 29 19.6529904669363 9.34700953306367 112 21 21.6843188351038 -0.684318835103755 113 20 18.1346889866415 1.86531101335854 114 22 24.3299317082594 -2.32993170825941 115 13 16.2610351212007 -3.2610351212007 116 26 25.0267827187664 0.973217281233622 117 17 16.0709045789130 0.929095421087023 118 25 19.0029908103164 5.99700918968363 119 20 19.4631200556095 0.536879944390472 120 19 16.9993299196298 2.00067008037024 121 21 23.1645906951455 -2.16459069514546 122 22 22.7316573108145 -0.731657310814519 123 24 23.6054684937591 0.394531506240948 124 21 22.5851984251227 -1.58519842512267 125 26 25.5952644597697 0.404735540230294 126 24 21.3827389988765 2.61726100112351 127 16 19.5603147467725 -3.56031474677254 128 23 23.7349476798571 -0.734947679857064 129 18 20.3710345866985 -2.37103458669855 130 16 21.1908014811978 -5.19080148119779 131 26 23.1174877098554 2.88251229014461 132 19 17.7258947284971 1.27410527150287 133 21 17.1994634315024 3.80053656849757 134 21 23.8168540089534 -2.81685400895344 135 22 19.2632076286628 2.73679237133718 136 23 19.5038793472856 3.4961206527144 137 29 24.6209624668823 4.37903753311771 138 21 19.7877020621918 1.21229793780821 139 21 20.0509303145513 0.949069685448718 140 23 23.1818954345004 -0.181895434500434 141 27 22.8850403208132 4.11495967918679 142 25 24.3836581641059 0.616341835894139 143 21 19.7358468313077 1.26415316869225 144 10 15.4672663388472 -5.46726633884718 145 20 23.0429323517082 -3.04293235170825 146 26 23.9789885207690 2.02101147923097 147 24 24.7331758273740 -0.733175827373961 148 29 31.8117532548780 -2.81175325487804 149 19 18.5648823023217 0.435117697678269 150 24 22.7172677208657 1.28273227913428 151 19 20.3128634310799 -1.31286343107994 152 24 25.2000184493812 -1.20001844938116 153 22 21.2618240039359 0.738175996064113 154 17 22.5276834587409 -5.52768345874089 155 24 22.1075077355649 1.89249226443507 156 25 21.1456179357438 3.85438206425619 157 30 24.4094249216569 5.59057507834313 158 19 22.0424546916396 -3.04245469163955 159 22 21.0148044048236 0.985195595176392 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.834919278070552 0.330161443858897 0.165080721929448 22 0.735821764708785 0.52835647058243 0.264178235291215 23 0.630748862484954 0.738502275030092 0.369251137515046 24 0.528037286630829 0.943925426738342 0.471962713369171 25 0.488176484780283 0.976352969560566 0.511823515219717 26 0.393552091921837 0.787104183843674 0.606447908078163 27 0.482454556990943 0.964909113981885 0.517545443009057 28 0.3986294843707 0.7972589687414 0.6013705156293 29 0.354322881225502 0.708645762451004 0.645677118774498 30 0.275331014216759 0.550662028433518 0.724668985783241 31 0.54026524173632 0.91946951652736 0.45973475826368 32 0.706039123092386 0.587921753815227 0.293960876907614 33 0.662149423884915 0.675701152230169 0.337850576115085 34 0.674498712263519 0.651002575472963 0.325501287736481 35 0.715111683409435 0.56977663318113 0.284888316590565 36 0.672031748414676 0.655936503170648 0.327968251585324 37 0.656273491739658 0.687453016520683 0.343726508260342 38 0.682745849520617 0.634508300958766 0.317254150479383 39 0.768638231058171 0.462723537883657 0.231361768941829 40 0.725679171959634 0.548641656080731 0.274320828040366 41 0.739595409268033 0.520809181463935 0.260404590731967 42 0.698465829300289 0.603068341399423 0.301534170699711 43 0.711553131839049 0.576893736321902 0.288446868160951 44 0.6798679788732 0.640264042253599 0.320132021126800 45 0.69351783800899 0.61296432398202 0.30648216199101 46 0.778357856192638 0.443284287614724 0.221642143807362 47 0.736056917680975 0.52788616463805 0.263943082319025 48 0.783710488935557 0.432579022128887 0.216289511064443 49 0.738732674181637 0.522534651636726 0.261267325818363 50 0.713114234534918 0.573771530930163 0.286885765465082 51 0.765432502569644 0.469134994860713 0.234567497430356 52 0.726385911905444 0.547228176189112 0.273614088094556 53 0.770197641166273 0.459604717667453 0.229802358833727 54 0.770522069336677 0.458955861326646 0.229477930663323 55 0.747139238191423 0.505721523617154 0.252860761808577 56 0.707273494354803 0.585453011290394 0.292726505645197 57 0.660181951000377 0.679636097999245 0.339818048999623 58 0.628791053365127 0.742417893269746 0.371208946634873 59 0.657698545723058 0.684602908553885 0.342301454276942 60 0.628832463253202 0.742335073493596 0.371167536746798 61 0.580552006974226 0.838895986051547 0.419447993025774 62 0.555238535377447 0.889522929245105 0.444761464622552 63 0.507258786354927 0.985482427290146 0.492741213645073 64 0.501077595926743 0.997844808146513 0.498922404073257 65 0.611881198362759 0.776237603274482 0.388118801637241 66 0.67272290728084 0.654554185438321 0.327277092719161 67 0.654535559167333 0.690928881665334 0.345464440832667 68 0.612770076587587 0.774459846824826 0.387229923412413 69 0.674980139159261 0.650039721681478 0.325019860840739 70 0.638713484731596 0.722573030536808 0.361286515268404 71 0.590987751764653 0.818024496470694 0.409012248235347 72 0.54379915121147 0.91240169757706 0.45620084878853 73 0.503111356840559 0.993777286318883 0.496888643159441 74 0.52431515055592 0.95136969888816 0.47568484944408 75 0.481463578511919 0.962927157023838 0.518536421488081 76 0.435208165228557 0.870416330457115 0.564791834771443 77 0.385729161569356 0.771458323138712 0.614270838430644 78 0.338923536354961 0.677847072709923 0.661076463645039 79 0.43713187559011 0.87426375118022 0.56286812440989 80 0.464134319828455 0.92826863965691 0.535865680171545 81 0.429452556184949 0.858905112369897 0.570547443815051 82 0.427236968530507 0.854473937061015 0.572763031469493 83 0.398064907927126 0.796129815854253 0.601935092072874 84 0.487807024205652 0.975614048411304 0.512192975794348 85 0.450240315652623 0.900480631305247 0.549759684347377 86 0.411852963549789 0.823705927099578 0.588147036450211 87 0.456622041680423 0.913244083360847 0.543377958319577 88 0.574571006088161 0.850857987823679 0.425428993911839 89 0.556199993917863 0.887600012164274 0.443800006082137 90 0.51067332536604 0.97865334926792 0.48932667463396 91 0.470826376151094 0.941652752302188 0.529173623848906 92 0.459094435916463 0.918188871832926 0.540905564083537 93 0.463992811721931 0.927985623443862 0.536007188278069 94 0.433592336314196 0.867184672628392 0.566407663685804 95 0.407036037196958 0.814072074393916 0.592963962803042 96 0.369243081538924 0.738486163077848 0.630756918461076 97 0.325425736580925 0.650851473161851 0.674574263419075 98 0.332386283644305 0.66477256728861 0.667613716355695 99 0.314565939992685 0.62913187998537 0.685434060007315 100 0.270473612397624 0.540947224795249 0.729526387602376 101 0.287119175123308 0.574238350246616 0.712880824876692 102 0.281764682042339 0.563529364084679 0.71823531795766 103 0.242397028980858 0.484794057961716 0.757602971019142 104 0.226176360049068 0.452352720098135 0.773823639950932 105 0.188778205531510 0.377556411063021 0.81122179446849 106 0.165091937884378 0.330183875768757 0.834908062115622 107 0.15645348702027 0.31290697404054 0.84354651297973 108 0.264324537756426 0.528649075512852 0.735675462243574 109 0.242648327455489 0.485296654910978 0.757351672544511 110 0.634117109524736 0.731765780950528 0.365882890475264 111 0.850748440179161 0.298503119641677 0.149251559820839 112 0.813991460914741 0.372017078170518 0.186008539085259 113 0.775961587889093 0.448076824221813 0.224038412110907 114 0.785535562925224 0.428928874149551 0.214464437074776 115 0.77694695745727 0.446106085085461 0.223053042542730 116 0.726454167130456 0.547091665739088 0.273545832869544 117 0.671628640130856 0.656742719738289 0.328371359869144 118 0.900533100326208 0.198933799347585 0.0994668996737924 119 0.878609190337074 0.242781619325853 0.121390809662926 120 0.84705266095313 0.305894678093742 0.152947339046871 121 0.836737336277846 0.326525327444309 0.163262663722154 122 0.789953056187223 0.420093887625554 0.210046943812777 123 0.732614758710528 0.534770482578944 0.267385241289472 124 0.688155056079555 0.62368988784089 0.311844943920445 125 0.66990367787515 0.6601926442497 0.33009632212485 126 0.61047188315979 0.77905623368042 0.38952811684021 127 0.612700584558427 0.774598830883147 0.387299415441573 128 0.533411166716481 0.933177666567037 0.466588833283519 129 0.467590806165785 0.93518161233157 0.532409193834215 130 0.42405274731003 0.84810549462006 0.57594725268997 131 0.442297826861988 0.884595653723976 0.557702173138012 132 0.431134923207977 0.862269846415955 0.568865076792023 133 0.430633254966308 0.861266509932617 0.569366745033692 134 0.337669836929723 0.675339673859447 0.662330163070276 135 0.291511978229051 0.583023956458103 0.708488021770949 136 0.41486161057856 0.82972322115712 0.58513838942144 137 0.306110846397526 0.612221692795051 0.693889153602474 138 0.72925737627067 0.54148524745866 0.27074262372933 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 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 5 ; par2 = Include Monthly 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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