*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, 21 Dec 2010 19:18:27 +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/21/t1292958969jl88ltc2ps165cl.htm/, Retrieved Tue, 21 Dec 2010 20:16:23 +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/21/t1292958969jl88ltc2ps165cl.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 «

8 350 165 3693 11.5 8 318 150 3436 11 8 302 140 3449 10.5 8 429 198 4341 10 8 440 215 4312 8.5 8 455 225 4425 10 8 383 170 3563 10 8 340 160 3609 8 8 455 225 3086 10 4 113 95 2372 15 6 199 97 2774 15.5 4 97 46 1835 20.5 4 110 87 2672 17.5 4 104 95 2375 17.5 4 121 113 2234 12.5 8 360 215 4615 14 8 307 200 4376 15 8 304 193 4732 18.5 4 97 88 2130 14.5 4 113 95 2228 14 6 250 100 3329 15.5 6 232 100 3288 15.5 8 350 165 4209 12 8 318 150 4096 13 8 400 170 4746 12 8 400 175 5140 12 4 140 72 2408 19 6 250 100 3282 15 4 122 86 2220 14 4 116 90 2123 14 4 88 76 2065 14.5 4 71 65 1773 19 4 97 60 1834 19 4 91 70 1955 20.5 4 97,5 80 2126 17 4 122 86 2226 16.5 8 350 165 4274 12 8 318 150 4135 13.5 8 351 153 4129 13 8 429 208 4633 11 8 350 155 4502 13.5 8 400 190 4422 12.5 3 70 97 2330 13.5 8 307 130 4098 14 8 302 140 4294 16 4 121 112 2933 14.5 4 121 76 2511 18 4 122 86 2395 16 4 120 97 2506 14.5 4 98 80 2164 15 8 350 175 4100 13 8 304 150 3672 11.5 8 302 137 4042 14.5 8 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 50 seconds R Server 'George Udny Yule' @ 72.249.76.132 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation acceleration [t] = + 17.3425380893823 -0.172973901455077cylinders[t] -0.00823600695068293engine.displacement[t] -0.0787884360084219horsepower[t] + 0.00303601366592021weight[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) 17.3425380893823 0.48078 36.0717 0 0 cylinders -0.172973901455077 0.129703 -1.3336 0.182816 0.091408 engine.displacement -0.00823600695068293 0.002869 -2.8711 0.004228 0.002114 horsepower -0.0787884360084219 0.00413 -19.0761 0 0 weight 0.00303601366592021 0.000227 13.3976 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.776356439088369 R-squared 0.602729320513972 Adjusted R-squared 0.600194898316294 F-TEST (value) 237.817251232325 F-TEST (DF numerator) 4 F-TEST (DF denominator) 627 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.72021529453132 Sum Squared Residuals 1855.38119353126 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11.5 11.2880509718559 0.211949028144124 2 11 11.9531742222632 -0.953174222263184 3 10.5 12.9123028712151 -2.41230287121514 4 10 10.0047248899907 -0.00472488999073533 5 8.5 8.48668100507838 0.0133189949216213 6 10 7.9183260849829 2.08167391501711 7 10 10.2276387858720 -0.227638785872049 8 8 11.5093280734680 -3.50932807346796 9 10 3.85310378631573 6.14689621368427 10 15 15.4364966928974 -0.436496692897405 11 15.5 15.4451529139116 0.0548470860883915 12 20.5 17.7985668299219 2.70143317007815 13 17.5 17.0023163015929 0.497683698407108 14 17.5 15.5197287964513 1.98027120354869 15 12.5 13.5334469032434 -1.03344690324336 16 14 10.0654737019068 3.93452629809317 17 15 10.9582013442644 4.04179865573557 18 18.5 12.6152492822430 5.88475071775698 19 14.5 15.3850765490146 -0.885076549014595 20 14 14.9993107250049 -0.999310725004895 21 15.5 16.4737388359872 -0.97373883598723 22 15.5 16.4975104007968 -0.997510400796794 23 12 12.8546340234712 -0.854634023471152 24 13 13.9569432417704 -0.956943241770351 25 12 13.6792308344940 -1.67923083449405 26 12 14.4814780388245 -2.4814780388245 27 19 17.1355550253958 1.86444497460420 28 15 16.3310461936890 -1.33104619368898 29 14 15.6099944771972 -1.60999447719718 30 14 15.0497634492733 -1.04976344927333 31 14.5 16.207320955387 -1.70732095538699 32 19 16.3274898791925 2.67251012080746 33 19 16.6924927121380 2.30750728786197 34 20.5 16.3213820473343 4.17861795266575 35 17 15.9991219789429 1.00087802105705 36 16.5 15.6282105591927 0.871789440807295 37 12 13.0519749117560 -1.05197491175597 38 13.5 14.0753477747412 -0.57534777474124 39 13 13.5489781553479 -0.548978155347915 40 11 10.1033565203552 0.896643479644774 41 13.5 14.53207038767 -1.03207038766999 42 12.5 11.1197936865675 1.38020631343254 43 13.5 15.6785294472464 -2.17852944724635 44 14 15.6293800657281 -1.62938006572814 45 16 15.4777344189177 0.5222655810823 46 14.5 15.73440889173 -1.23440889173001 47 18 17.2895948210149 0.710405178985133 48 16 16.1412968687332 -0.141296868733221 49 14.5 15.6280936034591 -1.12809360345909 50 15 16.1103724947726 -1.11037249477257 51 13 11.7358241738016 1.26417582619837 52 11.5 12.7849775447297 -1.28497754472974 53 14.5 14.9490242831311 -0.449024283131072 54 12.5 12.9884548823418 -0.488454882341804 55 12 14.398843700873 -2.39884370087299 56 13 13.8654631731311 -0.865463173131135 57 11 9.77091478576262 1.22908521423738 58 11 9.51526927325692 1.48473072674308 59 16.5 15.6542059872008 0.84579401279921 60 18 16.3189021390253 1.6810978609747 61 16.5 16.4841078589849 0.0158921410151325 62 16 16.0056475694488 -0.00564756944876255 63 14 16.0170389848085 -2.01703898480846 64 12.5 12.5532514464617 -0.0532514464616851 65 15 14.9825395815026 0.0174604184973918 66 19.5 17.1143029297344 2.38569707026565 67 16.5 15.5777172593207 0.922282740679317 68 18.5 15.9620241431384 2.53797585686158 69 14 14.1027767325495 -0.102776732549536 70 13 14.0448290080677 -1.04482900806772 71 9.5 7.53107027833808 1.96892972166192 72 15.5 16.3378504677069 -0.837850467706869 73 14 16.3809772998237 -2.38097729982365 74 11 11.8408417166240 -0.840841716623964 75 14 15.0631540329506 -1.06315403295063 76 11 10.0181800354183 0.981819964581691 77 16.5 16.6067782753010 -0.106778275300964 78 16 15.3225731120857 0.677426887914328 79 16.5 16.7840442500753 -0.284044250075284 80 21 16.5187587401455 4.48124125985449 81 17 17.8460170129832 -0.846017012983165 82 18 16.5398785610714 1.46012143892863 83 14 15.0132243280319 -1.01322432803191 84 14.5 15.5241072598984 -1.02410725989838 85 16 16.5221231199943 -0.522123119994252 86 15.5 14.5610455392931 0.938954460706933 87 15.5 16.6808675480951 -1.18086754809507 88 14.5 16.6890832323053 -2.18908323230525 89 19 17.2420946829797 1.75790531702032 90 14.5 16.4517981974493 -1.95179819744926 91 14 16.6050196703078 -2.60501967030785 92 15 15.5764813711384 -0.576481371138445 93 16 16.7932000537341 -0.79320005373412 94 16 16.8762403015116 -0.876240301511599 95 19.5 18.1606567073507 1.33934329264931 96 11.5 13.4424217685523 -1.94242176855227 97 14 15.1317219004672 -1.13172190046716 98 13.5 15.5459355509959 -2.04593555099590 99 21 17.5971545068679 3.40284549313213 100 19 16.8374079003316 2.16259209966845 101 19 18.4580034214560 0.541996578543971 102 13.5 14.9131851136653 -1.41318511366529 103 12 12.9288918408501 -0.928891840850102 104 17 16.9702013861307 0.0297986138692754 105 16 15.3620412897426 0.637958710257365 106 13.5 16.1866366206783 -2.68663662067831 107 16.5 17.0644812807431 -0.564481280743127 108 14.5 16.3133239783740 -1.81332397837398 109 15 16.3976210794223 -1.39762107942235 110 17 17.7064316908649 -0.706431690864901 111 13.5 14.7026080032336 -1.20260800323365 112 17.5 17.1750232729302 0.324976727069812 113 16.9 16.0533526989434 0.846647301056608 114 14.9 16.0576925464383 -1.15769254643827 115 15.3 15.9646676852002 -0.664667685200227 116 13 15.2131813184580 -2.21318131845795 117 13.9 16.0290745880993 -2.12907458809926 118 12.8 13.8888637666255 -1.08886376662547 119 14.5 16.1526609839272 -1.65266098392721 120 17.6 17.4201031355847 0.179896864415315 121 22.2 18.0318710304636 4.16812896953644 122 22.1 17.686141214941 4.41385878505899 123 17.7 17.6572354101806 0.0427645898193882 124 16.2 16.6452347943338 -0.445234794333798 125 17.8 16.3888951018587 1.41110489814127 126 17 16.4770585673456 0.522941432654445 127 16.4 16.4852265587721 -0.085226558772086 128 15.7 17.1069841547628 -1.40698415476277 129 13.2 13.4833251098868 -0.283325109886799 130 16.7 17.0640053957416 -0.364005395741617 131 12.1 12.1919658202172 -0.0919658202171803 132 15 14.9783489846517 0.0216510153482510 133 14 12.9216625816916 1.07833741830844 134 14.8 15.9759802814204 -1.17598028142041 135 18.6 16.9709935862739 1.62900641372612 136 16.8 16.3404379523791 0.459562047620856 137 12.5 13.8021745603326 -1.30217456033257 138 13.7 14.4844700231129 -0.784470023112951 139 16.9 16.5277380999364 0.372261900063562 140 17.7 17.5934791231963 0.106520876803713 141 11.1 11.2944032861358 -0.194403286135798 142 11.4 12.3271072421286 -0.927107242128553 143 14.5 14.4895507145612 0.0104492854388337 144 14.5 15.5961183125740 -1.09611831257397 145 18.2 16.8191880620233 1.38081193797669 146 15.8 16.8496483553269 -1.04964835532694 147 15.9 15.6038019704804 0.296198029519591 148 16.4 16.5994117236330 -0.199411723633025 149 14.5 16.0061378426005 -1.50613784260053 150 12.8 14.8809932129954 -2.08099321299542 151 21.5 18.1540440564478 3.34595594355218 152 14.4 16.1083016244955 -1.70830162449552 153 18.6 16.7199396606192 1.88006033938083 154 13.2 13.6488266684574 -0.448826668457375 155 12.8 13.3584489607999 -0.558448960799888 156 18.2 16.7512149856934 1.44878501430663 157 15.8 16.9622567492527 -1.16225674925275 158 17.2 16.9862763900122 0.213723609987755 159 17.2 17.0485856949392 0.151414305060763 160 16.7 17.2810381841744 -0.581038184174371 161 18.7 16.7752346264529 1.92476537354713 162 13.2 12.4207883423389 0.779211657661122 163 13.4 11.8611522127495 1.53884778725047 164 13.7 14.6962513831998 -0.996251383199848 165 16.5 17.0285096038804 -0.528509603880355 166 14.7 15.0109107952302 -0.310910795230209 167 14.5 16.6470395281106 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-0.499603812070855 213 19.4 16.8254605423989 2.57453945760114 214 17.3 17.2565828475654 0.0434171524345899 215 14.9 17.5469605552229 -2.64696055522290 216 16.2 16.9309134086544 -0.730913408654398 217 14.2 16.6043874174823 -2.40438741748225 218 14.8 15.7308897919698 -0.930889791969808 219 20.4 18.9926147637642 1.40738523623585 220 13.8 14.5431453859877 -0.743145385987653 221 15.8 16.1034357832351 -0.303435783235124 222 17.1 17.0143127394899 0.0856872605100983 223 16.6 18.2743634084458 -1.67436340844578 224 18.6 16.8099034143737 1.79009658562634 225 18 16.0660800662232 1.93391993377679 226 16 16.5864874269608 -0.586487426960813 227 18 16.6195435695426 1.3804564304574 228 15.3 15.966824547639 -0.666824547639005 229 17.6 16.5244991243399 1.07550087566010 230 14.7 17.2737193252901 -2.57371932529008 231 14.5 15.2867287991265 -0.786728799126493 232 14.5 16.5546671725613 -2.05466717256127 233 15.7 16.5881074920187 -0.888107492018718 234 16.4 15.0883097077868 1.31169029221323 235 17 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16.6791879019963 -0.679187901996324 283 16 16.7932000537341 -0.79320005373412 284 19 17.2420946829797 1.75790531702032 285 16 16.9508091367487 -0.950809136748667 286 19 16.9620811573653 2.03791884263473 287 18 16.6914798759655 1.30852012403449 288 22 18.0318710304636 3.96812896953644 289 16 16.9309134086544 -0.930913408654398 290 19 16.6945481006291 2.30545189937087 291 17 17.2565828475654 -0.256582847565411 292 17 17.1067063626668 -0.106706362666762 293 15 16.207320955387 -1.20732095538699 294 18 16.8422928169066 1.15770718309336 295 19 16.7199396606192 2.28006033938083 296 20 16.7814997569869 3.21850024301305 297 16 15.6038019704804 0.396198029519591 298 22 18.4576454230398 3.54235457696016 299 17 15.293996139037 1.70600386096301 300 16 16.4001859651286 -0.400185965128615 301 18 17.2270863803474 0.772913619652594 302 19 17.2353223872981 1.76467761270191 303 16 16.7646722535563 -0.764672253556304 304 14 15.0497634492733 -1.04976344927333 305 14 15.6046296841257 -1.60462968412574 306 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12.7849775447297 -0.784977544729743 543 12 11.2880509718563 0.711949028143677 544 13 14.6169154391017 -1.61691543910174 545 19 16.1125095696711 2.88749043032892 546 19 16.8374079003316 2.16259209966845 547 13 13.6488266684574 -0.648826668457374 548 14 12.9216625816916 1.07833741830844 549 10 12.2645260937311 -2.26452609373108 550 13 12.9884548823418 0.0115451176581960 551 17 17.8460170129832 -0.846017012983165 552 19 18.4580034214560 0.541996578543971 553 17 17.0640053957416 -0.0640053957416167 554 11 10.8064162915031 0.193583708496938 555 15 14.3311901467619 0.668809853238096 556 15 14.8625605538221 0.137439446177906 557 9 9.46555393916793 -0.465553939167929 558 15 14.9783489846517 0.0216510153482510 559 13 13.8021745603326 -0.802174560332574 560 13 13.4529005512322 -0.452900551232190 561 19 17.8042524181878 1.1957475818122 562 17 15.0680432410387 1.93195675896132 563 21 17.5971545068679 3.40284549313213 564 13 13.4833251098868 -0.483325109886798 565 13 13.1374128179581 -0.137412817958115 566 13 14.2025383176041 -1.20253831760413 567 14 16.0290745880993 -2.02907458809926 568 13 13.7594437234712 -0.759443723471224 569 15 14.9490242831311 0.0509757168689282 570 14 14.1879499264965 -0.187949926496540 571 12 13.9628566390879 -1.96285663908788 572 19 17.4768725932737 1.52312740672629 573 14 13.8992589821179 0.100741017882133 574 14 14.6962513831998 -0.696251383199847 575 13 14.0448290080677 -1.04482900806772 576 13 13.9569432417704 -0.956943241770351 577 14 15.6293800657281 -1.62938006572814 578 13 11.7358241738016 1.26417582619837 579 13 13.5489781553479 -0.548978155347915 580 14 14.0753477747412 -0.0753477747412397 581 14 14.4844700231129 -0.48447002311295 582 14 15.0132243280319 -1.01322432803191 583 14 13.6248784969959 0.375121503004080 584 11 12.3271072421286 -1.32710724212855 585 13 14.2423285263669 -1.24232852636685 586 12 12.8546340234712 -0.854634023471152 587 13 15.2131813184580 -2.21318131845795 588 13 13.8888637666255 -0.888863766625475 589 11 11.2944032861358 -0.294403286135798 590 15 14.3850211686651 0.614978831334899 591 16 14.5610455392931 1.43895446070693 592 12 13.0519749117560 -1.05197491175597 593 10 7.53107027833808 2.46892972166192 594 16 15.4777344189177 0.5222655810823 595 15 16.2686547926678 -1.26865479266784 596 9 8.48668100507837 0.513318994921628 597 12 10.8253003609732 1.1746996390268 598 15 14.4895507145612 0.510449285438834 599 10 10.0047248899907 -0.00472488999074368 600 9 8.10494730169535 0.89505269830465 601 15 14.1009564471093 0.899043552890677 602 13 13.8654631731311 -0.865463173131135 603 15 10.9582013442644 4.04179865573557 604 12 12.1919658202172 -0.19196582021718 605 14 10.0979369897182 3.90206301028178 606 12 12.1892877210547 -0.189287721054743 607 13 11.1197936865675 1.88020631343254 608 10 7.9183260849829 2.08167391501711 609 14 15.1317219004672 -1.13172190046716 610 14 13.9984715789956 0.00152842100444603 611 14 15.0529441751675 -1.05294417516755 612 12 12.4291328006624 -0.429132800662439 613 12 14.398843700873 -2.39884370087299 614 15 15.1774207354703 -0.177420735470276 615 13 12.5532514464617 0.446748553538315 616 14 14.53207038767 -0.532070387669993 617 14 10.0654737019068 3.93452629809317 618 11 10.1033565203552 0.896643479644774 619 16 16.5221231199943 -0.522123119994252 620 13 13.7293578552567 -0.729357855256707 621 14 15.5459355509959 -1.54593555099590 622 12 13.4424217685523 -1.44242176855227 623 15 15.5241072598984 -0.524107259898384 624 19 12.6152492822430 6.38475071775698 625 11 9.77091478576262 1.22908521423738 626 12 13.6792308344940 -1.67923083449405 627 13 14.4013583290665 -1.40135832906655 628 11 9.51526927325692 1.48473072674308 629 12 11.859729239868 0.140270760132007 630 12 13.6658854487488 -1.66588544874876 631 14 16.0170389848085 -2.01703898480846 632 12 14.4814780388245 -2.4814780388245 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.590728319131341 0.818543361737317 0.409271680868659 9 0.442871451088646 0.885742902177293 0.557128548911354 10 0.300323404365471 0.600646808730942 0.699676595634529 11 0.327142013010238 0.654284026020476 0.672857986989762 12 0.243670150539197 0.487340301078394 0.756329849460803 13 0.197507973018255 0.395015946036511 0.802492026981745 14 0.175479611498851 0.350959222997701 0.82452038850115 15 0.313758181990717 0.627516363981433 0.686241818009283 16 0.927911058722351 0.144177882555298 0.0720889412776489 17 0.961284805313706 0.0774303893725873 0.0387151946862936 18 0.990754924492119 0.0184901510157622 0.00924507550788108 19 0.99036256769707 0.0192748646058607 0.00963743230293035 20 0.989616844592895 0.0207663108142097 0.0103831554071049 21 0.985610070781558 0.0287798584368845 0.0143899292184422 22 0.978985166723435 0.0420296665531293 0.0210148332765646 23 0.972527071045397 0.0549458579092066 0.0274729289546033 24 0.962525339646123 0.0749493207077549 0.0374746603538774 25 0.952446820060522 0.0951063598789558 0.0475531799394779 26 0.946798177894425 0.106403644211149 0.0532018221055746 27 0.966327286500717 0.0673454269985661 0.0336727134992831 28 0.95550856982694 0.08898286034612 0.04449143017306 29 0.956639344892648 0.0867213102147031 0.0433606551073516 30 0.953201068952306 0.0935978620953887 0.0467989310476943 31 0.950985867340591 0.0980282653188177 0.0490141326594089 32 0.965864767514197 0.0682704649716059 0.0341352324858029 33 0.97706597750294 0.0458680449941191 0.0229340224970595 34 0.991813289661305 0.0163734206773897 0.00818671033869483 35 0.988744356898017 0.0225112862039653 0.0112556431019827 36 0.984750925462976 0.030498149074048 0.015249074537024 37 0.980496175622863 0.0390076487542746 0.0195038243771373 38 0.974120590805394 0.0517588183892113 0.0258794091946057 39 0.966442195389425 0.0671156092211498 0.0335578046105749 40 0.957159805603093 0.0856803887938143 0.0428401943969071 41 0.945785408156805 0.10842918368639 0.054214591843195 42 0.937338012360646 0.125323975278709 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0.00111339031208025 0.000556695156040124 608 0.998970657869464 0.00205868426107184 0.00102934213053592 609 0.998160510659167 0.00367897868166636 0.00183948934083318 610 0.99660727243616 0.00678545512767908 0.00339272756383954 611 0.996321083454292 0.00735783309141654 0.00367891654570827 612 0.993369130935333 0.0132617381293346 0.0066308690646673 613 0.990506312309133 0.0189873753817348 0.0094936876908674 614 0.983102917333914 0.0337941653321725 0.0168970826660862 615 0.981618311309614 0.0367633773807729 0.0183816886903865 616 0.966920566069966 0.0661588678600676 0.0330794339300338 617 0.952703687941607 0.0945926241167856 0.0472963120583928 618 0.919897700631052 0.160204598737895 0.0801022993689475 619 0.881735773607968 0.236528452784063 0.118264226392032 620 0.879660430694616 0.240679138610769 0.120339569305384 621 0.825103232308175 0.34979353538365 0.174896767691825 622 0.741747885270483 0.516504229459034 0.258252114729517 623 0.608270764794114 0.783458470411771 0.391729235205886 624 0.96939836770963 0.0612032645807399 0.0306016322903700 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 243 0.393841166936791 NOK 5% type I error level 280 0.453808752025932 NOK 10% type I error level 313 0.507293354943274 NOK

Charts produced by software:

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Parameters (Session):

par1 = kendall ;

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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