multiple regression - interaction effects

*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, 14 Dec 2010 09:53:37 +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/14/t1292320432xov6rgjuuokwcyc.htm/, Retrieved Tue, 14 Dec 2010 10:56:06 +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/14/t1292320432xov6rgjuuokwcyc.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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1 12 12 18 18 9 9 51 15 15 1 15 15 11 11 9 9 42 14 14 1 12 12 16 16 8 8 46 10 10 1 15 15 15 15 15 15 47 18 18 1 9 9 19 19 11 11 33 11 11 1 11 11 18 18 8 8 47 12 12 1 11 11 14 14 9 9 32 15 15 1 15 15 18 18 6 6 53 17 17 1 11 11 14 14 11 11 33 7 7 1 10 10 12 12 16 16 37 18 18 1 11 11 16 16 7 7 49 18 18 1 11 11 9 9 15 15 43 11 11 1 14 14 17 17 10 10 43 12 12 1 13 13 17 17 6 6 46 11 11 1 16 16 12 12 12 12 42 16 16 1 13 13 11 11 14 14 40 14 14 1 14 14 17 17 9 9 42 13 13 1 9 9 16 16 14 14 44 17 17 1 12 12 12 12 14 14 46 13 13 1 13 13 16 16 8 8 45 12 12 1 16 16 14 14 10 10 49 12 12 1 15 15 12 12 9 9 43 9 9 1 5 5 14 14 11 11 37 18 18 1 11 11 15 15 9 9 45 14 14 1 17 17 11 11 10 10 45 12 12 1 9 9 14 14 8 8 31 12 12 1 13 13 15 15 14 14 33 9 9 1 10 10 16 16 10 10 44 12 12 1 12 12 15 15 14 14 38 11 11 1 11 11 16 16 15 15 33 13 13 1 16 16 9 9 11 11 47 13 13 1 15 15 15 15 8 8 48 6 6 1 14 14 17 17 10 10 54 21 21 1 16 16 17 17 10 10 43 11 11 1 9 9 15 15 9 9 54 9 9 1 14 14 13 13 13 13 44 18 18 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 11 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation belonging[t] = + 27.1549127461159 + 11.0419253322257gender[t] + 0.711931817315218popularity[t] -0.26228362100035popularity_g[t] + 0.445659792121529hapiness[t] -0.107179522084186hapiness_g[t] -0.121412841291265doubsaboutactions[t] -0.656061525985646doubtsaboutactions_g[t] + 0.123162078539735parentalexpectations[t] + 0.176354302880337parentalexpectations_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) 27.1549127461159 8.171656 3.3231 0.00115 0.000575 gender 11.0419253322257 12.408857 0.8898 0.375157 0.187579 popularity 0.711931817315218 0.306965 2.3193 0.021905 0.010952 popularity_g -0.26228362100035 0.40884 -0.6415 0.522282 0.261141 hapiness 0.445659792121529 0.407042 1.0949 0.275551 0.137775 hapiness_g -0.107179522084186 0.548552 -0.1954 0.845389 0.422694 doubsaboutactions -0.121412841291265 0.328667 -0.3694 0.71241 0.356205 doubtsaboutactions_g -0.656061525985646 0.467712 -1.4027 0.163035 0.081518 parentalexpectations 0.123162078539735 0.286835 0.4294 0.66834 0.33417 parentalexpectations_g 0.176354302880337 0.367818 0.4795 0.632399 0.316199 Multiple Linear Regression - Regression Statistics Multiple R 0.435982056995364 R-squared 0.190080354021909 Adjusted R-squared 0.135273761436925 F-TEST (value) 3.46820236501965 F-TEST (DF numerator) 9 F-TEST (DF denominator) 133 p-value 0.000711537672054341 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.84167943760142 Sum Squared Residuals 6225.54081107744 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 51 47.1807377106007 3.81926228939927 2 42 45.8608040278641 -3.8608040278641 3 46 45.7836696307029 0.216330369297065 4 47 43.7479444300324 3.25205556996761 5 33 43.4172591314597 -10.4172591314597 6 47 46.6100147373029 0.389985262697105 7 32 45.3771684341368 -13.3771684341368 8 53 51.4611381642166 1.53886183578344 9 33 41.4260886482224 -8.42608864822242 10 37 39.7067882710691 -2.70678827106911 11 49 48.5076268530256 0.492373146974442 12 43 37.8218553546084 5.17814464539164 13 43 46.0655303216563 -3.06553032165634 14 46 48.4262632130290 -2.42626321302905 15 42 44.9155421552258 -2.91554215522582 16 40 41.0741357988499 -1.07413579884991 17 42 47.1425210703533 -5.14252107035332 18 44 41.8664935080374 2.13350649196263 19 46 40.6634514911523 5.33654850884769 20 45 46.832350589858 -1.83235058985795 21 49 45.9493859041740 3.05061409582596 22 43 44.7017023908012 -1.70170239080119 23 37 42.022879665954 -5.02287966595402 24 45 45.4161323227541 -0.416132322754103 25 45 45.3835932903769 -0.383593290376883 26 31 44.3567972645238 -13.3567972645238 27 33 40.9304749718989 -7.93047497189892 28 44 43.9284572663595 0.0715427336404779 29 38 41.0798595384242 -3.07985953842419 30 33 40.7902500077099 -7.7902500077099 31 47 43.7790265681305 3.22097343186951 32 48 45.5960684239299 2.40393157607009 33 54 48.761177754437 5.23882224556301 34 43 46.665310332866 -3.665310332866 35 54 43.019254023024 10.980745976976 36 44 44.1762844281967 -0.176284428196661 37 45 46.7367671221567 -1.73676712215674 38 44 44.7612272291995 -0.761227229199535 39 47 45.1994740780696 1.80052592193042 40 43 37.1165850249917 5.8834149750083 41 33 45.7241447923046 -12.7241447923046 42 46 43.4122826402549 2.58771735974507 43 47 43.0992936794997 3.90070632050032 44 47 44.1054043740573 2.89459562594275 45 43 43.8951709856128 -0.895170985612782 46 44 42.8953607657808 1.10463923421918 47 47 47.3648569229084 -0.364856922908372 48 47 43.1772214567342 3.82277854326578 49 46 45.8218862709507 0.178113729049310 50 47 46.6263464442487 0.373653555751269 51 46 47.9532355866732 -1.95323558667322 52 36 45.8466303318633 -9.84663033186326 53 30 41.4825783614389 -11.4825783614389 54 49 45.837470729527 3.162529270473 55 55 47.885961908514 7.11403809148603 56 52 47.1311197229085 4.8688802770915 57 47 48.8575084705077 -1.85750847050772 58 33 37.8374859448884 -4.83748594488842 59 44 43.6162155539738 0.383784446026212 60 42 40.0197772318244 1.98022276817564 61 55 44.5061818310491 10.4938181689509 62 42 44.8170995599140 -2.81709955991396 63 46 45.7694498029982 0.230550197001763 64 46 47.6636260559589 -1.66362605595892 65 33 41.8630115135716 -8.86301151357164 66 53 49.6746939747714 3.32530602522858 67 44 43.711799021675 0.288200978324997 68 53 46.5037771705264 6.49622282947361 69 44 46.1221499007403 -2.12214990074028 70 35 40.1748394062202 -5.17483940622017 71 40 40.5352046095594 -0.535204609559434 72 44 45.1760946480286 -1.17609464802862 73 46 47.1510171584837 -1.15101715848373 74 45 40.8001568584157 4.19984314158432 75 53 45.8558736683632 7.14412633163681 76 48 41.9968116215206 6.0031883784794 77 55 41.9231130871213 13.0768869128787 78 47 49.3517981633104 -2.35179816331039 79 43 41.8757368445373 1.1242631554627 80 47 41.4798897470465 5.52011025295351 81 47 42.4350584703907 4.56494152960935 82 44 44.3165093923857 -0.316509392385678 83 42 43.8845168865375 -1.88451688653748 84 51 43.278482532306 7.72151746769404 85 54 43.6182867858642 10.3817132141359 86 51 45.6667779648511 5.33322203514888 87 42 43.4801526238921 -1.48015262389209 88 41 39.1539894320460 1.84601056795396 89 49 42.6829899487444 6.3170100512556 90 42 39.0977637436579 2.90223625634206 91 41 40.1848010469885 0.81519895301149 92 41 43.2099869809082 -2.20998698090821 93 43 44.2717564722066 -1.27175647220657 94 33 37.3659831103569 -4.36598311035691 95 42 44.458356466401 -2.45835646640099 96 37 38.3822376150307 -1.38223761503068 97 42 43.2824703892834 -1.2824703892834 98 43 40.0218626736779 2.97813732632205 99 33 44.9023628580891 -11.9023628580891 100 44 42.2355809193744 1.76441908062561 101 52 43.0795168382868 8.9204831617132 102 45 44.3568914932239 0.643108506776054 103 36 40.0056285583334 -4.00562855833337 104 43 42.8551050648427 0.144894935157284 105 32 35.456587552019 -3.45658755201902 106 45 45.6629365978752 -0.662936597875154 107 45 40.4783290043781 4.5216709956219 108 49 35.6560190238762 13.3439809761238 109 44 41.1087437166305 2.89125628336951 110 41 37.9729514799981 3.02704852000186 111 44 43.0144491268412 0.985550873158757 112 37 38.2610164473696 -1.26101644736961 113 40 38.8355770098846 1.16442299011537 114 50 44.7263777288432 5.27362227115685 115 47 41.4439770710599 5.55602292894009 116 33 42.3407596453211 -9.34075964532109 117 33 34.5798486826872 -1.57984868268716 118 45 41.4527232573023 3.54727674269774 119 43 41.7664747846417 1.23352521535829 120 0 39.5310594335826 -39.5310594335826 121 46 42.9927520214786 3.00724797852144 122 36 40.4943714460925 -4.49437144609248 123 42 38.4837984250228 3.51620157497717 124 41 38.9184718135452 2.08152818645481 125 46 43.0110464891594 2.9889535108406 126 48 40.8100638843106 7.18993611568942 127 45 41.4492247828053 3.55077521719468 128 11 42.8965347600469 -31.8965347600469 129 33 35.0490506542349 -2.04905065423494 130 47 45.0254290998138 1.97457090018621 131 42 42.6884529387625 -0.688452938762508 132 55 44.8388291056194 10.1611708943806 133 40 36.1468222639716 3.85317773602845 134 46 45.4945352345465 0.505464765453524 135 45 44.0666821453108 0.933317854689244 136 46 44.4419070727837 1.55809292721628 137 38 39.7662055134327 -1.76620551343269 138 40 39.3534209039032 0.6465790960968 139 42 39.8478184553106 2.15218154468939 140 53 41.6668548855282 11.3331451144718 141 43 44.2717564722066 -1.27175647220657 142 41 43.0631868861271 -2.06318688612712 143 51 43.9075179483328 7.09248205166723 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 13 0.905005374478776 0.189989251042447 0.0949946255212236 14 0.826322697807402 0.347354604385195 0.173677302192598 15 0.762000148523767 0.475999702952467 0.237999851476233 16 0.655205410856942 0.689589178286117 0.344794589143058 17 0.573510258452893 0.852979483094214 0.426489741547107 18 0.491159675743088 0.982319351486176 0.508840324256912 19 0.479708083236582 0.959416166473164 0.520291916763418 20 0.384546982219145 0.76909396443829 0.615453017780855 21 0.319084269464753 0.638168538929507 0.680915730535247 22 0.241331479999174 0.482662959998348 0.758668520000826 23 0.179857608576077 0.359715217152153 0.820142391423923 24 0.134005095493491 0.268010190986983 0.865994904506509 25 0.0930678863928245 0.186135772785649 0.906932113607176 26 0.125217944573074 0.250435889146148 0.874782055426926 27 0.131097842975221 0.262195685950442 0.868902157024779 28 0.109562477610028 0.219124955220056 0.890437522389972 29 0.0795589436030875 0.159117887206175 0.920441056396913 30 0.0807319624348812 0.161463924869762 0.919268037565119 31 0.0611614799657141 0.122322959931428 0.938838520034286 32 0.056983815706054 0.113967631412108 0.943016184293946 33 0.0443760295666905 0.088752059133381 0.95562397043331 34 0.0346651180938993 0.0693302361877987 0.9653348819061 35 0.156542235326283 0.313084470652566 0.843457764673717 36 0.120562092680729 0.241124185361459 0.879437907319271 37 0.0927240995378924 0.185448199075785 0.907275900462108 38 0.0690707620625928 0.138141524125186 0.930929237937407 39 0.0527837155776031 0.105567431155206 0.947216284422397 40 0.0508278916207448 0.101655783241490 0.949172108379255 41 0.0881149450538424 0.176229890107685 0.911885054946158 42 0.075523192899128 0.151046385798256 0.924476807100872 43 0.0608023353184678 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0.0119569640672826 0.994021517966359 61 0.0133287001781153 0.0266574003562306 0.986671299821885 62 0.0104093581038355 0.0208187162076711 0.989590641896164 63 0.00732377885963196 0.0146475577192639 0.992676221140368 64 0.00534417499658161 0.0106883499931632 0.994655825003418 65 0.00703111833702992 0.0140622366740598 0.99296888166297 66 0.0052995465168169 0.0105990930336338 0.994700453483183 67 0.00376735878556214 0.00753471757112427 0.996232641214438 68 0.00361067694660858 0.00722135389321715 0.996389323053391 69 0.00284194242770416 0.00568388485540832 0.997158057572296 70 0.00243861687999844 0.00487723375999688 0.997561383120002 71 0.00232236378459949 0.00464472756919897 0.9976776362154 72 0.00157720313043053 0.00315440626086106 0.99842279686957 73 0.00107159072118996 0.00214318144237993 0.99892840927881 74 0.000934782331724827 0.00186956466344965 0.999065217668275 75 0.000997579533083287 0.00199515906616657 0.999002420466917 76 0.000898238232363497 0.00179647646472699 0.999101761767637 77 0.00199567818806884 0.00399135637613767 0.998004321811931 78 0.00160444174529034 0.00320888349058068 0.99839555825471 79 0.00113267967981546 0.00226535935963092 0.998867320320185 80 0.000906894147448666 0.00181378829489733 0.999093105852551 81 0.00069548411280417 0.00139096822560834 0.999304515887196 82 0.000441237148026261 0.000882474296052521 0.999558762851974 83 0.00027899602814393 0.00055799205628786 0.999721003971856 84 0.000250991257954571 0.000501982515909143 0.999749008742045 85 0.000312916010873847 0.000625832021747693 0.999687083989126 86 0.000230248287982175 0.000460496575964349 0.999769751712018 87 0.000141626571530727 0.000283253143061453 0.99985837342847 88 8.61643252772307e-05 0.000172328650554461 0.999913835674723 89 6.13124823159712e-05 0.000122624964631942 0.999938687517684 90 3.72037652550894e-05 7.44075305101788e-05 0.999962796234745 91 2.15587383948825e-05 4.31174767897651e-05 0.999978441261605 92 1.26591860769124e-05 2.53183721538249e-05 0.999987340813923 93 7.7567806640116e-06 1.55135613280232e-05 0.999992243219336 94 4.76758459534297e-06 9.53516919068594e-06 0.999995232415405 95 2.67525187449432e-06 5.35050374898865e-06 0.999997324748126 96 1.61987271482474e-06 3.23974542964949e-06 0.999998380127285 97 9.97627442262175e-07 1.99525488452435e-06 0.999999002372558 98 5.8492960533268e-07 1.16985921066536e-06 0.999999415070395 99 1.02787318424971e-06 2.05574636849942e-06 0.999998972126816 100 5.51563828503417e-07 1.10312765700683e-06 0.999999448436172 101 5.24598184462626e-07 1.04919636892525e-06 0.999999475401816 102 2.79064637810829e-07 5.58129275621658e-07 0.999999720935362 103 1.89404356814963e-07 3.78808713629926e-07 0.999999810595643 104 1.05184700900442e-07 2.10369401800884e-07 0.9999998948153 105 5.52017852536342e-08 1.10403570507268e-07 0.999999944798215 106 2.69002073974219e-08 5.38004147948439e-08 0.999999973099793 107 2.38182254060788e-08 4.76364508121576e-08 0.999999976181775 108 1.72165404015729e-07 3.44330808031457e-07 0.999999827834596 109 9.09569860658574e-08 1.81913972131715e-07 0.999999909043014 110 4.7835551866908e-08 9.5671103733816e-08 0.999999952164448 111 2.14388929272571e-08 4.28777858545142e-08 0.999999978561107 112 9.54739917522224e-09 1.90947983504445e-08 0.9999999904526 113 4.15281936940829e-09 8.30563873881658e-09 0.99999999584718 114 2.48698076144857e-09 4.97396152289713e-09 0.99999999751302 115 1.62082236621088e-09 3.24164473242177e-09 0.999999998379178 116 2.86491619292225e-09 5.7298323858445e-09 0.999999997135084 117 1.33050756566045e-09 2.66101513132091e-09 0.999999998669492 118 1.01824782829770e-09 2.03649565659539e-09 0.999999998981752 119 3.91524242288586e-10 7.83048484577172e-10 0.999999999608476 120 0.0257901369611993 0.0515802739223985 0.9742098630388 121 0.0168366894137104 0.0336733788274209 0.98316331058629 122 0.0148245248464841 0.0296490496929681 0.985175475153516 123 0.00892387937505064 0.0178477587501013 0.99107612062495 124 0.00490652680533282 0.00981305361066564 0.995093473194667 125 0.0035548077738254 0.0071096155476508 0.996445192226175 126 0.00232140522580753 0.00464281045161507 0.997678594774192 127 0.0017153089404885 0.003430617880977 0.998284691059512 128 0.649185017952172 0.701629964095655 0.350814982047828 129 0.558568954608368 0.882862090783264 0.441431045391632 130 0.391283074528123 0.782566149056246 0.608716925471877 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 57 0.483050847457627 NOK 5% type I error level 80 0.677966101694915 NOK 10% type I error level 85 0.720338983050847 NOK

Charts produced by software:

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Parameters (Session):

par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 8 ; 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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