Workshop 10 - 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: Fri, 10 Dec 2010 13:00:14 +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/10/t1291985909xg2nat7v1b7um13.htm/, Retrieved Fri, 10 Dec 2010 13:58:40 +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/10/t1291985909xg2nat7v1b7um13.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

0 1 24 14 11 12 24 26 1 1 25 11 7 8 25 23 1 0 17 6 17 8 30 25 0 1 18 12 10 8 19 23 1 0 16 10 12 7 22 29 1 1 20 10 11 4 25 25 1 1 16 11 11 11 23 21 1 1 18 16 12 7 17 22 1 1 17 11 13 7 21 25 0 1 23 13 14 12 19 24 1 1 30 12 16 10 19 18 1 1 18 12 10 8 16 15 0 1 15 11 11 8 23 22 0 1 12 4 15 4 27 28 1 1 21 9 9 9 22 20 0 1 20 8 17 7 22 24 1 1 27 15 11 9 23 21 0 1 34 16 18 11 21 20 1 1 21 9 14 13 19 21 0 1 31 14 10 8 18 23 0 1 19 11 11 8 20 28 1 1 16 8 15 9 23 24 1 1 20 9 15 6 25 24 0 1 21 9 13 9 19 24 0 1 22 9 16 9 24 23 1 1 17 9 13 6 22 23 0 1 24 10 9 6 25 29 1 1 25 16 18 16 26 24 1 1 26 11 18 5 29 18 1 1 25 8 12 7 32 25 1 1 17 9 17 9 25 21 0 1 32 16 9 6 29 26 0 1 33 11 9 6 28 22 0 0 32 12 18 12 28 22 0 1 25 12 12 7 29 23 0 1 29 14 18 10 26 30 1 1 22 9 14 9 25 23 0 1 18 10 15 8 14 17 1 1 17 9 16 5 25 23 0 1 20 10 10 8 26 23 0 1 15 12 11 8 20 25 1 1 20 14 14 10 18 24 0 1 33 14 9 6 32 24 1 1 23 14 17 7 25 21 0 1 26 16 5 4 23 24 0 1 18 9 12 8 21 24 1 1 20 10 12 8 20 28 1 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 14 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation PE[t] = + 7.09326325421717 + 0.185102752444152Geslacht[t] -0.543845428355601Browser[t] + 0.0973882515518827CM[t] -0.160262217439694DA[t] + 0.67954844361031PC[t] + 0.104347613234137PS[t] -0.0980134280835426O[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) 7.09326325421717 2.645068 2.6817 0.008433 0.004216 Geslacht 0.185102752444152 0.541857 0.3416 0.733286 0.366643 Browser -0.543845428355601 0.934059 -0.5822 0.561576 0.280788 CM 0.0973882515518827 0.05724 1.7014 0.09164 0.04582 DA -0.160262217439694 0.10618 -1.5094 0.134025 0.067013 PC 0.67954844361031 0.099789 6.8098 0 0 PS 0.104347613234137 0.072618 1.4369 0.153524 0.076762 O -0.0980134280835426 0.079632 -1.2308 0.220965 0.110482 Multiple Linear Regression - Regression Statistics Multiple R 0.660398523801121 R-squared 0.4361262102387 Adjusted R-squared 0.400884098378618 F-TEST (value) 12.3751440313854 F-TEST (DF numerator) 7 F-TEST (DF denominator) 112 p-value 1.18083320899132e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.73149971992306 Sum Squared Residuals 835.642160633255 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11 14.7536397297218 -3.75363972972184 2 7 13.1971115090806 -6.19711150908056 3 17 14.0888732222232 2.91112677777682 4 10 11.5439430989287 -1.54394309892871 5 12 11.4440530390949 0.555946960905061 6 11 9.95621183815252 1.04378816184748 7 11 14.3465942056434 -3.34659420564336 8 12 10.2977667396190 1.70223326038095 9 13 11.1250397439516 1.87496025604844 10 14 14.4908024856061 -0.490802485606132 11 16 14.7468688976338 1.25313110236621 12 10 12.2001104363388 -2.20011043633880 13 11 11.9274444427329 -0.927444442732853 14 15 9.86823132014912 5.13176867985088 15 9 13.7886288259109 -4.78862882591095 16 17 11.9152494397998 5.08475056020018 17 11 13.4177192157347 -2.41771921573467 18 18 15.0024870955499 2.99751290445011 19 14 16.0957663325662 -2.09576633256623 20 10 12.3851183209897 -2.38511832098967 21 11 11.4158740407367 -0.415874040736717 22 15 13.1742436864912 1.82575631350881 23 15 11.5735843708964 3.42641562910362 24 13 12.8984295214302 0.101570478569785 25 16 13.6155692672363 2.38443073276368 26 13 11.0663902046219 1.93360979537814 27 9 11.1277052668023 -2.12770526680235 28 18 17.8385221559152 0.161477844084839 29 18 12.1633120231558 5.83668797684422 30 12 13.5327561542612 -1.53275615426121 31 17 13.6141052313223 3.38589476867772 32 9 11.6566687117664 -2.65666871176642 33 9 12.8430741496168 -3.84307414961681 34 18 17.2065597706427 0.79344022935731 35 12 12.5895885485230 -0.589588548522955 36 18 13.6981256143948 4.30187438560518 37 14 13.9050196329146 0.0949803670853874 38 15 11.9308100361387 3.06918996386132 39 16 10.6998846007140 5.30011539928604 40 10 12.7896773295508 -2.78967732955083 41 11 11.1600991013401 -0.16009910134012 42 14 12.7600337655002 1.23996623449982 43 9 12.5836510940672 -3.58365109406719 44 17 12.0380267662145 4.96197323378551 45 5 9.28318349199677 -4.28318349199677 46 12 12.1354115496325 -0.135411549632531 47 12 11.8586272621724 0.141372737827555 48 6 9.55941116435487 -3.55941116435487 49 24 22.7553198373562 1.24468016264383 50 12 12.2815471440177 -0.281547144017664 51 12 12.7775028727646 -0.777502872764575 52 14 11.3482583241692 2.65174167583078 53 7 8.86570660165935 -1.86570660165935 54 12 12.9326011533098 -0.932601153309826 55 14 11.722402013423 2.27759798657699 56 8 12.4869539631865 -4.48695396318647 57 11 9.04671619056212 1.95328380943789 58 9 11.3029081148330 -2.30290811483304 59 11 13.6660686504808 -2.66606865048084 60 10 8.95206287413437 1.04793712586563 61 11 13.0579888235097 -2.05798882350967 62 12 12.8667898343578 -0.866789834357842 63 9 11.8363675381018 -2.8363675381018 64 18 14.7755657498920 3.22443425010803 65 15 12.0599004521241 2.94009954787587 66 12 12.8368860134129 -0.836886013412891 67 13 9.39004888937048 3.60995111062952 68 14 12.9157884612577 1.08421153874231 69 10 11.4706412349159 -1.47064123491589 70 13 12.2281928045991 0.771807195400866 71 13 13.4885915285442 -0.488591528544163 72 11 12.7317290736477 -1.73172907364773 73 13 11.9341212816679 1.06587871833209 74 16 14.4520403627773 1.54795963722269 75 11 10.9355095746324 0.0644904253676084 76 16 17.7130133625102 -1.71301336251019 77 14 11.6958160219126 2.30418397808743 78 8 10.6146650457315 -2.61466504573150 79 9 9.80593368432105 -0.805933684321045 80 15 11.5020067767481 3.49799322325195 81 11 13.2978564041544 -2.29785640415441 82 21 17.0962900186611 3.90370998133888 83 14 12.8611583132559 1.13884168674409 84 18 15.7629702580805 2.23702974191952 85 12 11.5342488021223 0.465751197877679 86 13 12.7268293915598 0.273170608440180 87 12 10.890019400418 1.10998059958199 88 19 14.5541475038353 4.44585249616473 89 11 12.5857238537622 -1.58572385376224 90 13 14.9373663248922 -1.93736632489221 91 15 14.6379542040571 0.362045795942916 92 12 11.0739206659254 0.926079334074593 93 16 15.8598099697740 0.140190030225968 94 18 18.0522078388685 -0.0522078388684962 95 8 14.8962463552164 -6.89624635521639 96 9 10.7441215031642 -1.74412150316422 97 15 12.7997142801417 2.20028571985832 98 6 10.6271538363224 -4.62715383632243 99 8 9.48365831118565 -1.48365831118565 100 10 10.1186110320092 -0.118611032009228 101 11 12.3117823538364 -1.31178235383638 102 14 12.6437736720802 1.35622632791979 103 11 13.4037516262436 -2.40375162624359 104 12 11.8980400170529 0.101959982947141 105 11 10.0120463375509 0.987953662449092 106 9 9.3527768303525 -0.352776830352503 107 12 11.8435894487613 0.156410551238657 108 20 14.3503305018472 5.6496694981528 109 13 13.5974238022869 -0.597423802286877 110 12 16.453229122563 -4.453229122563 111 9 14.5562401844148 -5.55624018441481 112 24 21.6303020406828 2.36969795931718 113 11 11.5369383392537 -0.536938339253733 114 17 15.1735676092157 1.82643239078427 115 11 12.7716415022599 -1.77164150225991 116 11 14.2331286060079 -3.23312860600792 117 16 12.4856041352201 3.51439586477994 118 13 10.9493742210865 2.05062577891347 119 11 12.6210258176553 -1.62102581765530 120 19 17.8757768584534 1.12422314154660 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.87158898067261 0.256822038654780 0.128411019327390 12 0.865575905121387 0.268848189757226 0.134424094878613 13 0.786547785030987 0.426904429938026 0.213452214969013 14 0.749533434369727 0.500933131260546 0.250466565630273 15 0.809536669484933 0.380926661030134 0.190463330515067 16 0.81580210762886 0.36839578474228 0.18419789237114 17 0.763840459072816 0.472319081854368 0.236159540927184 18 0.778668229552464 0.442663540895073 0.221331770447537 19 0.73211673994928 0.535766520101441 0.267883260050721 20 0.843574147008532 0.312851705982936 0.156425852991468 21 0.798568561390652 0.402862877218695 0.201431438609348 22 0.798408330683812 0.403183338632375 0.201591669316188 23 0.805525032481944 0.388949935036112 0.194474967518056 24 0.754946218829733 0.490107562340533 0.245053781170267 25 0.71981650693725 0.5603669861255 0.28018349306275 26 0.669424769693095 0.661150460613809 0.330575230306905 27 0.70670592824129 0.586588143517419 0.293294071758709 28 0.765443560361397 0.469112879277205 0.234556439638602 29 0.836315920292126 0.327368159415748 0.163684079707874 30 0.833023320311231 0.333953359377538 0.166976679688769 31 0.84220189480698 0.315596210386040 0.157798105193020 32 0.84278237375515 0.314435252489699 0.157217626244849 33 0.882827065608852 0.234345868782296 0.117172934391148 34 0.850528541585804 0.298942916828392 0.149471458414196 35 0.815354638259348 0.369290723481305 0.184645361740652 36 0.899152500846268 0.201694998307463 0.100847499153732 37 0.869650525651537 0.260698948696927 0.130349474348463 38 0.863111391129852 0.273777217740297 0.136888608870148 39 0.9188240068086 0.162351986382802 0.081175993191401 40 0.9250757510136 0.149848497972799 0.0749242489863995 41 0.90292942171693 0.194141156566141 0.0970705782830705 42 0.88316385923951 0.233672281520980 0.116836140760490 43 0.891823869160696 0.216352261678608 0.108176130839304 44 0.941081722580764 0.117836554838473 0.0589182774192366 45 0.963613093394388 0.0727738132112249 0.0363869066056125 46 0.951238862592792 0.0975222748144156 0.0487611374072078 47 0.935768959578131 0.128462080843738 0.064231040421869 48 0.957659201482546 0.0846815970349074 0.0423407985174537 49 0.946908899434688 0.106182201130624 0.0530911005653118 50 0.929888943519546 0.140222112960908 0.0701110564804538 51 0.911657991252059 0.176684017495883 0.0883420087479414 52 0.909303468633406 0.181393062733188 0.0906965313665938 53 0.900154873194493 0.199690253611015 0.0998451268055074 54 0.877261515839669 0.245476968320662 0.122738484160331 55 0.869597091159964 0.260805817680072 0.130402908840036 56 0.910272345753468 0.179455308493064 0.089727654246532 57 0.9002493993562 0.199501201287600 0.0997506006438001 58 0.893892639202304 0.212214721595392 0.106107360797696 59 0.907211381002212 0.185577237995575 0.0927886189977876 60 0.890220272842859 0.219559454314282 0.109779727157141 61 0.882297300123219 0.235405399753563 0.117702699876781 62 0.860304757391533 0.279390485216935 0.139695242608467 63 0.860484975266406 0.279030049467189 0.139515024733594 64 0.875634259180342 0.248731481639316 0.124365740819658 65 0.877852465298488 0.244295069403023 0.122147534701512 66 0.850133073939693 0.299733852120613 0.149866926060307 67 0.893029946419443 0.213940107161114 0.106970053580557 68 0.875327189073112 0.249345621853777 0.124672810926888 69 0.85051292737627 0.298974145247460 0.149487072623730 70 0.816494721664152 0.367010556671695 0.183505278335848 71 0.777916164511319 0.444167670977363 0.222083835488682 72 0.748507559030668 0.502984881938663 0.251492440969331 73 0.706605498466452 0.586789003067095 0.293394501533548 74 0.684212706811903 0.631574586376193 0.315787293188097 75 0.637923780902695 0.72415243819461 0.362076219097305 76 0.604611354435544 0.790777291128912 0.395388645564456 77 0.57982861005015 0.8403427798997 0.42017138994985 78 0.554639287427666 0.890721425144667 0.445360712572334 79 0.50076636953895 0.9984672609221 0.49923363046105 80 0.51943568253419 0.96112863493162 0.48056431746581 81 0.512989824534018 0.974020350931964 0.487010175465982 82 0.581932810088761 0.836134379822479 0.418067189911239 83 0.530904860725254 0.93819027854949 0.469095139274746 84 0.499961799265934 0.999923598531867 0.500038200734066 85 0.438866006997201 0.877732013994401 0.561133993002799 86 0.377258674390584 0.754517348781168 0.622741325609416 87 0.323998637034717 0.647997274069435 0.676001362965283 88 0.451660619544089 0.903321239088177 0.548339380455911 89 0.447415476774877 0.894830953549754 0.552584523225123 90 0.408124442582045 0.81624888516409 0.591875557417955 91 0.346938775113602 0.693877550227204 0.653061224886398 92 0.315558666665728 0.631117333331457 0.684441333334272 93 0.269979247791475 0.53995849558295 0.730020752208525 94 0.230040359611438 0.460080719222877 0.769959640388562 95 0.391429147014706 0.782858294029412 0.608570852985294 96 0.336466899428460 0.672933798856921 0.66353310057154 97 0.281815198219469 0.563630396438938 0.718184801780531 98 0.376122362509142 0.752244725018284 0.623877637490858 99 0.349915305509255 0.69983061101851 0.650084694490745 100 0.281227642093196 0.562455284186393 0.718772357906804 101 0.24425055283523 0.48850110567046 0.75574944716477 102 0.181500405479084 0.363000810958167 0.818499594520916 103 0.163890783910683 0.327781567821367 0.836109216089317 104 0.110508491271964 0.221016982543928 0.889491508728036 105 0.0708451613628645 0.141690322725729 0.929154838637135 106 0.0414568034268908 0.0829136068537816 0.95854319657311 107 0.0247560559537247 0.0495121119074495 0.975243944046275 108 0.0686330272448579 0.137266054489716 0.931366972755142 109 0.0417010455902699 0.0834020911805398 0.95829895440973 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 1 0.0101010101010101 OK 10% type I error level 6 0.0606060606060606 OK

Charts produced by software:

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Parameters (Session):

par1 = 5 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

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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