invoer-textiel

*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, 19 Dec 2008 12:31:41 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/19/t12297152406cfpdx1724hjtl4.htm/, Retrieved Fri, 19 Dec 2008 20:34:00 +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/2008/Dec/19/t12297152406cfpdx1724hjtl4.htm/}, year = {2008}, } @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 = {2008}, 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 «

101.3 163095 102 159044 109.2 155511 88.6 153745 94.3 150569 98.3 150605 86.4 179612 80.6 194690 104.1 189917 108.2 184128 93.4 175335 71.9 179566 94.1 181140 94.9 177876 96.4 175041 91.1 169292 84.4 166070 86.4 166972 88 206348 75.1 215706 109.7 202108 103 195411 82.1 193111 68 195198 96.4 198770 94.3 194163 90 190420 88 189733 76.1 186029 82.5 191531 81.4 232571 66.5 243477 97.2 227247 94.1 217859 80.7 208679 70.5 213188 87.8 216234 89.5 213586 99.6 209465 84.2 204045 75.1 200237 92 203666 80.8 241476 73.1 260307 99.8 243324 90 244460 83.1 233575 72.4 237217 78.8 235243 87.3 230354 91 227184 80.1 221678 73.6 217142 86.4 219452 74.5 256446 71.2 265845 92.4 248624 81.5 241114 85.3 229245 69.9 231805 84.2 219277 90.7 219313 100.3 212610 79.4 214771 84.8 211142 92.9 211457 81.6 240048 76 240636 98.7 230580 89.1 208795 88.7 197922 67.1 194596

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation textiel[t] = + 105.294187220432 -0.000169359383272681invoer[t] + 19.3993920598461M1[t] + 21.5344808429619M2[t] + 25.4874128539972M3[t] + 12.4918260779993M4[t] + 8.01872468037523M5[t] + 16.7380540361434M6[t] + 15.1118415743643M7[t] + 8.55619124616013M8[t] + 32.8968828587823M9[t] + 25.4846231882353M10[t] + 15.1965447285024M11[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) 105.294187220432 5.088971 20.6907 0 0 invoer -0.000169359383272681 2.3e-05 -7.4501 0 0 M1 19.3993920598461 2.616299 7.4148 0 0 M2 21.5344808429619 2.621358 8.215 0 0 M3 25.4874128539972 2.630488 9.6892 0 0 M4 12.4918260779993 2.638791 4.7339 1.4e-05 7e-06 M5 8.01872468037523 2.651889 3.0238 0.003692 0.001846 M6 16.7380540361434 2.644159 6.3302 0 0 M7 15.1118415743643 2.642451 5.7189 0 0 M8 8.55619124616013 2.68978 3.181 0.002341 0.00117 M9 32.8968828587823 2.634647 12.4863 0 0 M10 25.4846231882353 2.616809 9.7388 0 0 M11 15.1965447285024 2.61289 5.816 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.9206019022485 R-squared 0.847507862423556 Adjusted R-squared 0.816492512408008 F-TEST (value) 27.3254327937200 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.52476415380287 Sum Squared Residuals 1207.93594820482 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.3 97.0719106654196 4.22808933458041 2 102 99.8930743101732 2.10692568982683 3 109.2 104.444353022311 4.75564697768913 4 88.6 91.7478549171725 -3.14785491717251 5 94.3 87.8126389208225 6.48736107917753 6 98.3 96.5258713387928 1.77412866120719 7 86.4 89.987051246423 -3.58705124642304 8 80.6 80.8778001372334 -0.277800137233435 9 104.1 106.026844086216 -1.92684408621614 10 108.2 99.5950058854347 8.60499411456534 11 93.4 90.7961044828184 2.60389551718158 12 71.9 74.8830002036893 -2.98300020368930 13 94.1 94.0158205942643 0.0841794057357357 14 94.9 96.703698404382 -1.80369840438204 15 96.4 101.136764266995 -4.73676426699543 16 91.1 89.1148245854321 1.98517541456785 17 84.4 85.1873991207126 -0.787399120712642 18 86.4 93.7539663127688 -7.35396631276883 19 88 85.4590587752447 2.54094122475534 20 75.1 77.3185433383748 -2.21854333837478 21 109.7 103.962183844739 5.73781615526113 22 103 97.684123963969 5.315876036031 23 82.1 87.7855720857633 -5.68557208576326 24 68 72.2355743243708 -4.23557432437078 25 96.4 91.0300146671669 5.36998533283311 26 94.3 93.9453421290199 0.354657870980104 27 90 98.5321863116449 -8.53218631164488 28 88 85.6529494319553 2.34705056804472 29 76.1 81.8071551899732 -5.70715518997322 30 82.5 89.594669218975 -7.09466921897507 31 81.4 81.0179476676851 0.382052332314856 32 66.5 72.6152639055092 -6.11526390550916 33 97.2 99.704658308647 -2.50465830864695 34 94.1 93.8823445282639 0.217655471736119 35 80.7 85.1489852069742 -4.44898520697417 36 70.5 69.1887990192952 1.31120098070476 37 87.8 88.0723223976928 -0.272322397692804 38 89.5 90.6558748277146 -1.15587482771462 39 99.6 95.3067368572167 4.29326314278332 40 84.2 83.2290779385567 0.970922061443331 41 75.1 79.400897072435 -4.30089707243497 42 92 87.5394931029611 4.4605068970389 43 80.8 79.509802359642 1.29019764035807 44 73.1 69.76494548503 3.33505451497005 45 99.8 96.981867503772 2.81813249622793 46 90 89.3772155738273 0.622784426172701 47 83.1 80.9326140010175 2.16738599898248 48 72.4 65.119262398636 7.280737601364 49 78.8 84.8529698810624 -6.05296988106242 50 87.3 87.8160566889983 -0.51605668899831 51 91 92.305857945008 -1.30585794500805 52 80.1 80.2427639333095 -0.142763933309500 53 73.6 76.5378766982103 -2.93787669821031 54 86.4 84.8659858786186 1.53401412138145 55 74.5 76.9744923920499 -2.4744923920499 56 71.2 68.8270332204658 2.37296677953416 57 92.4 96.0842627724269 -3.68426277242686 58 81.5 89.9438920702577 -8.4438920702577 59 85.3 81.6659401305882 3.63405986941178 60 69.9 66.0358353809078 3.86416461909225 61 84.2 87.556961794394 -3.35696179439403 62 90.7 89.685953639712 1.01404636028803 63 100.3 94.7741015968241 5.5258984031759 64 79.4 81.4125291935739 -2.01252919357389 65 84.8 77.5540329978464 7.24596700215361 66 92.9 86.2200141478836 6.67998585211637 67 81.6 79.7516475589553 1.84835244104467 68 76 73.0964139133868 2.90358608661315 69 98.7 99.1401834841991 -0.440183484199113 70 89.1 95.4174179782475 -6.31741797824746 71 88.7 86.9707840928384 1.7292159071616 72 67.1 72.3375286731009 -5.23752867310092 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.492462716315496 0.984925432630993 0.507537283684504 17 0.382950005881629 0.765900011763258 0.617049994118371 18 0.342925357845126 0.685850715690251 0.657074642154874 19 0.605630728276434 0.788738543447132 0.394369271723566 20 0.484818880692523 0.969637761385046 0.515181119307477 21 0.596887751522251 0.806224496955498 0.403112248477749 22 0.601640091833292 0.796719816333415 0.398359908166708 23 0.59011683584052 0.81976632831896 0.40988316415948 24 0.506200432142021 0.987599135715959 0.493799567857979 25 0.619124613300966 0.761750773398069 0.380875386699034 26 0.550932926087142 0.898134147825715 0.449067073912858 27 0.645838769259296 0.708322461481408 0.354161230740704 28 0.65499725241283 0.690005495174339 0.345002747587169 29 0.66050945528074 0.678981089438519 0.339490544719260 30 0.716395779516006 0.567208440967988 0.283604220483994 31 0.680665588468809 0.638668823062383 0.319334411531191 32 0.720889562998828 0.558220874002345 0.279110437001172 33 0.652824716414443 0.694350567171114 0.347175283585557 34 0.664491528879055 0.671016942241889 0.335508471120944 35 0.670565176980074 0.658869646039852 0.329434823019926 36 0.685020789236505 0.62995842152699 0.314979210763495 37 0.657731268881016 0.684537462237968 0.342268731118984 38 0.584377715190318 0.831244569619364 0.415622284809682 39 0.677718356985766 0.644563286028468 0.322281643014234 40 0.62575758024176 0.748484839516481 0.374242419758241 41 0.622328304344776 0.755343391310448 0.377671695655224 42 0.68377670441073 0.632446591178541 0.316223295589270 43 0.619872340870406 0.760255318259189 0.380127659129594 44 0.596705031933148 0.806589936133704 0.403294968066852 45 0.569150735770857 0.861698528458287 0.430849264229143 46 0.621449471174168 0.757101057651664 0.378550528825832 47 0.560200409576058 0.879599180847883 0.439799590423942 48 0.711782751719354 0.576434496561292 0.288217248280646 49 0.681696187377395 0.636607625245209 0.318303812622605 50 0.584782485827527 0.830435028344946 0.415217514172473 51 0.595341434960754 0.809317130078492 0.404658565039246 52 0.48555735058048 0.97111470116096 0.51444264941952 53 0.694671669113483 0.610656661773034 0.305328330886517 54 0.687811554630495 0.62437689073901 0.312188445369505 55 0.663071322899373 0.673857354201255 0.336928677100627 56 0.52080467032871 0.95839065934258 0.47919532967129 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 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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