multiple regression with seasonal dummies and linear trend, totale industrie zonder de bouwnijverheid, prijsindex van de industriele grondstoffen

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 19 Nov 2009 08:28:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/19/t12586447142swiozkgqmuja4x.htm/, Retrieved Thu, 19 Nov 2009 16:32:07 +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/2009/Nov/19/t12586447142swiozkgqmuja4x.htm/}, year = {2009}, } @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 = {2009}, 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 «

97.6 82.9 96.9 83.8 105.6 86.2 102.8 86.1 101.7 86.2 104.2 88.8 92.7 89.6 91.9 87.8 106.5 88.3 112.3 88.6 102.8 91 96.5 91.5 101 95.4 98.9 98.7 105.1 99.9 103 98.6 99 100.3 104.3 100.2 94.6 100.4 90.4 101.4 108.9 103 111.4 109.1 100.8 111.4 102.5 114.1 98.2 121.8 98.7 127.6 113.3 129.9 104.6 128 99.3 123.5 111.8 124 97.3 127.4 97.7 127.6 115.6 128.4 111.9 131.4 107 135.1 107.1 134 100.6 144.5 99.2 147.3 108.4 150.9 103 148.7 99.8 141.4 115 138.9 90.8 139.8 95.9 145.6 114.4 147.9 108.2 148.5 112.6 151.1 109.1 157.5 105 167.5 105 172.3 118.5 173.5 103.7 187.5 112.5 205.5 116.6 195.1 96.6 204.5 101.9 204.5 116.5 201.7 119.3 207 115.4 206.6 108.5 210.6 111.5 211.1 108.8 215 121.8 223.9 109.6 238.2 112.2 238.9 119.6 229.6 104.1 232.2 105.3 222.1 115 221.6 124.1 227.3 116.8 221 107.5 213.6 115.6 243.4

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation tot_indus[t] = + 90.832085622519 + 0.102540997522223prijsindex[t] -1.02882141864122M1[t] -2.96881131069401M2[t] + 7.59567990197284M3[t] -0.427850750705502M4[t] -0.910410059206618M5[t] + 7.2838462707706M6[t] -8.87902180084571M7[t] -7.59582151496311M8[t] + 8.03783230706095M9[t] + 9.4283972869726M10[t] + 4.08770137665445M11[t] -0.032791804572772t + 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) 90.832085622519 2.270998 39.9965 0 0 prijsindex 0.102540997522223 0.032593 3.1461 0.002593 0.001296 M1 -1.02882141864122 1.672555 -0.6151 0.540841 0.270421 M2 -2.96881131069401 1.739573 -1.7066 0.093149 0.046575 M3 7.59567990197284 1.744359 4.3544 5.4e-05 2.7e-05 M4 -0.427850750705502 1.753935 -0.2439 0.808125 0.404063 M5 -0.910410059206618 1.74596 -0.5214 0.604014 0.302007 M6 7.2838462707706 1.713049 4.252 7.7e-05 3.8e-05 M7 -8.87902180084571 1.714484 -5.1788 3e-06 1e-06 M8 -7.59582151496311 1.702849 -4.4607 3.7e-05 1.9e-05 M9 8.03783230706095 1.698533 4.7322 1.4e-05 7e-06 M10 9.4283972869726 1.69997 5.5462 1e-06 0 M11 4.08770137665445 1.697389 2.4082 0.019174 0.009587 t -0.032791804572772 0.078074 -0.42 0.676006 0.338003 Multiple Linear Regression - Regression Statistics Multiple R 0.940800839498478 R-squared 0.88510621960104 Adjusted R-squared 0.859790640869066 F-TEST (value) 34.9629067923750 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.93862008885469 Sum Squared Residuals 509.493793570601 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.6 98.2711210938972 -0.671121093897202 2 96.9 96.3906262950418 0.509373704958178 3 105.6 107.168424097189 -1.56842409718921 4 102.8 99.101847540186 3.69815245981413 5 101.7 98.5967505268642 3.10324947313581 6 104.2 107.024821645826 -2.82482164582643 7 92.7 90.9111945676551 1.78880543234487 8 91.9 91.977029253425 -0.0770292534249414 9 106.5 107.629161769637 -1.12916176963735 10 112.3 109.017697244233 3.28230275576709 11 102.8 103.890307923395 -1.09030792339531 12 96.5 99.8210852409292 -3.3210852409292 13 101 99.1593819080519 1.84061809194812 14 98.9 97.5249855032497 1.37501449675035 15 105.1 108.179734108370 -3.07973410837040 16 103 99.9901083543404 3.00989164565961 17 99 99.6490769370543 -0.649076937054284 18 104.3 107.800287362707 -3.50028736270651 19 94.6 91.6251356860219 2.97486431397812 20 90.4 92.978085164854 -2.57808516485391 21 108.9 108.743012778341 0.156987221659233 22 111.4 110.726286038565 0.673713961434789 23 100.8 105.588642617975 -4.78864261797541 24 102.5 101.745010130058 0.754989869941816 25 98.2 101.472962587765 -3.27296258776531 26 98.7 100.094918676769 -1.39491867676865 27 113.3 110.862462379164 2.43753762083616 28 104.6 102.611312026620 1.9886879733795 29 99.3 101.634526424697 -2.33452642469660 30 111.8 109.847261448862 1.95273855113784 31 97.3 94.0002409642486 3.29975903575136 32 97.7 95.2711576450629 2.42884235493710 33 115.6 110.954052460532 4.64594753946801 34 111.9 112.619448628438 -0.719448628437527 35 107 107.625362604379 -0.625362604378833 36 107.1 103.392074325877 3.70792567412283 37 100.6 103.407141576647 -2.80714157664653 38 99.2 101.721474673083 -2.52147467308318 39 108.4 112.622321672257 -4.22232167225726 40 103 104.340409020457 -1.34040902045726 41 99.8 103.076508625471 -3.27650862547114 42 115 110.98162065707 4.01837934292998 43 90.8 94.878247678651 -4.07824767865095 44 95.9 96.7233939455897 -0.823393945589662 45 114.4 112.560100257342 1.83989974265793 46 108.2 113.979398031194 -5.77939803119428 47 112.6 108.872516909861 3.72748309013885 48 109.1 105.408286112776 3.69171388722384 49 105 105.372082864784 -0.372082864784393 50 105 103.891497956266 1.10850204373449 51 118.5 114.546246561386 3.95375343861376 52 103.7 107.925498069446 -4.22549806944626 53 112.5 109.255884911772 3.24411508822761 54 116.6 116.350923062946 0.249076937054285 55 96.6 101.119148563466 -4.51914856346554 56 101.9 102.369557044775 -0.469557044775349 57 116.5 117.683304269164 -1.18330426916442 58 119.3 119.584544731371 -0.284544731371096 59 115.4 114.170040617471 1.22995938252873 60 108.5 110.459711426333 -1.95971142633294 61 111.5 109.44936870188 2.05063129811993 62 108.8 107.876496895591 0.923503104408818 63 121.8 119.320811181633 2.47918881836696 64 109.6 112.730824988950 -3.13082498894972 65 112.2 112.287252574141 -0.087252574141383 66 119.6 119.495085822589 0.104914177410842 67 104.1 103.566032539958 0.53396746004214 68 105.3 103.780776946293 1.51922305370677 69 115 119.330368464983 -4.33036846498340 70 124.1 121.272625326199 2.82737467380103 71 116.8 115.253129326918 1.54687067308197 72 107.5 110.373832764026 -2.87383276402635 73 115.6 112.367941266975 3.23205873302538 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.219275880772119 0.438551761544239 0.780724119227881 18 0.120501671989001 0.241003343978002 0.879498328010999 19 0.0601983139844017 0.120396627968803 0.939801686015598 20 0.0354210331246286 0.0708420662492573 0.964578966875371 21 0.02704889731903 0.05409779463806 0.97295110268097 22 0.0117718101769025 0.0235436203538051 0.988228189823097 23 0.00722037137403094 0.0144407427480619 0.99277962862597 24 0.0502307556337114 0.100461511267423 0.949769244366289 25 0.0443620753438663 0.0887241506877325 0.955637924656134 26 0.0255457437808291 0.0510914875616582 0.974454256219171 27 0.0967362542388432 0.193472508477686 0.903263745761157 28 0.0762170419283511 0.152434083856702 0.92378295807165 29 0.0678561504215706 0.135712300843141 0.93214384957843 30 0.127313064604664 0.254626129209328 0.872686935395336 31 0.125859526364989 0.251719052729978 0.874140473635011 32 0.130464876940359 0.260929753880717 0.869535123059641 33 0.226503369383875 0.45300673876775 0.773496630616125 34 0.205504408000844 0.411008816001689 0.794495591999156 35 0.165038571309374 0.330077142618749 0.834961428690626 36 0.234791971679011 0.469583943358023 0.765208028320989 37 0.232396222220453 0.464792444440906 0.767603777779547 38 0.225807366795107 0.451614733590215 0.774192633204893 39 0.379705713495384 0.759411426990768 0.620294286504616 40 0.387662082777613 0.775324165555227 0.612337917222387 41 0.418967023008544 0.837934046017087 0.581032976991456 42 0.532371891355168 0.935256217289664 0.467628108644832 43 0.582354360377208 0.835291279245584 0.417645639622792 44 0.501015333795673 0.997969332408654 0.498984666204327 45 0.54246264698232 0.91507470603536 0.45753735301768 46 0.828608864656134 0.342782270687731 0.171391135343865 47 0.83760158968721 0.324796820625579 0.162398410312789 48 0.962442900895 0.0751141982099994 0.0375570991049997 49 0.953121392153946 0.0937572156921082 0.0468786078460541 50 0.918505548533945 0.162988902932109 0.0814944514660547 51 0.899744692801104 0.200510614397793 0.100255307198896 52 0.86330840716606 0.273383185667879 0.136691592833939 53 0.904482263284098 0.191035473431805 0.0955177367159023 54 0.870098325017004 0.259803349965991 0.129901674982996 55 0.882841711880623 0.234316576238754 0.117158288119377 56 0.794072458411595 0.411855083176809 0.205927541588405 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 2 0.05 NOK 10% type I error level 8 0.2 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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