Q3 omzet MLR

*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, 21 Nov 2008 10:02:44 -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/Nov/21/t12272870348xzxwrncbxab7r6.htm/, Retrieved Fri, 21 Nov 2008 17:04:03 +0000

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/Nov/21/t12272870348xzxwrncbxab7r6.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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89.3 0 87.5 0 106.7 0 102.5 0 109.2 0 123.7 0 83.1 0 97 0 119.1 0 125.1 0 113.6 0 122.4 0 92.8 0 97.2 0 115.6 0 111.3 0 114.6 0 137.5 0 83.7 0 106 0 123.4 0 126.5 0 120 0 141.6 0 90.5 0 96.5 0 113.5 0 120.1 0 123.9 0 144.4 0 90.8 0 114.2 0 138.1 0 135 0 131.3 0 144.6 0 101.7 1 108.7 1 135.3 1 124.3 1 138.3 1 158.2 1 93.5 1 124.8 1 154.4 1 152.8 1 148.9 1 170.3 1 124.8 1 134.4 1 154 1 147.9 1 168.1 1 175.7 1 116.7 1 140.8 1 164.2 1 173.8 1 167.8 1 166.6 1 135.1 1 158.1 1 151.8 1 168.7 1 166.9 1

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 116.007058823529 + 4.97647058823531d[t] -39.5778758169935M1[t] -32.4084967320262M2[t] -17.5224509803922M3[t] -18.7364052287581M4[t] -11.9003594771242M5[t] + 3.98372549019607M6[t] -51.22022875817M7[t] -29.0841830065359M8[t] -6.66813725490194M9[t] -4.73209150326797M10[t] -11.9160457516340M11[t] + 0.863954248366013t + 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) 116.007058823529 3.816675 30.3948 0 0 d 4.97647058823531 3.509288 1.4181 0.162247 0.081124 M1 -39.5778758169935 4.262456 -9.2852 0 0 M2 -32.4084967320262 4.246662 -7.6315 0 0 M3 -17.5224509803922 4.232849 -4.1396 0.000131 6.5e-05 M4 -18.7364052287581 4.221037 -4.4388 4.9e-05 2.4e-05 M5 -11.9003594771242 4.211243 -2.8259 0.006717 0.003358 M6 3.98372549019607 4.410442 0.9032 0.370641 0.18532 M7 -51.22022875817 4.399663 -11.6419 0 0 M8 -29.0841830065359 4.390823 -6.6239 0 0 M9 -6.66813725490194 4.383936 -1.521 0.134426 0.067213 M10 -4.73209150326797 4.37901 -1.0806 0.284945 0.142473 M11 -11.9160457516340 4.376051 -2.723 0.008834 0.004417 t 0.863954248366013 0.092917 9.2981 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.970408173310642 R-squared 0.941692022828097 Adjusted R-squared 0.926829205117612 F-TEST (value) 63.3589162681966 F-TEST (DF numerator) 13 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.91758492257896 Sum Squared Residuals 2440.50203921568 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 89.3 77.2931372549021 12.0068627450979 2 87.5 85.3264705882353 2.17352941176466 3 106.7 101.076470588235 5.6235294117647 4 102.5 100.726470588235 1.77352941176479 5 109.2 108.426470588235 0.773529411764749 6 123.7 125.174509803922 -1.47450980392158 7 83.1 70.8345098039215 12.2654901960785 8 97 93.8345098039216 3.16549019607843 9 119.1 117.114509803921 1.98549019607850 10 125.1 119.914509803922 5.18549019607842 11 113.6 113.594509803922 0.00549019607843104 12 122.4 126.374509803922 -3.97450980392155 13 92.8 87.6605882352941 5.13941176470591 14 97.2 95.6939215686274 1.50607843137256 15 115.6 111.443921568627 4.15607843137254 16 111.3 111.093921568627 0.206078431372536 17 114.6 118.793921568627 -4.19392156862747 18 137.5 135.541960784314 1.95803921568628 19 83.7 81.2019607843137 2.49803921568627 20 106 104.201960784314 1.79803921568627 21 123.4 127.481960784314 -4.08196078431373 22 126.5 130.281960784314 -3.78196078431372 23 120 123.961960784314 -3.96196078431373 24 141.6 136.741960784314 4.85803921568628 25 90.5 98.0280392156862 -7.52803921568623 26 96.5 106.061372549020 -9.5613725490196 27 113.5 121.811372549020 -8.31137254901961 28 120.1 121.461372549020 -1.36137254901962 29 123.9 129.161372549020 -5.26137254901961 30 144.4 145.909411764706 -1.50941176470587 31 90.8 91.5694117647059 -0.769411764705899 32 114.2 114.569411764706 -0.369411764705885 33 138.1 137.849411764706 0.250588235294092 34 135 140.649411764706 -5.64941176470588 35 131.3 134.329411764706 -3.02941176470588 36 144.6 147.109411764706 -2.50941176470588 37 101.7 113.371960784314 -11.6719607843137 38 108.7 121.405294117647 -12.7052941176470 39 135.3 137.155294117647 -1.85529411764705 40 124.3 136.805294117647 -12.5052941176471 41 138.3 144.505294117647 -6.20529411764707 42 158.2 161.253333333333 -3.05333333333334 43 93.5 106.913333333333 -13.4133333333333 44 124.8 129.913333333333 -5.11333333333334 45 154.4 153.193333333333 1.20666666666665 46 152.8 155.993333333333 -3.19333333333333 47 148.9 149.673333333333 -0.773333333333336 48 170.3 162.453333333333 7.84666666666669 49 124.8 123.739411764706 1.06058823529415 50 134.4 131.772745098039 2.6272549019608 51 154 147.522745098039 6.47725490196078 52 147.9 147.172745098039 0.727254901960772 53 168.1 154.872745098039 13.2272549019608 54 175.7 171.620784313725 4.07921568627451 55 116.7 117.280784313726 -0.580784313725497 56 140.8 140.280784313725 0.519215686274517 57 164.2 163.560784313726 0.639215686274479 58 173.8 166.360784313726 7.43921568627452 59 167.8 160.040784313725 7.75921568627452 60 166.6 172.820784313725 -6.22078431372549 61 135.1 134.106862745098 0.993137254901984 62 158.1 142.140196078431 15.9598039215686 63 151.8 157.890196078431 -6.09019607843136 64 168.7 157.540196078431 11.1598039215686 65 166.9 165.240196078431 1.65980392156862 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0503158303017684 0.100631660603537 0.949684169698232 18 0.0614594909615038 0.122918981923008 0.938540509038496 19 0.0926116555505677 0.185223311101135 0.907388344449432 20 0.0513482987284108 0.102696597456822 0.94865170127159 21 0.0276323369563258 0.0552646739126515 0.972367663043674 22 0.0229646086615860 0.0459292173231719 0.977035391338414 23 0.0100580135546128 0.0201160271092256 0.989941986445387 24 0.0668522303333152 0.133704460666630 0.933147769666685 25 0.135175072080045 0.27035014416009 0.864824927919955 26 0.110127798590984 0.220255597181967 0.889872201409016 27 0.0905873194490425 0.181174638898085 0.909412680550957 28 0.0755255123472874 0.151051024694575 0.924474487652713 29 0.0531566450534595 0.106313290106919 0.94684335494654 30 0.0394980739240924 0.0789961478481848 0.960501926075908 31 0.0294699967281163 0.0589399934562327 0.970530003271884 32 0.0212992468260536 0.0425984936521072 0.978700753173946 33 0.0215078090349515 0.0430156180699031 0.978492190965048 34 0.0120717546935724 0.0241435093871448 0.987928245306428 35 0.00802421223798582 0.0160484244759716 0.991975787762014 36 0.00432160169905456 0.00864320339810912 0.995678398300945 37 0.0022144001995613 0.0044288003991226 0.997785599800439 38 0.0033732674154234 0.0067465348308468 0.996626732584577 39 0.0044885177919551 0.0089770355839102 0.995511482208045 40 0.00550718471190207 0.0110143694238041 0.994492815288098 41 0.00665735659214255 0.0133147131842851 0.993342643407857 42 0.00486881977661529 0.00973763955323058 0.995131180223385 43 0.00997737328993234 0.0199547465798647 0.990022626710068 44 0.00567452325032767 0.0113490465006553 0.994325476749672 45 0.00530962915435644 0.0106192583087129 0.994690370845644 46 0.00566588773236318 0.0113317754647264 0.994334112267637 47 0.00673927499415411 0.0134785499883082 0.993260725005846 48 0.0189655720921011 0.0379311441842022 0.981034427907899 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.15625 NOK 5% type I error level 19 0.59375 NOK 10% type I error level 22 0.6875 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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