voeding

*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: Sat, 20 Dec 2008 01:24:52 -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/20/t1229761579eekcghb39fgcys2.htm/, Retrieved Sat, 20 Dec 2008 09:26:19 +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/20/t1229761579eekcghb39fgcys2.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:

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99.2 11554.5 93.6 13182.1 104.2 14800.1 95.3 12150.7 102.7 14478.2 103.1 13253.9 100 12036.8 107.2 12653.2 107 14035.4 119 14571.4 110.4 15400.9 101.7 14283.2 102.4 14485.3 98.8 14196.3 105.6 15559.1 104.4 13767.4 106.3 14634 107.2 14381.1 108.5 12509.9 106.9 12122.3 114.2 13122.3 125.9 13908.7 110.6 13456.5 110.5 12441.6 106.7 12953 104.7 13057.2 107.4 14350.1 109.8 13830.2 103.4 13755.5 114.8 13574.4 114.3 12802.6 109.6 11737.3 118.3 13850.2 127.3 15081.8 112.3 13653.3 114.9 14019.1 108.2 13962 105.4 13768.7 122.1 14747.1 113.5 13858.1 110 13188 125.3 13693.1 114.3 12970 115.6 11392.8 127.1 13985.2 123 14994.7 122.2 13584.7 126.4 14257.8 112.7 13553.4 105.8 14007.3 120.9 16535.8 116.3 14721.4 115.7 13664.6 127.9 16405.9 108.3 13829.4 121.1 13735.6 128.6 15870.5 123.1 15962.4 127.7 15744.1 126.6 16083.7 118.4 14863.9 110 15533.1 129.6 17473.1 115.8 15925.5 125.9 15573.7 128.4 17495 114 14155.8 125.6 14913.9 128.5 17250.4 136.6 15879.8 133.1 17647.8 124.6 17749.9

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Voeding[t] = + 99.7132835995293 + 0.000269825565465987Invoer[t] -5.58202020815621M1[t] -10.8992351489706M2[t] + 0.253103534374366M3[t] -5.44314119882378M4[t] -4.33379269453077M5[t] + 2.29786941418459M6[t] -5.44050223231386M7[t] -1.25568034298642M8[t] + 4.1806549508592M9[t] + 8.9507217908195M10[t] + 2.23119587326295M11[t] + 0.327183584710254t + 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) 99.7132835995293 7.299939 13.6595 0 0 Invoer 0.000269825565465987 0.000541 0.4991 0.61962 0.30981 M1 -5.58202020815621 2.289651 -2.4379 0.017857 0.008928 M2 -10.8992351489706 2.259539 -4.8237 1.1e-05 5e-06 M3 0.253103534374366 2.328868 0.1087 0.913831 0.456915 M4 -5.44314119882378 2.255473 -2.4133 0.018988 0.009494 M5 -4.33379269453077 2.247537 -1.9282 0.058725 0.029363 M6 2.29786941418459 2.244071 1.024 0.3101 0.15505 M7 -5.44050223231386 2.390344 -2.276 0.026553 0.013277 M8 -1.25568034298642 2.458261 -0.5108 0.61143 0.305715 M9 4.1806549508592 2.23723 1.8687 0.066721 0.03336 M10 8.9507217908195 2.244366 3.9881 0.000189 9.5e-05 M11 2.23119587326295 2.237813 0.997 0.322885 0.161443 t 0.327183584710254 0.031575 10.3619 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.935937649433023 R-squared 0.875979283626213 Adjusted R-squared 0.848181536852778 F-TEST (value) 31.5126003113082 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.87326476172561 Sum Squared Residuals 870.126435036672 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.2 97.5761464722598 1.6238535277402 2 93.6 93.0252832065083 0.57471679349168 3 104.2 104.941383239488 -0.741383239487508 4 95.3 98.857446237854 -3.55744623785403 5 102.7 100.921997330479 1.77800266952062 6 103.1 107.550495584105 -4.45049558410498 7 100 99.8109028265881 0.189097173411861 8 107.2 104.489228779179 2.71077122082093 9 107 110.625700554322 -3.62570055432202 10 119 115.867577482082 3.13242251791766 11 110.4 109.69905545579 0.700944544209911 12 101.7 107.493459132716 -5.79345913271605 13 102.4 102.293154256051 0.106845743949226 14 98.8 97.225143311527 1.57485668847303 15 105.6 109.072383860199 -3.47238386019925 16 104.4 103.219876246066 1.18012375393406 17 106.3 104.890239170102 1.40976082989797 18 107.2 111.780845978021 -4.58084597802129 19 108.5 103.864760318133 4.63523968186686 20 106.9 108.272181402996 -1.37218140299622 21 114.2 114.305525847018 -0.105525847018079 22 125.9 119.614967096371 6.28503290362892 23 110.6 113.100609642821 -2.50060964282108 24 110.5 110.922751387877 -0.422751387876953 25 106.7 105.805903558610 0.894096441389697 26 104.7 100.843988026428 3.85601197357228 27 107.4 112.672367768074 -5.27236776807391 28 109.8 107.163024308100 2.63697569189973 29 103.4 108.579400427363 -5.17940042736321 30 114.8 115.489380710883 -0.689380710882936 31 114.3 107.869941277668 6.43005872233191 32 109.6 112.094501576815 -2.49450157681488 33 118.3 118.428134892644 -0.128134892643825 34 127.3 123.857702483742 3.44229751625771 35 112.3 117.079914330628 -4.77991433062783 36 114.9 115.274604233923 -0.37460423392259 37 108.2 110.004360570689 -1.80436057068854 38 105.4 104.962171932780 0.437828067220184 39 122.1 116.705691534087 5.39430846591303 40 113.5 111.096755457900 2.40324454210019 41 110 112.352477435484 -2.35247743548431 42 125.3 119.447612022027 5.8523879779732 43 114.3 111.841313093850 2.45868690614985 44 115.6 115.927749686035 -0.327749686034889 45 127.1 122.390764360505 4.70923563949521 46 123 127.760403693513 -4.76040369351325 47 122.2 120.98760731336 1.21239268664009 48 126.4 119.265214612922 7.13478538707763 49 112.7 113.820312861162 -1.12031286116218 50 105.8 108.952755329223 -3.15275532922306 51 120.9 121.114531539559 -0.214531539559017 52 116.3 115.255898885090 1.04410111491035 53 115.7 116.407279316508 -0.707279316508451 54 127.9 124.105797832546 3.79420216745403 55 108.3 115.999404201335 -7.69940420133467 56 121.1 120.486100037332 0.61389996266834 57 128.6 126.825669515601 1.77433048439913 58 123.1 131.947716909738 -8.84771690973774 59 127.7 125.496471655950 2.20352834404979 60 126.6 123.684092129430 2.91590787057022 61 118.4 118.100122281228 0.299877718771595 62 110 113.290658193534 -3.29065819353411 63 129.6 125.293642058593 4.30635794140666 64 115.8 119.506998864990 -3.7069988649903 65 125.9 120.848606320063 5.05139367993739 66 128.4 128.325867872418 0.0741321275819747 67 114 120.013678282426 -6.01367828242581 68 125.6 124.730238517643 0.869761482356719 69 128.5 131.124204829910 -2.62420482991042 70 136.6 135.851632334553 0.748367665446706 71 133.1 129.936341601451 3.16365839854913 72 124.6 128.059878503132 -3.45987850313225 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.185257445611126 0.370514891222252 0.814742554388874 18 0.0901189626888996 0.180237925377799 0.9098810373111 19 0.0827226851908559 0.165445370381712 0.917277314809144 20 0.0796520026316204 0.159304005263241 0.92034799736838 21 0.0625644932688816 0.125128986537763 0.937435506731118 22 0.0469159893175975 0.093831978635195 0.953084010682402 23 0.0402213891298092 0.0804427782596183 0.95977861087019 24 0.0434089619786663 0.0868179239573326 0.956591038021334 25 0.0243794417803436 0.0487588835606872 0.975620558219656 26 0.0159947352998190 0.0319894705996379 0.984005264700181 27 0.0280709093493552 0.0561418186987104 0.971929090650645 28 0.0217368261870446 0.0434736523740891 0.978263173812955 29 0.0720963836501321 0.144192767300264 0.927903616349868 30 0.071002445442359 0.142004890884718 0.928997554557641 31 0.104413124207752 0.208826248415503 0.895586875792248 32 0.0974573985891273 0.194914797178255 0.902542601410873 33 0.068826049576934 0.137652099153868 0.931173950423066 34 0.096151062905049 0.192302125810098 0.903848937094951 35 0.149125605613070 0.298251211226141 0.85087439438693 36 0.131233890246945 0.262467780493890 0.868766109753055 37 0.115930553027737 0.231861106055473 0.884069446972263 38 0.0924955085102483 0.184991017020497 0.907504491489752 39 0.183945300405246 0.367890600810491 0.816054699594755 40 0.148467518814984 0.296935037629967 0.851532481185016 41 0.147623606697332 0.295247213394663 0.852376393302668 42 0.213482512896294 0.426965025792588 0.786517487103706 43 0.420812046563774 0.841624093127548 0.579187953436226 44 0.393877788897882 0.787755577795765 0.606122211102118 45 0.385891222274957 0.771782444549915 0.614108777725043 46 0.500889670660025 0.99822065867995 0.499110329339975 47 0.572352965067248 0.855294069865504 0.427647034932752 48 0.636105007146804 0.727789985706392 0.363894992853196 49 0.550257834798762 0.899484330402475 0.449742165201238 50 0.487477389095912 0.974954778191825 0.512522610904088 51 0.418288957538240 0.836577915076479 0.58171104246176 52 0.385543138707823 0.771086277415646 0.614456861292177 53 0.665268552996058 0.669462894007884 0.334731447003942 54 0.607900318096165 0.784199363807671 0.392099681903836 55 0.604153526402737 0.791692947194527 0.395846473597263 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 3 0.076923076923077 NOK 10% type I error level 7 0.179487179487179 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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