Regressiemodel zonder fixed seasonal effects

*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, 14 Nov 2009 04:09:10 -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/14/t1258197057z3e7b7ecj5khi9n.htm/, Retrieved Sat, 14 Nov 2009 12:11:09 +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/14/t1258197057z3e7b7ecj5khi9n.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:

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5560 36.68 3922 36.7 3759 36.71 4138 36.72 4634 36.73 3996 36.73 4308 36.87 4429 37.31 5219 37.39 4929 37.42 5755 37.51 5592 37.67 4163 37.67 4962 37.71 5208 37.78 4755 37.79 4491 37.84 5732 37.88 5731 38.34 5040 38.58 6102 38.72 4904 38.83 5369 38.9 5578 38.92 4619 38.94 4731 39.1 5011 39.14 5299 39.16 4146 39.32 4625 39.34 4736 39.44 4219 39.92 5116 40.19 4205 40.2 4121 40.27 5103 40.28 4300 40.3 4578 40.34 3809 40.4 5526 40.43 4247 40.48 3830 40.48 4394 40.63 4826 40.74 4409 40.77 4569 40.91 4106 40.92 4794 41.03 3914 41 3793 41.04 4405 41.33 4022 41.44 4100 41.46 4788 41.55 3163 41.55 3585 41.81 3903 41.78 4178 41.84 3863 41.84 4187 41.86

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 Y[t] = + 10478.8954186677 -149.383931152047X[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) 10478.8954186677 1807.863488 5.7963 0 0 X -149.383931152047 45.83193 -3.2594 0.00187 0.000935 Multiple Linear Regression - Regression Statistics Multiple R 0.393458566501769 R-squared 0.154809643553627 Adjusted R-squared 0.140237396028689 F-TEST (value) 10.6235941496808 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0.00187029886726986 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 589.802071683868 Sum Squared Residuals 20176256.0582298 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 5560 4999.4928240107 560.507175989303 2 3922 4996.50514538762 -1074.50514538762 3 3759 4995.0113060761 -1236.0113060761 4 4138 4993.51746676458 -855.51746676458 5 4634 4992.02362745306 -358.023627453061 6 3996 4992.02362745306 -996.02362745306 7 4308 4971.10987709177 -663.109877091774 8 4429 4905.38094738487 -476.380947384873 9 5219 4893.43023289271 325.569767107291 10 4929 4888.94871495815 40.0512850418521 11 5755 4875.50416115446 879.495838845536 12 5592 4851.60273217014 740.397267829864 13 4163 4851.60273217014 -688.602732170136 14 4962 4845.62737492405 116.372625075945 15 5208 4835.17049974341 372.829500256589 16 4755 4833.67666043189 -78.676660431891 17 4491 4826.20746387429 -335.207463874288 18 5732 4820.23210662821 911.767893371794 19 5731 4751.51549829826 979.484501701735 20 5040 4715.66335482177 324.336645178226 21 6102 4694.74960446049 1407.25039553951 22 4904 4678.31737203376 225.682627966237 23 5369 4667.86049685312 701.13950314688 24 5578 4664.87281823008 913.127181769922 25 4619 4661.88513960704 -42.8851396070377 26 4731 4637.98371062271 93.0162893772903 27 5011 4632.00835337663 378.991646623372 28 5299 4629.02067475359 669.979325246412 29 4146 4605.11924576926 -459.11924576926 30 4625 4602.13156714622 22.8684328537817 31 4736 4587.19317403101 148.806825968986 32 4219 4515.48888707803 -296.488887078032 33 5116 4475.15522566698 640.84477433302 34 4205 4473.66138635546 -268.661386355458 35 4121 4463.20451117481 -342.204511174815 36 5103 4461.71067186329 641.289328136705 37 4300 4458.72299324025 -158.722993240255 38 4578 4452.74763599417 125.252364005828 39 3809 4443.78460012505 -634.78460012505 40 5526 4439.30308219049 1086.69691780951 41 4247 4431.83388563289 -184.833885632886 42 3830 4431.83388563289 -601.833885632886 43 4394 4409.42629596008 -15.4262959600784 44 4826 4392.99406353335 433.005936466647 45 4409 4388.51254559879 20.4874544012083 46 4569 4367.59879523751 201.401204762494 47 4106 4366.10495592598 -260.104955925985 48 4794 4349.67272349926 444.32727650074 49 3914 4354.15424143382 -440.154241433822 50 3793 4348.17888418774 -555.17888418774 51 4405 4304.85754415365 100.142455846354 52 4022 4288.42531172692 -266.425311726921 53 4100 4285.43763310388 -185.43763310388 54 4788 4271.9930793002 516.006920699804 55 3163 4271.9930793002 -1108.99307930020 56 3585 4233.15325720066 -648.153257200663 57 3903 4237.63477513523 -334.634775135225 58 4178 4228.6717392661 -50.6717392661020 59 3863 4228.6717392661 -365.671739266102 60 4187 4225.68406064306 -38.6840606430616 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.840761610928985 0.31847677814203 0.159238389071015 6 0.779874203090662 0.440251593818676 0.220125796909338 7 0.86062233070744 0.278755338585121 0.139377669292561 8 0.828813531172084 0.342372937655832 0.171186468827916 9 0.82038731086449 0.359225378271022 0.179612689135511 10 0.750490329054962 0.499019341890077 0.249509670945038 11 0.773757450550921 0.452485098898157 0.226242549449079 12 0.703709085222989 0.592581829554021 0.296290914777011 13 0.908496699584612 0.183006600830776 0.0915033004153882 14 0.877026749285321 0.245946501429357 0.122973250714679 15 0.827188866138269 0.345622267723462 0.172811133861731 16 0.82088551831739 0.35822896336522 0.17911448168261 17 0.880509265429625 0.23898146914075 0.119490734570375 18 0.876768644875125 0.24646271024975 0.123231355124875 19 0.847473224443893 0.305053551112215 0.152526775556107 20 0.840207597697557 0.319584804604887 0.159792402302443 21 0.885110225125658 0.229779549748684 0.114889774874342 22 0.901202567254354 0.197594865491292 0.098797432745646 23 0.880521609422731 0.238956781154538 0.119478390577269 24 0.876339019135346 0.247321961729308 0.123660980864654 25 0.905448349046457 0.189103301907085 0.0945516509535426 26 0.906788483146407 0.186423033707186 0.0932115168535931 27 0.883933019962118 0.232133960075763 0.116066980037882 28 0.868942377130492 0.262115245739016 0.131057622869508 29 0.9339525056457 0.132094988708598 0.066047494354299 30 0.923168235771638 0.153663528456724 0.0768317642283618 31 0.901512382201312 0.196975235597376 0.098487617798688 32 0.920209337680732 0.159581324638537 0.0797906623192684 33 0.913287493007245 0.173425013985509 0.0867125069927546 34 0.916828093029027 0.166343813941946 0.0831719069709728 35 0.922232769943995 0.155534460112009 0.0777672300560045 36 0.917305341384664 0.165389317230672 0.0826946586153359 37 0.89887751098165 0.202244978036701 0.101122489018351 38 0.861783895262261 0.276432209475477 0.138216104737739 39 0.907511765604227 0.184976468791546 0.0924882343957729 40 0.969865777420876 0.0602684451582485 0.0301342225791242 41 0.956890125783001 0.0862197484339975 0.0431098742169988 42 0.971774575843205 0.0564508483135889 0.0282254241567944 43 0.954951124767054 0.0900977504658926 0.0450488752329463 44 0.945085751980304 0.109828496039392 0.054914248019696 45 0.914492584405811 0.171014831188377 0.0855074155941885 46 0.886348052762388 0.227303894475223 0.113651947237612 47 0.8397588838408 0.3204822323184 0.1602411161592 48 0.874106309846758 0.251787380306483 0.125893690153242 49 0.822612914427839 0.354774171144323 0.177387085572161 50 0.791848619056918 0.416302761886164 0.208151380943082 51 0.721681235017386 0.556637529965228 0.278318764982614 52 0.610943545001389 0.778112909997222 0.389056454998611 53 0.484371771472236 0.968743542944473 0.515628228527764 54 0.970402796602053 0.0591944067958934 0.0295972033979467 55 0.92714739712114 0.145705205757720 0.0728526028788601 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 5 0.0980392156862745 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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