paper regression zonder trend en monthly

*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, 05 Dec 2008 05:51:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/05/t1228481537djysv6h14pznxrp.htm/, Retrieved Fri, 05 Dec 2008 12:52:17 +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/Dec/05/t1228481537djysv6h14pznxrp.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

12300.00 0 12092.80 0 12380.80 0 12196.90 0 9455.00 0 13168.00 0 13427.90 0 11980.50 0 11884.80 0 11691.70 0 12233.80 0 14341.40 0 13130.70 0 12421.10 0 14285.80 0 12864.60 0 11160.20 0 14316.20 0 14388.70 0 14013.90 0 13419.00 0 12769.60 0 13315.50 0 15332.90 0 14243.00 0 13824.40 0 14962.90 0 13202.90 0 12199.00 0 15508.90 0 14199.80 0 15169.60 0 14058.00 0 13786.20 0 14147.90 0 16541.70 0 13587.50 0 15582.40 0 15802.80 0 14130.50 0 12923.20 0 15612.20 1 16033.70 1 16036.60 1 14037.80 1 15330.60 1 15038.30 1 17401.80 1 14992.50 1 16043.70 1 16929.60 1 15921.30 1 14417.20 1 15961.00 1 17851.90 1 16483.90 1 14215.50 1 17429.70 1 17839.50 1 17629.20 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 13474.2073170732 + 2589.26636713736D[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) 13474.2073170732 210.821764 63.9128 0 0 D 2589.26636713736 374.640105 6.9113 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.67202906519124 R-squared 0.451623064461811 Adjusted R-squared 0.442168289711153 F-TEST (value) 47.7666656659758 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 4.12919731740402e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1349.91794466238 Sum Squared Residuals 105692150.524647 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12300 13474.2073170732 -1174.20731707319 2 12092.8 13474.2073170732 -1381.40731707317 3 12380.8 13474.2073170732 -1093.40731707317 4 12196.9 13474.2073170732 -1277.30731707317 5 9455 13474.2073170732 -4019.20731707317 6 13168 13474.2073170732 -306.20731707317 7 13427.9 13474.2073170732 -46.3073170731706 8 11980.5 13474.2073170732 -1493.70731707317 9 11884.8 13474.2073170732 -1589.40731707317 10 11691.7 13474.2073170732 -1782.50731707317 11 12233.8 13474.2073170732 -1240.40731707317 12 14341.4 13474.2073170732 867.19268292683 13 13130.7 13474.2073170732 -343.507317073169 14 12421.1 13474.2073170732 -1053.10731707317 15 14285.8 13474.2073170732 811.592682926829 16 12864.6 13474.2073170732 -609.60731707317 17 11160.2 13474.2073170732 -2314.00731707317 18 14316.2 13474.2073170732 841.99268292683 19 14388.7 13474.2073170732 914.49268292683 20 14013.9 13474.2073170732 539.692682926829 21 13419 13474.2073170732 -55.2073170731702 22 12769.6 13474.2073170732 -704.60731707317 23 13315.5 13474.2073170732 -158.707317073170 24 15332.9 13474.2073170732 1858.69268292683 25 14243 13474.2073170732 768.79268292683 26 13824.4 13474.2073170732 350.192682926829 27 14962.9 13474.2073170732 1488.69268292683 28 13202.9 13474.2073170732 -271.307317073171 29 12199 13474.2073170732 -1275.20731707317 30 15508.9 13474.2073170732 2034.69268292683 31 14199.8 13474.2073170732 725.592682926829 32 15169.6 13474.2073170732 1695.39268292683 33 14058 13474.2073170732 583.79268292683 34 13786.2 13474.2073170732 311.992682926830 35 14147.9 13474.2073170732 673.692682926829 36 16541.7 13474.2073170732 3067.49268292683 37 13587.5 13474.2073170732 113.292682926830 38 15582.4 13474.2073170732 2108.19268292683 39 15802.8 13474.2073170732 2328.59268292683 40 14130.5 13474.2073170732 656.29268292683 41 12923.2 13474.2073170732 -551.00731707317 42 15612.2 16063.4736842105 -451.273684210526 43 16033.7 16063.4736842105 -29.7736842105257 44 16036.6 16063.4736842105 -26.8736842105261 45 14037.8 16063.4736842105 -2025.67368421053 46 15330.6 16063.4736842105 -732.873684210526 47 15038.3 16063.4736842105 -1025.17368421053 48 17401.8 16063.4736842105 1338.32631578947 49 14992.5 16063.4736842105 -1070.97368421053 50 16043.7 16063.4736842105 -19.7736842105257 51 16929.6 16063.4736842105 866.126315789472 52 15921.3 16063.4736842105 -142.173684210527 53 14417.2 16063.4736842105 -1646.27368421053 54 15961 16063.4736842105 -102.473684210526 55 17851.9 16063.4736842105 1788.42631578947 56 16483.9 16063.4736842105 420.426315789475 57 14215.5 16063.4736842105 -1847.97368421053 58 17429.7 16063.4736842105 1366.22631578947 59 17839.5 16063.4736842105 1776.02631578947 60 17629.2 16063.4736842105 1565.72631578947 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.73581029907142 0.52837940185716 0.26418970092858 6 0.718231396640557 0.563537206718885 0.281768603359443 7 0.706322123767914 0.587355752464172 0.293677876232086 8 0.611919744200216 0.776160511599568 0.388080255799784 9 0.52749072956353 0.945018540872941 0.472509270436471 10 0.468917612631898 0.937835225263795 0.531082387368102 11 0.393169946128898 0.786339892257797 0.606830053871102 12 0.578793884541207 0.842412230917585 0.421206115458793 13 0.526423398055889 0.947153203888222 0.473576601944111 14 0.4647839695724 0.9295679391448 0.5352160304276 15 0.548593346064708 0.902813307870585 0.451406653935292 16 0.48667661493419 0.97335322986838 0.51332338506581 17 0.620214644982044 0.759570710035911 0.379785355017955 18 0.674684599756433 0.650630800487135 0.325315400243567 19 0.710946752850308 0.578106494299383 0.289053247149692 20 0.696193457975166 0.607613084049668 0.303806542024834 21 0.650544681878741 0.698910636242519 0.349455318121259 22 0.61993644290907 0.760127114181861 0.380063557090930 23 0.576709932391872 0.846580135216257 0.423290067608129 24 0.704397875624217 0.591204248751567 0.295602124375783 25 0.680692578603048 0.638614842793905 0.319307421396952 26 0.63520660742727 0.72958678514546 0.36479339257273 27 0.662539529822129 0.674920940355743 0.337460470177871 28 0.621766256808334 0.756467486383333 0.378233743191666 29 0.690077582073768 0.619844835852464 0.309922417926232 30 0.758073229687353 0.483853540625294 0.241926770312647 31 0.718487543102147 0.563024913795706 0.281512456897853 32 0.729273228632919 0.541453542734162 0.270726771367081 33 0.679766220931608 0.640467558136784 0.320233779068392 34 0.631276209615532 0.737447580768937 0.368723790384469 35 0.579183935171264 0.841632129657472 0.420816064828736 36 0.759952746422807 0.480094507154385 0.240047253577193 37 0.71654432813509 0.56691134372982 0.28345567186491 38 0.738558380301324 0.522883239397351 0.261441619698676 39 0.815041539694205 0.369916920611589 0.184958460305795 40 0.777483762542092 0.445032474915817 0.222516237457909 41 0.712622353635367 0.574755292729267 0.287377646364633 42 0.642513496956168 0.714973006087663 0.357486503043832 43 0.559727235010622 0.880545529978757 0.440272764989378 44 0.472199610244293 0.944399220488585 0.527800389755707 45 0.575439081887988 0.849121836224024 0.424560918112012 46 0.517211081567898 0.965577836864203 0.482788918432102 47 0.492955541818339 0.985911083636679 0.507044458181661 48 0.475855672156668 0.951711344313336 0.524144327843332 49 0.461216892377512 0.922433784755025 0.538783107622488 50 0.365241234953961 0.730482469907922 0.634758765046039 51 0.285688330651584 0.571376661303167 0.714311669348416 52 0.203283024640033 0.406566049280067 0.796716975359967 53 0.31014839029382 0.62029678058764 0.68985160970618 54 0.230729637521798 0.461459275043596 0.769270362478202 55 0.182947266529817 0.365894533059634 0.817052733470183 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 = 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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