Ws7 correctie

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

Title produced by software: Multiple Regression

Date of computation: Fri, 27 Nov 2009 12:25:57 -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/27/t1259350141vcv0in2i037te8o.htm/, Retrieved Fri, 27 Nov 2009 20:29:13 +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/27/t1259350141vcv0in2i037te8o.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:

ShwWs7 correctie

Dataseries X:

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1.3 2 1.2 2.1 1.1 2.1 1.4 2.5 1.2 2.2 1.5 2.3 1.1 2.3 1.3 2.2 1.5 2.2 1.1 1.6 1.4 1.8 1.3 1.7 1.5 1.9 1.6 1.8 1.7 1.9 1.1 1.5 1.6 1 1.3 0.8 1.7 1.1 1.6 1.5 1.7 1.7 1.9 2.3 1.8 2.4 1.9 3 1.6 3 1.5 3.2 1.6 3.2 1.6 3.2 1.7 3.5 2 4 2 4.3 1.9 4.1 1.7 4 1.8 4.1 1.9 4.2 1.7 4.5 2 5.6 2.1 6.5 2.4 7.6 2.5 8.5 2.5 8.7 2.6 8.3 2.2 8.3 2.5 8.5 2.8 8.7 2.8 8.7 2.9 8.5 3 7.9 3.1 7 2.9 5.8 2.7 4.5 2.2 3.7 2.5 3.1 2.3 2.7 2.6 2.3 2.3 1.8 2.2 1.5 1.8 1.2 1.8 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 inflatie[t] = + 0.972023860168438 + 0.098796834385658inflatie_levensmiddelen[t] + 0.058818758366768M1[t] + 0.00144070596005138M2[t] + 0.0240626535533356M3[t] -0.137267272228807M4[t] + 0.00116216886618223M5[t] + 0.0297119265226059M6[t] -0.0135939359472494M7[t] -0.0289960516662525M8[t] + 0.0116499592393184M9[t] -0.103752156479684M10[t] -0.0431061455741136M11[t] + 0.0193539890944291t + 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) 0.972023860168438 0.136163 7.1387 0 0 inflatie_levensmiddelen 0.098796834385658 0.014819 6.6669 0 0 M1 0.058818758366768 0.161693 0.3638 0.717735 0.358868 M2 0.00144070596005138 0.161603 0.0089 0.992926 0.496463 M3 0.0240626535533356 0.161545 0.149 0.882256 0.441128 M4 -0.137267272228807 0.161507 -0.8499 0.399873 0.199936 M5 0.00116216886618223 0.161604 0.0072 0.994294 0.497147 M6 0.0297119265226059 0.161714 0.1837 0.85505 0.427525 M7 -0.0135939359472494 0.161757 -0.084 0.933398 0.466699 M8 -0.0289960516662525 0.161905 -0.1791 0.858669 0.429334 M9 0.0116499592393184 0.162044 0.0719 0.943005 0.471502 M10 -0.103752156479684 0.162264 -0.6394 0.525803 0.262901 M11 -0.0431061455741136 0.162465 -0.2653 0.79197 0.395985 t 0.0193539890944291 0.002171 8.9162 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.92103391960866 R-squared 0.84830348106969 Adjusted R-squared 0.8044800422676 F-TEST (value) 19.3573006650780 F-TEST (DF numerator) 13 F-TEST (DF denominator) 45 p-value 3.10862446895044e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.240635030923153 Sum Squared Residuals 2.6057348148324 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.3 1.24779027640095 0.0522097235990519 2 1.2 1.21964589652723 -0.0196458965272296 3 1.1 1.26162183321494 -0.161621833214943 4 1.4 1.15916463028149 0.240835369718507 5 1.2 1.28730901015521 -0.087309010155214 6 1.5 1.34509244034463 0.154907559655368 7 1.1 1.32114056696921 -0.221140566969206 8 1.3 1.31521275690607 -0.0152127569060665 9 1.5 1.37521275690607 0.124787243093934 10 1.1 1.21988652965010 -0.119886529650098 11 1.4 1.31964589652723 0.0803541034727705 12 1.3 1.37222634775721 -0.0722263477572063 13 1.5 1.47015846209553 0.0298415379044651 14 1.6 1.42225471534468 0.177745284655318 15 1.7 1.47411033547096 0.225889664529039 16 1.1 1.29261566502898 -0.192615665028984 17 1.6 1.40100067802557 0.198999321974426 18 1.3 1.42914505789929 -0.129145057899295 19 1.7 1.43483223483957 0.265167765160434 20 1.6 1.47830284196926 0.121697158030745 21 1.7 1.55806220884639 0.141937791153613 22 1.9 1.52129218285321 0.378707817146792 23 1.8 1.61117186629177 0.188828133708226 24 1.9 1.73291010159171 0.167089898408289 25 1.6 1.81108284905291 -0.211082849052908 26 1.5 1.79281815261775 -0.292818152617752 27 1.6 1.83479408930547 -0.234794089305466 28 1.6 1.69281815261775 -0.0928181526177524 29 1.7 1.88024063312287 -0.180240633122868 30 2 1.97754279706655 0.02245720293345 31 2 1.98322997400682 0.0167700259931787 32 1.9 1.96742248050512 -0.0674224805051158 33 1.7 2.01754279706655 -0.31754279706655 34 1.8 1.93137435388054 -0.131374353880542 35 1.9 2.02125403731911 -0.121254037319108 36 1.7 2.11335322230335 -0.413353222303348 37 2 2.30020248758877 -0.300202487588769 38 2.1 2.35109557522357 -0.251095575223573 39 2.4 2.50174802973551 -0.101748029735511 40 2.5 2.44868924399489 0.0513107560051105 41 2.5 2.62623204106144 -0.126232041061440 42 2.6 2.63461705405803 -0.0346170540580291 43 2.2 2.6106651806826 -0.410665180682603 44 2.5 2.63437642093516 -0.134376420935161 45 2.8 2.71413578781229 0.0858642121877074 46 2.8 2.61808766118772 0.181912338812281 47 2.9 2.67832829431059 0.221671705689413 48 3 2.68151032834774 0.318489671652265 49 3.1 2.67076592486184 0.42923407513816 50 2.9 2.51418566028676 0.385814339713237 51 2.7 2.42772571227312 0.27227428772688 52 2.2 2.20671230807688 -0.0067123080768805 53 2.5 2.30521763763490 0.194782362365096 54 2.3 2.31360265063149 -0.0136026506314939 55 2.6 2.25013204350180 0.349867956498196 56 2.3 2.2046854996844 0.0953145003155984 57 2.2 2.23504644936870 -0.0350464493687038 58 1.8 2.10935927242843 -0.309359272428433 59 1.8 2.1695999055513 -0.369599905551301 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.515555238040539 0.968889523918922 0.484444761959461 18 0.358196684731949 0.716393369463899 0.64180331526805 19 0.472901313774787 0.945802627549575 0.527098686225213 20 0.345628013870725 0.691256027741449 0.654371986129275 21 0.258403102832187 0.516806205664375 0.741596897167813 22 0.251483645480160 0.502967290960319 0.74851635451984 23 0.252400783389724 0.504801566779448 0.747599216610276 24 0.22621963946209 0.45243927892418 0.77378036053791 25 0.339669519259095 0.679339038518191 0.660330480740905 26 0.373520612656271 0.747041225312541 0.62647938734373 27 0.307539437034663 0.615078874069326 0.692460562965337 28 0.228418870569766 0.456837741139533 0.771581129430233 29 0.160955303070555 0.32191060614111 0.839044696929445 30 0.13818734996896 0.27637469993792 0.86181265003104 31 0.120510067046503 0.241020134093006 0.879489932953497 32 0.0978689251809265 0.195737850361853 0.902131074819073 33 0.086805863048793 0.173611726097586 0.913194136951207 34 0.0912315887006142 0.182463177401228 0.908768411299386 35 0.234433144337484 0.468866288674968 0.765566855662516 36 0.217552896758519 0.435105793517037 0.782447103241481 37 0.158904570819950 0.317809141639901 0.84109542918005 38 0.112105190551235 0.224210381102471 0.887894809448765 39 0.0990504014529217 0.198100802905843 0.900949598547078 40 0.244351239833215 0.48870247966643 0.755648760166785 41 0.159506752816504 0.319013505633008 0.840493247183496 42 0.952977087059852 0.0940458258802967 0.0470229129401484 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 1 0.0384615384615385 OK

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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