Multiple Regression werklh inflatie 2 vertragingen

*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, 19 Dec 2009 06:55:22 -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/Dec/19/t1261230996rt9xr2s79rq7v91.htm/, Retrieved Sat, 19 Dec 2009 14:56:48 +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/Dec/19/t1261230996rt9xr2s79rq7v91.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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8.7 4.7 9.3 9.3 8.2 4.3 8.7 9.3 8.3 3.9 8.2 8.7 8.5 4 8.3 8.2 8.6 4.3 8.5 8.3 8.5 4.8 8.6 8.5 8.2 4.4 8.5 8.6 8.1 4.3 8.2 8.5 7.9 4.7 8.1 8.2 8.6 4.7 7.9 8.1 8.7 4.9 8.6 7.9 8.7 5 8.7 8.6 8.5 4.2 8.7 8.7 8.4 4.3 8.5 8.7 8.5 4.8 8.4 8.5 8.7 4.8 8.5 8.4 8.7 4.8 8.7 8.5 8.6 4.2 8.7 8.7 8.5 4.6 8.6 8.7 8.3 4.8 8.5 8.6 8 4.5 8.3 8.5 8.2 4.4 8 8.3 8.1 4.3 8.2 8 8.1 3.9 8.1 8.2 8 3.7 8.1 8.1 7.9 4 8 8.1 7.9 4.1 7.9 8 8 3.7 7.9 7.9 8 3.8 8 7.9 7.9 3.8 8 8 8 3.8 7.9 8 7.7 3.3 8 7.9 7.2 3.3 7.7 8 7.5 3.3 7.2 7.7 7.3 3.2 7.5 7.2 7 3.4 7.3 7.5 7 4.2 7 7.3 7 4.9 7 7 7.2 5.1 7 7 7.3 5.5 7.2 7 7.1 5.6 7.3 7.2 6.8 6.4 7.1 7.3 6.4 6.1 6.8 7.1 6.1 7.1 6.4 6.8 6.5 7.8 6.1 6.4 7.7 7.9 6.5 6.1 7.9 7.4 7.7 6.5 7.5 7.5 7.9 7.7 6.9 6.8 7.5 7.9 6.6 5.2 6.9 7.5 6.9 4.7 6.6 6.9 7.7 4.1 6.9 6.6 8 3.9 7.7 6.9 8 2.6 8 7.7 7.7 2.7 8 8 7.3 1.8 7.7 8 7.4 1 7.3 7.7 8.1 0.3 7.4 7.3

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] = + 4.65678240334479 -0.0829633938000221X[t] + 1.13419397565917Y1[t] -0.630531861707417Y2[t] -0.0134843776706883t + 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) 4.65678240334479 0.92492 5.0348 6e-06 3e-06 X -0.0829633938000221 0.028815 -2.8792 0.005739 0.002869 Y1 1.13419397565917 0.117757 9.6316 0 0 Y2 -0.630531861707417 0.124907 -5.048 6e-06 3e-06 t -0.0134843776706883 0.003752 -3.5938 0.000714 0.000357 Multiple Linear Regression - Regression Statistics Multiple R 0.922654065517599 R-squared 0.851290524616153 Adjusted R-squared 0.84006716798341 F-TEST (value) 75.8499041305156 F-TEST (DF numerator) 4 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.26644339847414 Sum Squared Residuals 3.76258048329381 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.7 8.93742773456528 -0.23742773456528 2 8.2 8.27661232901909 -0.0766123290190865 3 8.3 8.10753543806328 0.192464561936723 4 8.5 8.51444004943221 -0.0144400494322090 5 8.6 8.6398522625826 -0.0398522625826046 6 8.5 8.57219921323634 -0.0721992132363381 7 8.2 8.415427609349 -0.215427609349002 8 8.1 8.1330345645313 -0.0330345645313061 9 7.9 8.16210499028692 -0.262104990286917 10 8.6 7.98483500365514 0.615164996344861 11 8.7 8.87480010252734 -0.174800102527345 12 8.7 8.52506647984738 0.174933520152621 13 8.5 8.51489963104597 -0.0148996310459668 14 8.4 8.26628011886344 0.133719881136556 15 8.5 8.22400101906831 0.275998980931689 16 8.7 8.38698922513428 0.313010774865719 17 8.7 8.53729045642468 0.162709543575316 18 8.6 8.44747774269253 0.152522257307474 19 8.5 8.28738860993591 0.212611390064088 20 8.3 8.20694534211004 0.093054657889956 21 8 8.05456437361827 -0.054564373618272 22 8.2 7.83522451497132 0.364775485028681 23 8.1 8.24603483032469 -0.146034830324690 24 8.1 8.02621004026661 0.0737899597333881 25 8 8.09237152752667 -0.092371527526669 26 7.9 7.94057873415006 -0.0405787341500577 27 7.9 7.8684318057042 0.0315681942958075 28 8 7.95118597172425 0.0488140282757452 29 8 8.04282465223948 -0.0428246522394806 30 7.9 7.96628708839805 -0.0662870883980505 31 8 7.83938331316145 0.160616686838554 32 7.7 8.04385321612743 -0.343853216127427 33 7.2 7.62705745958825 -0.427057459588247 34 7.5 7.2356356526002 0.264364347399799 35 7.3 7.88597173786097 -0.585971737860973 36 7 7.43989632778622 -0.439896327786222 37 7 7.14588941471925 -0.145889414719250 38 7 7.26349021990077 -0.263490219900771 39 7.2 7.23341316347008 -0.0334131634700781 40 7.3 7.41358222341121 -0.113582223411215 41 7.1 7.37911453158496 -0.279114531584957 42 6.8 7.00936745757168 -0.209367457571676 43 6.4 6.80662027768473 -0.406620277684728 44 6.1 6.44565447446258 -0.345654474462577 45 6.5 6.28605027311709 0.213949726882911 46 7.7 6.90710670484229 0.79289329515771 47 7.9 8.04392405017965 -0.143924050179646 48 7.5 7.49234389421189 0.0076561057881112 49 6.9 6.95714992959607 -0.0571499295960653 50 6.6 6.64810334129288 -0.0481033412928808 51 6.9 6.7141615848489 0.185838415151098 52 7.7 7.2798729946682 0.420127005331797 53 8 8.00117691777263 -0.00117691777262699 54 8 7.93137765537378 0.0686223446262161 55 7.7 7.72043737981087 -0.0204373798108681 56 7.3 7.44136186386245 -0.141361863862450 57 7.4 7.22973016948034 0.170269830519662 58 8.1 7.63995230971855 0.460047690281451 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0154362647075466 0.0308725294150931 0.984563735292453 9 0.0395240967016111 0.0790481934032221 0.960475903298389 10 0.487589535875604 0.975179071751207 0.512410464124396 11 0.394610638586574 0.789221277173149 0.605389361413426 12 0.434750544921641 0.869501089843283 0.565249455078359 13 0.323480909511942 0.646961819023884 0.676519090488058 14 0.231041769980270 0.462083539960540 0.76895823001973 15 0.174165524901695 0.348331049803390 0.825834475098305 16 0.146594062584650 0.293188125169300 0.85340593741535 17 0.0997169796192663 0.199433959238533 0.900283020380734 18 0.0660484472603532 0.132096894520706 0.933951552739647 19 0.0468600973609166 0.0937201947218331 0.953139902639083 20 0.0422060150245351 0.0844120300490702 0.957793984975465 21 0.0611890579965765 0.122378115993153 0.938810942003424 22 0.0653799847534955 0.130759969506991 0.934620015246505 23 0.0736935639644746 0.147387127928949 0.926306436035525 24 0.057195088281561 0.114390176563122 0.942804911718439 25 0.041522441610226 0.083044883220452 0.958477558389774 26 0.0335973560775033 0.0671947121550066 0.966402643922497 27 0.0276528863107457 0.0553057726214914 0.972347113689254 28 0.0224396577690520 0.0448793155381039 0.977560342230948 29 0.0169004916680975 0.033800983336195 0.983099508331903 30 0.0142633579720612 0.0285267159441224 0.985736642027939 31 0.0343608188190876 0.0687216376381753 0.965639181180912 32 0.0302008538139143 0.0604017076278286 0.969799146186086 33 0.0478501182947393 0.0957002365894786 0.95214988170526 34 0.264557528830695 0.529115057661389 0.735442471169305 35 0.300858320136419 0.601716640272838 0.69914167986358 36 0.341775886448858 0.683551772897717 0.658224113551142 37 0.394099088559018 0.788198177118037 0.605900911440982 38 0.395768682076984 0.791537364153968 0.604231317923016 39 0.385847424212953 0.771694848425906 0.614152575787047 40 0.382909507015546 0.765819014031091 0.617090492984455 41 0.404861156390525 0.80972231278105 0.595138843609475 42 0.55233847961305 0.8953230407739 0.44766152038695 43 0.625388439886618 0.749223120226763 0.374611560113382 44 0.546698974130775 0.90660205173845 0.453301025869225 45 0.505247483529479 0.989505032941041 0.494752516470521 46 0.899964519131957 0.200070961736085 0.100035480868043 47 0.88120285971525 0.237594280569502 0.118797140284751 48 0.8512236552099 0.297552689580199 0.148776344790100 49 0.908827264426153 0.182345471147695 0.0911727355738474 50 0.797629879049607 0.404740241900785 0.202370120950393 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 4 0.0930232558139535 NOK 10% type I error level 13 0.302325581395349 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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