consumer price indices

*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: Thu, 19 Nov 2009 09:19:17 -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/19/t1258647832me5ai9n74ps5c74.htm/, Retrieved Thu, 19 Nov 2009 17:24:03 +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/19/t1258647832me5ai9n74ps5c74.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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114 106.3 93.5 113.8 107.2 93.1 113.6 107.8 91 113.7 109.2 91.1 114.2 109.7 91.9 114.8 108.7 92.4 115.2 109.3 92.8 115.3 110.4 92.5 114.9 111.1 91.3 115.1 110.1 91.2 116 109.5 92.8 116 109 92.9 116 108.5 93 115.9 108.8 92.4 115.6 109.8 90.7 116.6 110.7 91.3 116.9 110.6 91.7 117.9 111.2 92.2 117.9 112 92.3 117.7 111.1 92.1 117.4 111.6 90.5 117.3 110.2 90.1 119 111.5 91.7 119.1 110.6 92.1 119 110.6 92.4 118.5 110.3 92.4 117 111.7 90 117.5 113.8 90.5 118.2 113.9 91.8 118.2 114.3 91.7 118.3 113.8 91.6 118.2 114.3 91.4 117.9 116.4 89.8 117.8 115.6 89.7 118.6 115.2 90.9 118.9 113.6 91 120.8 115.5 91.4 121.8 115.6 91.3 121.3 115.3 89.5 121.9 117.3 90.2 122 118.7 90.9 121.9 118.3 91.2 122 120.6 91.3 122.2 119.3 90.5 123 121.8 89.9 123.1 120.8 89.6 124.9 121.6 90.9 125.4 121.6 91.1 124.7 121.1 91.1 124.4 122.4 90.8 124 121.9 89.5 125 125.1 90.9 125.1 124.5 91.9 125.4 123.5 92.4 125.7 124.9 92.7 126.4 125.2 92.4 125.7 125.7 91.3 125.4 124.5 90.8 126.4 124.7 92.5 etc...

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 x[t] = + 49.8477598332706 + 0.199099762966021y[t] + 0.456711187033412z[t] + 0.166158579526877t + 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) 49.8477598332706 11.422293 4.3641 5.5e-05 2.8e-05 y 0.199099762966021 0.063757 3.1228 0.002834 0.001417 z 0.456711187033412 0.108296 4.2172 9.1e-05 4.6e-05 t 0.166158579526877 0.021415 7.7589 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.981353702016435 R-squared 0.963055088461362 Adjusted R-squared 0.961075896771792 F-TEST (value) 486.590103190381 F-TEST (DF numerator) 3 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.783395793075165 Sum Squared Residuals 34.3677022420405 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 114 113.880719203709 0.119280796290517 2 113.8 114.043383095092 -0.243383095092458 3 113.6 113.369908039629 0.230091960371214 4 113.7 113.860477406011 -0.160477406011423 5 114.2 114.491554816648 -0.291554816648046 6 114.8 114.686969226726 0.113030773274386 7 115.2 115.155272138845 0.0447278611545424 8 115.3 115.403427101525 -0.103427101524943 9 114.9 115.160902090688 -0.260902090687929 10 115.1 115.082289788545 0.0177102114545427 11 116 115.859726409546 0.140273590453826 12 116 115.972006226293 0.0279937737066145 13 116 116.084286043041 -0.0842860430405909 14 115.9 116.036147839237 -0.136147839237224 15 115.6 115.624997163773 -0.0249971637733318 16 116.6 116.244372242190 0.355627757810326 17 116.9 116.573305320233 0.326694679766697 18 117.9 117.087279351057 0.8127206489435 19 117.9 117.458388859660 0.441611140340468 20 117.7 117.354015415110 0.345984584889692 21 117.4 116.888985976867 0.511014023133263 22 117.3 116.593720413428 0.706279586572172 23 119 117.749446584064 1.25055341593601 24 119.1 117.919099851735 1.18090014826518 25 119 118.222271787372 0.777728212628285 26 118.5 118.328700438009 0.171299561991213 27 117 117.677491836808 -0.677491836807904 28 117.5 118.490115512080 -0.99011551208013 29 118.2 119.269908611047 -1.06990861104704 30 118.2 119.470035977057 -1.27003597705699 31 118.3 119.490973556398 -1.19097355639751 32 118.2 119.665339780001 -1.46533978000072 33 117.9 119.518869962503 -1.61886996250278 34 117.8 119.480077612954 -1.68007761295350 35 118.6 120.114649711734 -1.51464971173407 36 118.9 120.007919789219 -1.10791978921864 37 120.8 120.735052393194 0.0649476068056636 38 121.8 120.875449830314 0.924550169685530 39 121.3 120.159798344291 1.1402016557086 40 121.9 121.043854280674 0.856145719326299 41 122 121.808450359276 0.191549640723596 42 121.9 122.031982389727 -0.131982389726888 43 122 122.701741542779 -0.701741542778957 44 122.2 122.243701480823 -0.0437014808232769 45 123 122.633582755545 0.366417244454835 46 123.1 122.463628215996 0.636371784004002 47 124.9 123.382791149039 1.51720885096088 48 125.4 123.640291965973 1.75970803402733 49 124.7 123.706900664017 0.993099335983456 50 124.4 123.994875579289 0.405124420710774 51 124 123.467759734190 0.532240265810336 52 125 124.910433217055 0.0895667829454147 53 125.1 125.413843125835 -0.313843125835268 54 125.4 125.609257535913 -0.209257535912820 55 125.7 126.191169139702 -0.491169139702152 56 126.4 126.280044292009 0.119955707991190 57 125.7 126.043370447282 -0.343370447281944 58 125.4 125.742253717733 -0.342253717732886 59 126.4 126.724641267810 -0.324641267809769 60 126.2 126.578091392701 -0.378091392701150 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.00333073989334265 0.0066614797866853 0.996669260106657 8 0.000420127998039443 0.000840255996078886 0.99957987200196 9 0.000173656921383911 0.000347313842767821 0.999826343078616 10 9.68204327802015e-05 0.000193640865560403 0.99990317956722 11 1.56311650853392e-05 3.12623301706783e-05 0.999984368834915 12 7.85246446315106e-06 1.57049289263021e-05 0.999992147535537 13 5.63820355499963e-06 1.12764071099993e-05 0.999994361796445 14 2.15561747366569e-06 4.31123494733138e-06 0.999997844382526 15 3.84756534675376e-07 7.69513069350752e-07 0.999999615243465 16 5.71733412890327e-07 1.14346682578065e-06 0.999999428266587 17 2.57476373656807e-07 5.14952747313614e-07 0.999999742523626 18 3.12560078184292e-06 6.25120156368584e-06 0.999996874399218 19 1.00419154292086e-06 2.00838308584172e-06 0.999998995808457 20 2.69834164790103e-07 5.39668329580205e-07 0.999999730165835 21 8.80993241492482e-08 1.76198648298496e-07 0.999999911900676 22 3.64897345920761e-08 7.29794691841521e-08 0.999999963510265 23 5.89768451677386e-07 1.17953690335477e-06 0.999999410231548 24 1.47729237574290e-06 2.95458475148580e-06 0.999998522707624 25 1.66518748057375e-06 3.33037496114750e-06 0.99999833481252 26 1.14260623403192e-05 2.28521246806384e-05 0.99998857393766 27 0.000580618617633538 0.00116123723526708 0.999419381382366 28 0.00483128226353624 0.00966256452707249 0.995168717736464 29 0.0125330434795475 0.025066086959095 0.987466956520452 30 0.0183059278566079 0.0366118557132158 0.981694072143392 31 0.0205760662504206 0.0411521325008411 0.97942393374958 32 0.0257183847822968 0.0514367695645936 0.974281615217703 33 0.038163710477163 0.076327420954326 0.961836289522837 34 0.123031856092509 0.246063712185018 0.87696814390749 35 0.262649294710555 0.525298589421111 0.737350705289445 36 0.498439707730293 0.996879415460587 0.501560292269707 37 0.545240727707036 0.909518544585929 0.454759272292964 38 0.680888750668807 0.638222498662386 0.319111249331193 39 0.746833370321693 0.506333259356613 0.253166629678307 40 0.788473274542078 0.423053450915845 0.211526725457922 41 0.762207206860107 0.475585586279785 0.237792793139893 42 0.739420523838982 0.521158952322037 0.260579476161018 43 0.8848529099706 0.230294180058802 0.115147090029401 44 0.974866832453922 0.0502663350921559 0.0251331675460780 45 0.98468571530503 0.0306285693899397 0.0153142846949698 46 0.99162935601279 0.01674128797442 0.00837064398721 47 0.990561823814605 0.0188763523707910 0.00943817618539552 48 0.999308761427698 0.00138247714460367 0.000691238572301833 49 0.999343907799846 0.00131218440030848 0.000656092200154239 50 0.997618946876975 0.00476210624604997 0.00238105312302499 51 0.99490674376383 0.0101865124723415 0.00509325623617073 52 0.988206104200814 0.0235877915983726 0.0117938957991863 53 0.95738745057707 0.0852250988458595 0.0426125494229297 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.531914893617021 NOK 5% type I error level 33 0.702127659574468 NOK 10% type I error level 37 0.787234042553192 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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