*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: Wed, 18 Nov 2009 07:33:37 -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/18/t1258554891zkc9rndmgdj1vzc.htm/, Retrieved Wed, 18 Nov 2009 15:35:03 +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/18/t1258554891zkc9rndmgdj1vzc.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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8.9 95.05 8.8 96.84 8.3 96.92 7.5 97.44 7.2 97.78 7.4 97.69 8.8 96.67 9.3 98.29 9.3 98.2 8.7 98.71 8.2 98.54 8.3 98.2 8.5 96.92 8.6 99.06 8.5 99.65 8.2 99.82 8.1 99.99 7.9 100.33 8.6 99.31 8.7 101.1 8.7 101.1 8.5 100.93 8.4 100.85 8.5 100.93 8.7 99.6 8.7 101.88 8.6 101.81 8.5 102.38 8.3 102.74 8 102.82 8.2 101.72 8.1 103.47 8.1 102.98 8 102.68 7.9 102.9 7.9 103.03 8 101.29 8 103.69 7.9 103.68 8 104.2 7.7 104.08 7.2 104.16 7.5 103.05 7.3 104.66 7 104.46 7 104.95 7 105.85 7.2 106.23 7.3 104.86 7.1 107.44 6.8 108.23 6.4 108.45 6.1 109.39 6.5 110.15 7.7 109.13 7.9 110.28 7.5 110.17 6.9 109.99 6.6 109.26 6.9 109.11

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 Werkloosheidsgraad[t] = + 21.9173451552953 -0.136785943529424Consumptieprijs[t] -0.0211251926024103M1[t] + 0.245001749016449M2[t] + 0.062754669430571M3[t] -0.182530953157660M4[t] -0.376297304244715M5[t] -0.42428939345883M6[t] + 0.191538222061157M7[t] + 0.508207156611765M8[t] + 0.343859258663527M9[t] + 0.0534342747105871M10[t] -0.142735718870589M11[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) 21.9173451552953 1.626843 13.4723 0 0 Consumptieprijs -0.136785943529424 0.015588 -8.7753 0 0 M1 -0.0211251926024103 0.30247 -0.0698 0.944616 0.472308 M2 0.245001749016449 0.297326 0.824 0.414092 0.207046 M3 0.062754669430571 0.29697 0.2113 0.833554 0.416777 M4 -0.182530953157660 0.296563 -0.6155 0.541202 0.270601 M5 -0.376297304244715 0.296321 -1.2699 0.210373 0.105186 M6 -0.42428939345883 0.296209 -1.4324 0.158647 0.079323 M7 0.191538222061157 0.297069 0.6448 0.522218 0.261109 M8 0.508207156611765 0.296119 1.7162 0.092706 0.046353 M9 0.343859258663527 0.296124 1.1612 0.251424 0.125712 M10 0.0534342747105871 0.296119 0.1804 0.857576 0.428788 M11 -0.142735718870589 0.296118 -0.482 0.632027 0.316013 Multiple Linear Regression - Regression Statistics Multiple R 0.826999799282124 R-squared 0.683928668012673 Adjusted R-squared 0.603229604526547 F-TEST (value) 8.4750508676009 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 3.13289227893421e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.468203505624164 Sum Squared Residuals 10.3030825659016 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.9 8.89471603022127 0.00528396977873334 2 8.8 8.91599613292241 -0.115996132922411 3 8.3 8.72280617785418 -0.422806177854178 4 7.5 8.40639186463065 -0.906391864630648 5 7.2 8.16611829274359 -0.966118292743588 6 7.4 8.13043693844712 -0.730436938447122 7 8.8 8.88578621636712 -0.0857862163671204 8 9.3 8.98086192240006 0.319138077599939 9 9.3 8.82882475936947 0.471175240630528 10 8.7 8.46863894421653 0.231361055783471 11 8.2 8.29572256103535 -0.0957225610353523 12 8.3 8.48496550070595 -0.184965500705945 13 8.5 8.6389263158212 -0.138926315821198 14 8.6 8.61233133828709 -0.0123313382870908 15 8.5 8.34938055201885 0.150619447981148 16 8.2 8.08084131903062 0.119158680969379 17 8.1 7.86382135754356 0.236178642456436 18 7.9 7.76932204752944 0.130677952470556 19 8.6 8.52467132544944 0.0753286745505567 20 8.7 8.59649342108238 0.103506578917616 21 8.7 8.43214552313415 0.267854476865854 22 8.5 8.1649741495812 0.335025850418794 23 8.4 7.97974703148239 0.420252968517615 24 8.5 8.11153987487062 0.388460125129381 25 8.7 8.27233998716234 0.427660012837656 26 8.7 8.22659497753412 0.473405022465883 27 8.6 8.0539229139953 0.546077086004702 28 8.5 7.7306693035953 0.769330696404705 29 8.3 7.48766001283765 0.812339987162353 30 8 7.42872504814118 0.57127495185882 31 8.2 8.19501720154353 0.00498279845646693 32 8.1 8.27231073491765 -0.172310734917649 33 8.1 8.17498794929883 -0.074987949298828 34 8 7.92559874840471 0.0744012515952858 35 7.9 7.69933584724706 0.200664152752935 36 7.9 7.82428939345883 0.0757106065411707 37 8 8.04117174259762 -0.0411717425976161 38 8 7.97901241974586 0.0209875802541405 39 7.9 7.79813319959527 0.101866800404726 40 8 7.48171888637174 0.518281113628256 41 7.7 7.30436684850822 0.39563315149178 42 7.2 7.24543188381175 -0.0454318838117513 43 7.5 8.0130918966494 -0.513091896649399 44 7.3 8.10953546211763 -0.809535462117634 45 7 7.97254475287528 -0.972544752875282 46 7 7.61509465659292 -0.615094656592923 47 7 7.29581731383527 -0.295817313835267 48 7.2 7.38657437416467 -0.186574374164673 49 7.3 7.55284592419757 -0.252845924197575 50 7.1 7.46606513151052 -0.366065131510521 51 6.8 7.1757571565364 -0.375757156536398 52 6.4 6.9003786263717 -0.500378626371692 53 6.1 6.57803348836698 -0.478033488366981 54 6.5 6.4260840820705 0.0739159179294972 55 7.7 7.1814333599905 0.518566640009497 56 7.9 7.34079845948227 0.559201540517727 57 7.5 7.19149701532227 0.308502984677728 58 6.9 6.92569350120463 -0.0256935012046285 59 6.6 6.82937724639993 -0.229377246399931 60 6.9 6.99263085679993 -0.0926308567999336 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.374761562581837 0.749523125163674 0.625238437418163 17 0.439748841098595 0.87949768219719 0.560251158901405 18 0.306449690877210 0.612899381754420 0.69355030912279 19 0.263950436474122 0.527900872948243 0.736049563525878 20 0.323405224239607 0.646810448479215 0.676594775760393 21 0.326618426352391 0.653236852704781 0.67338157364761 22 0.241802261669389 0.483604523338778 0.758197738330611 23 0.173126714152264 0.346253428304527 0.826873285847736 24 0.117661264142715 0.235322528285429 0.882338735857285 25 0.0786116852709974 0.157223370541995 0.921388314729003 26 0.0530857087681754 0.106171417536351 0.946914291231825 27 0.0381727579446639 0.0763455158893278 0.961827242055336 28 0.0506573634538857 0.101314726907771 0.949342636546114 29 0.0662570234573664 0.132514046914733 0.933742976542634 30 0.0514656121586405 0.102931224317281 0.94853438784136 31 0.0588878558037069 0.117775711607414 0.941112144196293 32 0.106372936294537 0.212745872589074 0.893627063705463 33 0.140561354871877 0.281122709743754 0.859438645128123 34 0.133583771216065 0.267167542432131 0.866416228783935 35 0.119119580113557 0.238239160227115 0.880880419886443 36 0.0956722606979288 0.191344521395858 0.904327739302071 37 0.0812717200761305 0.162543440152261 0.91872827992387 38 0.0719926325297302 0.143985265059460 0.92800736747027 39 0.0672820512982942 0.134564102596588 0.932717948701706 40 0.159429067486786 0.318858134973573 0.840570932513214 41 0.598884222840997 0.802231554318006 0.401115777159003 42 0.767560897697265 0.464878204605469 0.232439102302735 43 0.671270185701048 0.657459628597903 0.328729814298952 44 0.714259336303033 0.571481327393934 0.285740663696967 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 0.0344827586206897 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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