Model 5

*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 14:28:01 -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/t1258666223bgcop1ly9ip7j40.htm/, Retrieved Thu, 19 Nov 2009 22:30:35 +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/t1258666223bgcop1ly9ip7j40.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:

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Dataseries X:

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4.1 96.8 96.2 3.9 109.9 96.8 3.8 88 109.9 3.7 91.1 88 3.7 106.4 91.1 4.1 68.6 106.4 4.1 100.1 68.6 3.8 108 100.1 3.7 106 108 3.5 108.6 106 3.6 91.5 108.6 4.1 99.2 91.5 3.8 98 99.2 3.7 96.6 98 3.6 102.8 96.6 3.3 96.9 102.8 3.4 110 96.9 3.7 70.5 110 3.7 101.9 70.5 3.4 109.6 101.9 3.3 107.8 109.6 3 113 107.8 3 93.8 113 3.3 108 93.8 3 102.8 108 2.9 116.3 102.8 2.8 89.2 116.3 2.5 106.7 89.2 2.6 112.1 106.7 2.8 74.2 112.1 2.7 108.8 74.2 2.4 111.5 108.8 2.2 118.8 111.5 2.1 118.9 118.8 2.1 97.6 118.9 2.3 116.4 97.6 2.1 107.9 116.4 2 121.2 107.9 1.9 97.9 121.2 1.7 113.4 97.9 1.8 117.6 113.4 2.1 79.6 117.6 2 115.9 79.6 1.8 115.7 115.9 1.7 129.1 115.7 1.6 123.3 129.1 1.6 96.7 123.3 1.8 121.2 96.7 1.7 118.2 121.2 1.7 102.1 118.2 1.5 125.4 102.1 1.5 116.7 125.4 1.5 121.3 116.7 1.8 85.3 121.3 1.8 114.2 85.3 1.7 124.4 114.2 1.7 131 124.4 1.8 118.3 131 2 99.6 118.3

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 unempl[t] = + 6.95863385692966 -0.0172255661383461proman[t] -0.0105823825619524`Y(t-1)`[t] -0.0995119353824613M1[t] -0.120160349506485M2[t] -0.301406028532639M3[t] -0.459125195627519M4[t] -0.168063033871873M5[t] -0.390920463878512M6[t] -0.232041804640464M7[t] + 0.00860172150904735M8[t] + 0.0882542609004675M9[t] + 0.020269351968893M10[t] -0.257871356949066M11[t] -0.038796093240543t + 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) 6.95863385692966 1.085142 6.4126 0 0 proman -0.0172255661383461 0.006944 -2.4806 0.017015 0.008507 `Y(t-1)` -0.0105823825619524 0.007009 -1.5098 0.138236 0.069118 M1 -0.0995119353824613 0.189178 -0.526 0.601515 0.300757 M2 -0.120160349506485 0.179817 -0.6682 0.507474 0.253737 M3 -0.301406028532639 0.190444 -1.5826 0.120664 0.060332 M4 -0.459125195627519 0.16797 -2.7334 0.008995 0.004497 M5 -0.168063033871873 0.181497 -0.926 0.359507 0.179753 M6 -0.390920463878512 0.277812 -1.4071 0.166411 0.083206 M7 -0.232041804640464 0.219876 -1.0553 0.297035 0.148517 M8 0.00860172150904735 0.186889 0.046 0.963498 0.481749 M9 0.0882542609004675 0.219093 0.4028 0.689034 0.344517 M10 0.020269351968893 0.232632 0.0871 0.930963 0.465482 M11 -0.257871356949066 0.213585 -1.2073 0.233748 0.116874 t -0.038796093240543 0.004869 -7.9681 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.97138574167357 R-squared 0.94359025912671 Adjusted R-squared 0.925641705212483 F-TEST (value) 52.5719377525283 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.240855151191974 Sum Squared Residuals 2.55249296965118 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.1 4.13486582365492 -0.0348658236549180 2 3.9 3.84341697034086 0.0565830296591427 3 3.8 3.86198588494237 -0.0619858849423663 4 3.7 3.84382554768483 -0.143825547684825 5 3.7 3.79973506834118 -0.0997350683411813 6 4.1 4.02729749192561 0.0727025080743886 7 4.1 4.00478878540701 0.0952112145929868 8 3.8 3.73720919512155 0.0627908048784517 9 3.7 3.72891595130969 -0.0289159513096931 10 3.5 3.59851324230178 -0.0985132423017812 11 3.6 3.54861942644792 0.0513805735520787 12 4.1 3.81601657270057 0.283983427299435 13 3.8 3.61689487771654 0.183105122283458 14 3.7 3.59426502202 0.105734977979997 15 3.6 3.28224007528229 0.317759924717706 16 3.3 3.12174488327901 0.178255116720993 17 3.4 3.21079209249730 0.189207907502704 18 3.7 3.49091922015321 0.209080779846791 19 3.7 3.48812312060376 0.211876879396236 20 3.4 3.22504688180216 0.174953118197836 21 3.3 3.21542500127503 0.0845749987249688 22 3 3.03811934379503 -0.038119343795028 23 3 2.99688502217062 0.00311497782938105 24 3.3 3.17453899190411 0.125461008095887 25 3 2.97553407482078 0.0244659251792153 26 2.9 2.7385728139107 0.161427186089302 27 2.8 2.84248171940682 -0.0424817194068233 28 2.5 2.63130161907925 -0.131301619079252 29 2.6 2.60535793561312 -0.00535793561312037 30 2.8 2.93940850317471 -0.139408503174713 31 2.7 2.86455877988344 -0.164558779883437 32 2.4 2.65374674757532 -0.253746747575319 33 2.2 2.540284127999 -0.340284127998998 34 2.1 2.35452917651079 -0.254529176510794 35 2.1 2.40343869484287 -0.303438694842869 36 2.3 2.52407806372007 -0.224078063720071 37 2.1 2.33323855510830 -0.233238555108303 38 2 2.13464426988033 -0.134644269880329 39 1.9 2.17521250056313 -0.275212500563130 40 1.7 1.95827047877683 -0.258270478776832 41 1.8 1.97416223980062 -0.174162239800621 42 2.1 2.32263422305039 -0.22263422305039 43 2 2.21955927558012 -0.219559275580121 44 1.8 2.04071133471789 -0.240711334717888 45 1.7 1.85286167112732 -0.152861671127318 46 1.6 1.70418502622745 -0.104185026227446 47 1.6 1.90682610220827 -0.306826102208274 48 1.8 1.98536637167525 -0.185366371675251 49 1.7 1.63946666869945 0.0605333313005481 50 1.7 1.88910092384811 -0.189100923848114 51 1.5 1.43807981980539 0.0619201801946135 52 1.5 1.14485747118008 0.355142528819916 53 1.5 1.40995266374778 0.0900473362522189 54 1.8 1.71974056169608 0.0802594383039226 55 1.8 1.72297003852566 0.0770299614743352 56 1.7 1.44328584078308 0.256714159216920 57 1.7 1.26251324828896 0.437486751711041 58 1.8 1.30465321116495 0.495346788835049 59 2 1.44423075433032 0.555769245669683 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.00551462655045917 0.0110292531009183 0.99448537344954 19 0.00290674892083762 0.00581349784167524 0.997093251079162 20 0.00122979081787151 0.00245958163574302 0.998770209182128 21 0.000435157711113495 0.00087031542222699 0.999564842288887 22 0.00045748068209976 0.00091496136419952 0.9995425193179 23 0.00109620120737725 0.00219240241475449 0.998903798792623 24 0.0119834232474734 0.0239668464949468 0.988016576752527 25 0.0153828749397672 0.0307657498795345 0.984617125060233 26 0.022435268723649 0.044870537447298 0.977564731276351 27 0.03018263007978 0.06036526015956 0.96981736992022 28 0.0566120746105059 0.113224149221012 0.943387925389494 29 0.0673630801090563 0.134726160218113 0.932636919890944 30 0.149617234575709 0.299234469151419 0.85038276542429 31 0.304091419584134 0.608182839168269 0.695908580415866 32 0.408336165112742 0.816672330225484 0.591663834887258 33 0.42602367896535 0.8520473579307 0.57397632103465 34 0.341566754947391 0.683133509894781 0.65843324505261 35 0.291748975538301 0.583497951076603 0.708251024461699 36 0.382481419687431 0.764962839374862 0.617518580312569 37 0.31667238181094 0.63334476362188 0.68332761818906 38 0.534634006119714 0.930731987760572 0.465365993880286 39 0.408522543835811 0.817045087671623 0.591477456164189 40 0.537781996160622 0.924436007678756 0.462218003839378 41 0.469571710004563 0.939143420009126 0.530428289995437 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.208333333333333 NOK 5% type I error level 9 0.375 NOK 10% type I error level 10 0.416666666666667 NOK

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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