W 7

*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 13:45:25 -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/t12585774993i1fhu68w93o9c1.htm/, Retrieved Wed, 18 Nov 2009 21:51:52 +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/t12585774993i1fhu68w93o9c1.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:

W7

Dataseries X:

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13132.1 12002.4 17665.9 15525.5 16913 14247.9 17318.8 15000.7 16224.2 14931.4 15469.6 13333.7 16557.5 14711.2 19414.8 17197.3 17335 14985.2 16525.2 14734.4 18160.4 15937.8 15553.8 13028.1 15262.2 13836.8 18581 16677.5 17564.1 15130 18948.6 17504 17187.8 16979.9 17564.8 16012.5 17668.4 16247.7 20811.7 19268.2 17257.8 15533 18984.2 16803.3 20532.6 17396.1 17082.3 15155.4 16894.9 15692.4 20274.9 18063.7 20078.6 17568.6 19900.9 18154.3 17012.2 15467.4 19642.9 16956.1 19024 16854 21691 19396.4 18835.9 16457.6 19873.4 17284.5 21468.2 18395.3 19406.8 16938.7 18385.3 16414.3 20739.3 18173.4 22268.3 19919.7 21569 19623.8 17514.8 17228.1 21124.7 18730.3 21251 19039.1 21393 19413.3 22145.2 20013.6 20310.5 17917.2 23466.9 21270.3 21264.6 18766.1 18388.1 16790.8 22635.4 19960.6 22014.3 19586.7 18422.7 17179 16120.2 14964.9 16037.7 13918.5 16410.7 14401.3 17749.8 15994.6 16349.8 14521.1 15662.3 13746.5 17782.3 15956 16398.9 14332.2

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 Uitvoer[t] = + 899.267901263949 + 1.06617846666678Invoer[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) 899.267901263949 588.472262 1.5281 0.131914 0.065957 Invoer 1.06617846666678 0.035147 30.3344 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.969899980296102 R-squared 0.94070597177838 Adjusted R-squared 0.939683660946972 F-TEST (value) 920.176078427589 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 548.735318387848 Sum Squared Residuals 17464406.0794803 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13132.1 13695.9683295853 -563.868329585333 2 17665.9 17452.221685499 213.678314501008 3 16913 16090.0720764855 822.927923514483 4 17318.8 16892.6912261923 426.108773807732 5 16224.2 16818.8050584523 -594.605058452258 6 15469.6 15115.3717222588 354.228277741248 7 16557.5 16584.0325600922 -26.5325600922356 8 19414.8 19234.6588460725 180.141153927494 9 17335 16876.1654599589 458.834540041068 10 16525.2 16608.7679005189 -83.567900518903 11 18160.4 17891.8070673057 268.5929326943 12 15553.8 14789.5475828454 764.252417154615 13 15262.2 15651.7661088388 -389.566108838805 14 18581 18680.4592790991 -99.4592790991164 15 17564.1 17030.5481019323 533.551898067718 16 18948.6 19561.6557817992 -613.055781799208 17 17187.8 19002.8716474191 -1815.07164741915 18 17564.8 17971.4505987657 -406.650598765711 19 17668.4 18222.2157741257 -553.815774125736 20 20811.7 21442.6078326927 -630.907832692733 21 17257.8 17460.218023999 -202.418023998992 22 18984.2 18814.5845302058 169.615469794205 23 20532.6 19446.6151252459 1085.98487475414 24 17082.3 17057.6290349856 24.6709650143828 25 16894.9 17630.1668715857 -735.266871585674 26 20274.9 20158.3958695926 116.504130407399 27 20078.6 19630.5309107459 448.06908925412 28 19900.9 20254.9916386726 -354.091638672609 29 17012.2 17390.2767165856 -378.07671658565 30 19642.9 18977.4965999125 665.403400087523 31 19024 18868.6397784658 155.360221534197 32 21691 21579.2919121194 111.708087880585 33 18835.9 18446.0066342791 389.893365720911 34 19873.4 19327.6296083658 545.770391634152 35 21468.2 20511.9406491393 956.259350860697 36 19406.8 18958.9450945925 447.85490540752 37 18385.3 18399.8411066724 -14.541106672421 38 20739.3 20275.3556473859 463.944352614051 39 22268.3 22137.2231037261 131.076896273861 40 21569 21821.7408954394 -252.740895439438 41 17514.8 19267.4971428458 -1752.69714284584 42 21124.7 20869.1104354727 255.589564527327 43 21251 21198.3463459794 52.6536540206271 44 21393 21597.3103282061 -204.310328206082 45 22145.2 22237.3372617461 -92.1372617461454 46 20310.5 20002.2007242259 308.299275774080 47 23466.9 23577.2037408063 -110.303740806283 48 21264.6 20907.2796245793 357.320375420655 49 18388.1 18801.2572993725 -413.157299372463 50 22635.4 22180.8298030128 454.570196987195 51 22014.3 21782.1856743261 232.114325673897 52 18422.7 19215.1477801325 -792.447780132504 53 16120.2 16854.5220370856 -734.322037085595 54 16037.7 15738.8728895655 298.827110434519 55 16410.7 16253.6238532722 157.076146727800 56 17749.8 17952.3660042124 -202.566004212376 57 16349.8 16381.3520335789 -31.5520335788819 58 15662.3 15555.4901932988 106.809806701203 59 17782.3 17911.2115153990 -128.911515399038 60 16398.9 16179.9509212255 218.949078774474 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.757783633017492 0.484432733965016 0.242216366982508 6 0.682121477961863 0.635757044076275 0.317878522038137 7 0.556875308992626 0.886249382014749 0.443124691007374 8 0.438190821542587 0.876381643085175 0.561809178457413 9 0.360545628329946 0.721091256659893 0.639454371670054 10 0.270531908692544 0.541063817385088 0.729468091307456 11 0.187064688963885 0.37412937792777 0.812935311036115 12 0.26865450389084 0.53730900778168 0.73134549610916 13 0.259311228964056 0.518622457928111 0.740688771035944 14 0.204800352518431 0.409600705036862 0.795199647481569 15 0.184801906939701 0.369603813879401 0.815198093060299 16 0.236931407721540 0.473862815443081 0.76306859227846 17 0.871298284650818 0.257403430698363 0.128701715349182 18 0.837266124030926 0.325467751938148 0.162733875969074 19 0.815149776256657 0.369700447486685 0.184850223743343 20 0.796037190228012 0.407925619543976 0.203962809771988 21 0.73853916716086 0.522921665678279 0.261460832839140 22 0.701103232956064 0.597793534087872 0.298896767043936 23 0.903008978073473 0.193982043853053 0.0969910219265266 24 0.865641534952928 0.268716930094145 0.134358465047072 25 0.888028078668528 0.223943842662945 0.111971921331472 26 0.85741943845042 0.285161123099161 0.142580561549581 27 0.8520025759543 0.295994848091399 0.147997424045699 28 0.820097290264679 0.359805419470643 0.179902709735321 29 0.790384621729133 0.419230756541735 0.209615378270867 30 0.821807004809721 0.356385990380558 0.178192995190279 31 0.773847305363993 0.452305389272014 0.226152694636007 32 0.71942553402076 0.561148931958480 0.280574465979240 33 0.688244382474193 0.623511235051615 0.311755617525807 34 0.690221233347742 0.619557533304517 0.309778766652258 35 0.816426128318186 0.367147743363628 0.183573871681814 36 0.804894305790537 0.390211388418927 0.195105694209463 37 0.746179995167355 0.50764000966529 0.253820004832645 38 0.735281657439153 0.529436685121694 0.264718342560847 39 0.671253828398257 0.657492343203485 0.328746171601743 40 0.607744942523221 0.784510114953557 0.392255057476779 41 0.992623616788179 0.0147527664236419 0.00737638321182095 42 0.98858463784721 0.0228307243055807 0.0114153621527904 43 0.979550228945382 0.0408995421092357 0.0204497710546179 44 0.967936554531352 0.0641268909372959 0.0320634454686480 45 0.94781822606482 0.104363547870362 0.0521817739351808 46 0.929868687081038 0.140262625837924 0.0701313129189619 47 0.894443218492217 0.211113563015566 0.105556781507783 48 0.867419033485413 0.265161933029174 0.132580966514587 49 0.840108013390596 0.319783973218808 0.159891986609404 50 0.85259519960626 0.294809600787479 0.147404800393740 51 0.971599945987496 0.0568001080250078 0.0284000540125039 52 0.949597832934336 0.100804334131327 0.0504021670656637 53 0.999471912111451 0.00105617577709692 0.00052808788854846 54 0.998318664685753 0.00336267062849380 0.00168133531424690 55 0.99195790870392 0.0160841825921605 0.00804209129608023 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0392156862745098 NOK 5% type I error level 6 0.117647058823529 NOK 10% type I error level 8 0.156862745098039 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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