*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: Tue, 07 Dec 2010 12:59:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/07/t1291726647vy7ri2gi81a90cb.htm/, Retrieved Tue, 07 Dec 2010 13:57:35 +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/2010/Dec/07/t1291726647vy7ri2gi81a90cb.htm/}, year = {2010}, } @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 = {2010}, 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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112,3 0 117,2 96,8 80 126,1 117,3 0 112,3 117,2 96,8 80 111,1 1 117,3 112,3 117,2 96,8 102,2 1 111,1 117,3 112,3 117,2 104,3 1 102,2 111,1 117,3 112,3 122,9 1 104,3 102,2 111,1 117,3 107,6 1 122,9 104,3 102,2 111,1 121,3 1 107,6 122,9 104,3 102,2 131,5 1 121,3 107,6 122,9 104,3 89 1 131,5 121,3 107,6 122,9 104,4 1 89 131,5 121,3 107,6 128,9 1 104,4 89 131,5 121,3 135,9 1 128,9 104,4 89 131,5 133,3 1 135,9 128,9 104,4 89 121,3 1 133,3 135,9 128,9 104,4 120,5 0 121,3 133,3 135,9 128,9 120,4 0 120,5 121,3 133,3 135,9 137,9 0 120,4 120,5 121,3 133,3 126,1 0 137,9 120,4 120,5 121,3 133,2 0 126,1 137,9 120,4 120,5 151,1 0 133,2 126,1 137,9 120,4 105 0 151,1 133,2 126,1 137,9 119 0 105 151,1 133,2 126,1 140,4 0 119 105 151,1 133,2 156,6 0 140,4 119 105 151,1 137,1 0 156,6 140,4 119 105 122,7 0 137,1 156,6 140,4 119 125,8 0 122,7 137,1 156,6 140,4 139,3 0 125,8 122,7 137,1 156,6 134,9 0 139,3 125,8 122,7 137,1 149,2 0 134,9 139,3 125,8 122,7 132,3 0 149,2 134,9 139,3 125,8 149 0 132,3 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation X[t] = + 24.1698363156218 + 3.12409265557007Y[t] + 0.354106572914146`y(t)`[t] + 0.386685471568013`y(t-1)`[t] + 0.316297204680138`y(t-2)`[t] -0.0792357995923454`y(t-3)`[t] + 4.29883047671241M1[t] -22.2968495935551M2[t] -39.5691693349632M3[t] -35.9297143015368M4[t] -20.3378644943873M5[t] -6.9663341972657M6[t] -15.9323504617263M7[t] -22.9939682907714M8[t] -6.55872286116876M9[t] -44.2832772039972M10[t] -31.4045454857822M11[t] -0.0983757038209553t + 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) 24.1698363156218 18.638984 1.2967 0.201801 0.100901 Y 3.12409265557007 3.773085 0.828 0.412354 0.206177 `y(t)` 0.354106572914146 0.153497 2.3069 0.02606 0.01303 `y(t-1)` 0.386685471568013 0.161454 2.395 0.021157 0.010578 `y(t-2)` 0.316297204680138 0.156269 2.0241 0.049356 0.024678 `y(t-3)` -0.0792357995923454 0.157901 -0.5018 0.618423 0.309212 M1 4.29883047671241 9.799488 0.4387 0.663142 0.331571 M2 -22.2968495935551 10.749129 -2.0743 0.044218 0.022109 M3 -39.5691693349632 7.999304 -4.9466 1.3e-05 6e-06 M4 -35.9297143015368 5.974976 -6.0134 0 0 M5 -20.3378644943873 6.115281 -3.3257 0.001838 0.000919 M6 -6.9663341972657 6.522986 -1.068 0.291636 0.145818 M7 -15.9323504617263 7.900121 -2.0167 0.050148 0.025074 M8 -22.9939682907714 7.837306 -2.9339 0.005404 0.002702 M9 -6.55872286116876 6.469515 -1.0138 0.316488 0.158244 M10 -44.2832772039972 7.364443 -6.0131 0 0 M11 -31.4045454857822 8.394784 -3.741 0.00055 0.000275 t -0.0983757038209553 0.065916 -1.4924 0.143057 0.071528 Multiple Linear Regression - Regression Statistics Multiple R 0.938958363418636 R-squared 0.881642808233803 Adjusted R-squared 0.833736325852247 F-TEST (value) 18.4034135758888 F-TEST (DF numerator) 17 F-TEST (DF denominator) 42 p-value 3.19744231092045e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.73467319800471 Sum Squared Residuals 2512.65711815716 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.3 122.614877127651 -10.3148771276511 2 117.3 111.040646166104 6.25935383389579 3 111.1 101.791118972656 9.3088810273439 4 102.2 101.903898293417 0.296101706582654 5 104.3 113.818115415492 -9.5181154154915 6 122.9 122.036171447978 0.863828552022036 7 107.6 118.046418062012 -10.4464180620117 8 121.3 114.030366480924 7.26963351907558 9 131.5 135.018941368546 -3.51894136854592 10 89 99.7923562220788 -10.7923562220788 11 104.4 107.012954135496 -2.61295413549615 12 128.9 129.478933632017 -0.578933632017009 13 135.9 134.059119348705 1.84088065129534 14 133.3 127.55610207318 5.74389792681967 15 121.3 118.500578040292 2.79942195970812 16 120.5 113.935706956029 6.56429304397087 17 120.4 123.128646812895 -2.72864681289544 18 137.9 132.467488994429 5.43251100557129 19 126.1 130.259085336352 -4.15908533635198 20 133.2 125.719388914745 7.48061108525491 21 151.1 145.550651405576 5.54934859442373 22 105 111.692762354131 -6.69276235413127 23 119 118.251167886669 0.74883211333072 24 140.4 141.787775236812 -1.38777523681202 25 156.6 142.980085323561 13.619914676439 26 137.1 138.378556348966 -1.27855634896627 27 122.7 126.026546357175 -3.3265463571753 28 125.8 120.356492945783 5.44350705421719 29 139.3 123.928011189907 15.3719888100929 30 134.9 140.170747824066 -5.27074782406636 31 149.2 136.890057649769 12.309942350231 32 132.3 137.116753319122 -4.81675331912151 33 149 150.537433210987 -1.53743321098744 34 117.2 116.964786007637 0.235213992362869 35 119.6 118.463705685282 1.13629431471772 36 152 144.944381577644 7.05561842235639 37 149.4 150.164445482696 -0.764445482696067 38 127.3 138.357133616103 -11.0571336161034 39 114.1 122.21316419601 -8.11316419600972 40 102.1 109.144675202535 -7.04467520253496 41 107.7 108.500467061705 -0.800467061705028 42 104.4 116.692380873722 -12.2923808737218 43 102.1 105.875221954062 -3.77522195406175 44 96 102.470907844206 -6.47090784420568 45 109.3 111.146756981873 -1.84675698187297 46 90 78.3327502018773 11.6672497981227 47 83.9 87.6745955213964 -3.77459552139643 48 112 114.047776807078 -2.04777680707792 49 114.3 118.681472717387 -4.38147271738714 50 103.6 103.267561795646 0.332438204354196 51 91.7 92.368592433867 -0.668592433867005 52 80.8 86.0592266022358 -5.25922660223576 53 87.2 89.5247595200009 -2.3247595200009 54 109.2 97.9332108598052 11.2667891401948 55 102.7 96.6292169978056 6.07078300219443 56 95.1 98.5625834410033 -3.4625834410033 57 117.5 116.146217033017 1.3537829669826 58 85.1 79.5173452142755 5.58265478572454 59 92.1 87.5975767711558 4.50242322884415 60 113.5 116.541132746449 -3.04113274644943 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.0259973488116894 0.0519946976233789 0.97400265118831 22 0.00808627798476238 0.0161725559695248 0.991913722015238 23 0.00180360388777855 0.0036072077755571 0.998196396112221 24 0.00227512219887386 0.00455024439774773 0.997724877801126 25 0.000865485037479967 0.00173097007495993 0.99913451496252 26 0.0048725911712901 0.0097451823425802 0.99512740882871 27 0.114008741893156 0.228017483786311 0.885991258106844 28 0.307805443432945 0.61561088686589 0.692194556567055 29 0.332383312830079 0.664766625660157 0.667616687169921 30 0.291140181072004 0.582280362144007 0.708859818927996 31 0.593927548001024 0.812144903997951 0.406072451998976 32 0.517518877047329 0.964962245905342 0.482481122952671 33 0.704306281037771 0.591387437924458 0.295693718962229 34 0.599772058335018 0.800455883329965 0.400227941664982 35 0.512029590314382 0.975940819371237 0.487970409685618 36 0.744961238732765 0.510077522534471 0.255038761267235 37 0.638956286608274 0.722087426783452 0.361043713391726 38 0.634458320713501 0.731083358572997 0.365541679286499 39 0.527649135689453 0.944701728621093 0.472350864310547 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.210526315789474 NOK 5% type I error level 5 0.263157894736842 NOK 10% type I error level 6 0.315789473684211 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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