*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 09:31:11 -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/t1258562031h3utabkcc1niq5y.htm/, Retrieved Wed, 18 Nov 2009 17:34:03 +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/t1258562031h3utabkcc1niq5y.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:

ws7multipleregressionincludemonthlydummieswmanecogr

Dataseries X:

» Textbox « » Textfile « » CSV «

8,00 96,80 8,10 114,10 7,70 110,30 7,50 103,90 7,60 101,60 7,80 94,60 7,80 95,90 7,80 104,70 7,50 102,80 7,50 98,10 7,10 113,90 7,50 80,90 7,50 95,70 7,60 113,20 7,70 105,90 7,70 108,80 7,90 102,30 8,10 99,00 8,20 100,70 8,20 115,50 8,20 100,70 7,90 109,90 7,30 114,60 6,90 85,40 6,60 100,50 6,70 114,80 6,90 116,50 7,00 112,90 7,10 102,00 7,20 106,00 7,10 105,30 6,90 118,80 7,00 106,10 6,80 109,30 6,40 117,20 6,70 92,50 6,60 104,20 6,40 112,50 6,30 122,40 6,20 113,30 6,50 100,00 6,80 110,70 6,80 112,80 6,40 109,80 6,10 117,30 5,80 109,10 6,10 115,90 7,20 96,00 7,30 99,80 6,90 116,80 6,10 115,70 5,80 99,40 6,20 94,30 7,10 91,00 7,70 93,20 7,90 103,10 7,70 94,10 7,40 91,80 7,50 102,70 8,00 82,60

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 Wman[t] = + 11.1977497209993 -0.0450131426726024Ecogr[t] + 0.476556660657418M1[t] + 1.08635222362574M2[t] + 0.880950646505031M3[t] + 0.488365219133116M4[t] + 0.365365071967885M5[t] + 0.715267963355858M6[t] + 0.894685311683693M7[t] + 1.21080096720259M8[t] + 0.792619745485912M9[t] + 0.547412385589255M10[t] + 0.762433561030648M11[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) 11.1977497209993 1.283992 8.721 0 0 Ecogr -0.0450131426726024 0.014316 -3.1443 0.002884 0.001442 M1 0.476556660657418 0.435376 1.0946 0.279276 0.139638 M2 1.08635222362574 0.554648 1.9586 0.056105 0.028052 M3 0.880950646505031 0.553461 1.5917 0.118154 0.059077 M4 0.488365219133116 0.493856 0.9889 0.327785 0.163892 M5 0.365365071967885 0.439049 0.8322 0.409519 0.204759 M6 0.715267963355858 0.440348 1.6243 0.110995 0.055497 M7 0.894685311683693 0.448529 1.9947 0.051892 0.025946 M8 1.21080096720259 0.5176 2.3393 0.023623 0.011812 M9 0.792619745485912 0.466613 1.6987 0.095993 0.047997 M10 0.547412385589255 0.462551 1.1835 0.242577 0.121289 M11 0.762433561030648 0.540785 1.4099 0.165163 0.082582 Multiple Linear Regression - Regression Statistics Multiple R 0.511258890378526 R-squared 0.261385652991081 Adjusted R-squared 0.0728032665207192 F-TEST (value) 1.3860554948071 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.206207758380558 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.633309313388729 Sum Squared Residuals 18.8507922619704 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8 7.31703417094877 0.682965829051226 2 8.1 7.14810236568107 0.951897634318932 3 7.7 7.11375073071625 0.586249269283754 4 7.5 7.00924941644899 0.490750583551015 5 7.6 6.98977949743074 0.610220502569260 6 7.8 7.65477438752693 0.145225612473070 7 7.8 7.77567465038038 0.0243253496196196 8 7.8 7.69567465038038 0.104325349619619 9 7.5 7.36301839974164 0.136981600258357 10 7.5 7.32937281040622 0.170627189593784 11 7.1 6.83318633162049 0.266813668379506 12 7.5 7.55618647878572 -0.056186478785724 13 7.5 7.36654862788863 0.133451372111374 14 7.6 7.18861419408641 0.411385805913589 15 7.7 7.3118085584757 0.388191441524305 16 7.7 6.78868501735323 0.911314982646767 17 7.9 6.95827029755992 0.941729702440082 18 8.1 7.45671655976748 0.643283440232521 19 8.2 7.55961156555189 0.640388434448109 20 8.2 7.20953270951628 0.990467290483723 21 8.2 7.45754599935411 0.742454000645891 22 7.9 6.79821772686951 1.10178227313049 23 7.3 6.80167713174967 0.498322868250328 24 6.9 7.35362733675901 -0.453627336759013 25 6.6 7.15048554306014 -0.550485543060135 26 6.7 7.11659316581025 -0.416593165810247 27 6.9 6.83466924614611 0.06533075385389 28 7 6.60413113239556 0.395868867604437 29 7.1 6.9717742403617 0.128225759638300 30 7.2 7.14162456105926 0.058375438940738 31 7.1 7.35255110925792 -0.252551109257919 32 6.9 7.06098933869669 -0.160989338696688 33 7 7.21447502892206 -0.214475028922055 34 6.8 6.82522561247307 -0.0252256124730709 35 6.4 6.6846429608009 -0.284642960800905 36 6.7 7.03403402378354 -0.334034023783536 37 6.6 6.9839369151715 -0.383936915171506 38 6.4 7.22012339395723 -0.820123393957232 39 6.3 6.56909170437776 -0.269091704377756 40 6.2 6.58612587532652 -0.386125875326523 41 6.5 7.0618005257069 -0.561800525706904 42 6.8 6.93006279049803 -0.130062790498031 43 6.8 7.0149525392134 -0.214952539213402 44 6.4 7.46610762275011 -1.06610762275011 45 6.1 6.71032783098891 -0.610327830988909 46 5.8 6.83422824100759 -1.03422824100759 47 6.1 6.74316004627529 -0.643160046275289 48 7.2 6.87648802442943 0.323511975570572 49 7.3 7.18199474293096 0.118005257069043 50 6.9 7.02656688046504 -0.126566880465042 51 6.1 6.87067976028419 -0.770679760284192 52 5.8 7.2118085584757 -1.41180855847570 53 6.2 7.31837543894074 -1.11837543894074 54 7.1 7.8168217011483 -0.716821701148298 55 7.7 7.8972101355964 -0.197210135596408 56 7.9 7.76769567865655 0.132304321343455 57 7.7 7.75463274099328 -0.0546327409932838 58 7.4 7.61295560924361 -0.212955609243612 59 7.5 7.33733352955364 0.16266647044636 60 8 7.4796641362423 0.5203358637577 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0906214551425992 0.181242910285198 0.9093785448574 17 0.0484506193194329 0.0969012386388657 0.951549380680567 18 0.0190635011032857 0.0381270022065714 0.980936498896714 19 0.0075725168277239 0.0151450336554478 0.992427483172276 20 0.00410184345056514 0.00820368690113029 0.995898156549435 21 0.0212102950577578 0.0424205901155155 0.978789704942242 22 0.0196511128021643 0.0393022256043286 0.980348887197836 23 0.0122373302459302 0.0244746604918604 0.98776266975407 24 0.0276948772631128 0.0553897545262256 0.972305122736887 25 0.191691293270153 0.383382586540307 0.808308706729847 26 0.341134294663663 0.682268589327326 0.658865705336337 27 0.37035492743341 0.74070985486682 0.62964507256659 28 0.48179575157685 0.9635915031537 0.51820424842315 29 0.571941010340724 0.856117979318552 0.428058989659276 30 0.5448871937629 0.9102256124742 0.4551128062371 31 0.502839999777118 0.994320000445765 0.497160000222882 32 0.483894945067573 0.967789890135146 0.516105054932427 33 0.431344118100259 0.862688236200517 0.568655881899741 34 0.437176035931248 0.874352071862496 0.562823964068752 35 0.376368445177227 0.752736890354454 0.623631554822773 36 0.365178717709697 0.730357435419393 0.634821282290303 37 0.308219659408214 0.616439318816427 0.691780340591786 38 0.397525720798997 0.795051441597994 0.602474279201003 39 0.344145098681608 0.688290197363215 0.655854901318392 40 0.526467416966096 0.947065166067807 0.473532583033904 41 0.569721144117884 0.860557711764231 0.430278855882116 42 0.701517995591229 0.596964008817543 0.298482004408771 43 0.685379725815147 0.629240548369707 0.314620274184853 44 0.919813542109393 0.160372915781213 0.0801864578906065 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 1 0.0344827586206897 NOK 5% type I error level 6 0.206896551724138 NOK 10% type I error level 8 0.275862068965517 NOK

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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