w7

*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 14:21:33 -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/t1258579365q3qb6ctd3r81msz.htm/, Retrieved Wed, 18 Nov 2009 22:22:58 +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/t1258579365q3qb6ctd3r81msz.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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Uitvoer[t] = + 1759.89583601506 + 1.03809312850065Invoer[t] -823.37862132792M1[t] -91.8703965724779M2[t] + 102.518288888236M3[t] -640.979016258622M4[t] -1421.37817130003M5[t] -134.800925868524M6[t] -396.771399633361M7[t] -445.014237636709M8[t] -244.492657519431M9[t] -143.757487305076M10[t] + 110.384926787108M11[t] -1.62912632200185t + 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) 1759.89583601506 484.360778 3.6334 0.000702 0.000351 Invoer 1.03809312850065 0.031187 33.2857 0 0 M1 -823.37862132792 246.381189 -3.3419 0.00166 0.00083 M2 -91.8703965724779 257.623344 -0.3566 0.723016 0.361508 M3 102.518288888236 253.608616 0.4042 0.687911 0.343955 M4 -640.979016258622 254.60532 -2.5175 0.015364 0.007682 M5 -1421.37817130003 245.656024 -5.7861 1e-06 0 M6 -134.800925868524 245.106779 -0.55 0.585002 0.292501 M7 -396.771399633361 245.924652 -1.6134 0.113501 0.05675 M8 -445.014237636709 259.358745 -1.7158 0.092923 0.046462 M9 -244.492657519431 245.536367 -0.9957 0.324581 0.162291 M10 -143.757487305076 244.798122 -0.5872 0.559908 0.279954 M11 110.384926787108 253.538425 0.4354 0.665325 0.332662 t -1.62912632200185 3.223713 -0.5054 0.615721 0.307861 Multiple Linear Regression - Regression Statistics Multiple R 0.98829446174447 R-squared 0.976725943114793 Adjusted R-squared 0.97014849225593 F-TEST (value) 148.496121684996 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 386.036671611911 Sum Squared Residuals 6855118.34414332 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 13132.1 13394.4970538814 -262.397053881395 2 17665.9 17781.6820533354 -115.782053335410 3 16913 16648.1738315017 264.826168498309 4 17318.8 16684.5239071681 634.27609283188 5 16224.2 15830.5557719996 393.644228000384 6 15469.6 15456.9424997036 12.6575002963664 7 16557.5 16623.3161841264 -65.8161841264366 8 19414.8 19154.2475465665 260.552453433451 9 17335 17056.7741908055 278.225809194458 10 16525.2 16895.5264780699 -370.326478069930 11 18160.4 18397.2810366778 -236.881036677792 12 15553.8 15264.7274075703 289.072592429651 13 15262.2 15279.2255729389 -17.0255729388993 14 18581 18958.0158215041 -377.015821504132 15 17564.1 17544.3262642881 19.7737357119076 16 18948.6 19263.6329198798 -315.032919879771 17 17187.8 17937.5400298692 -749.740029869175 18 17564.8 18218.2368564671 -653.436856467148 19 17668.4 18198.7967602037 -530.39676020366 20 20811.7 21284.4850905145 -472.78509051452 21 17257.8 17605.8920907342 -348.092090734175 22 18984.2 19023.6878357609 -39.4878357608988 23 20532.6 19891.5827301063 641.017269893732 24 17082.3 17453.5134039658 -371.213403965755 25 16894.9 17185.9616663207 -291.061666320680 26 20274.9 20377.4710003677 -102.571000367708 27 20078.6 20056.2706515857 22.3293484142507 28 19900.9 19919.1553654797 -18.2553654797174 29 17012.2 16347.8746571479 664.32534285208 30 19642.9 19178.2320166563 464.667983343667 31 19024 18808.6431081496 215.356891850418 32 21691 21398.0191137243 292.980886275718 33 18835.9 18546.1634814818 289.736518518152 34 19873.4 19503.6687333314 369.731266668611 35 21468.2 20909.2958682401 558.904131759909 36 19406.8 19285.1953641569 121.604635843060 37 18385.3 17915.8115799213 469.488420078723 38 20739.3 20471.8003007002 267.499699299790 39 22268.3 22477.3818901396 -209.081890139602 40 21569 21425.0837019474 143.916298052601 41 17514.8 18156.095712635 -641.295712634989 42 21124.7 21000.4673293782 124.232670621837 43 21251 21057.4308873723 193.569112627676 44 21393 21396.0133717319 -3.01337173191836 45 22145.2 22218.0731305661 -72.8731305661319 46 20310.5 20140.9207398697 169.579260130271 47 23466.9 23874.2640968154 -407.364096815432 48 21264.6 21162.657231315 101.942768684999 49 18388.1 18287.1041269377 100.995873062250 50 22635.4 22307.5308240925 327.869175907459 51 22014.3 22112.1473624849 -97.8473624848649 52 18422.7 18867.604105525 -444.904105524992 53 16120.2 15787.1338283483 333.066171651701 54 16037.7 15985.8212977947 51.8787022052776 55 16410.7 16223.413060148 187.286939852004 56 17749.8 17827.5348774627 -77.7348774627317 57 16349.8 16496.7971064123 -146.997106412303 58 15662.3 15791.7962129681 -129.496212968053 59 17782.3 18337.9762681604 -555.676268160418 60 16398.9 16540.3065929920 -141.406592991954 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.577648103377316 0.844703793245369 0.422351896622684 18 0.484604086218607 0.969208172437215 0.515395913781393 19 0.394713425096026 0.789426850192053 0.605286574903974 20 0.321130581902949 0.642261163805897 0.678869418097051 21 0.337374739871809 0.674749479743618 0.662625260128191 22 0.569022744267067 0.861954511465866 0.430977255732933 23 0.857910479263068 0.284179041473865 0.142089520736932 24 0.850217006313828 0.299565987372344 0.149782993686172 25 0.900313185151612 0.199373629696776 0.0996868148483878 26 0.936020770793298 0.127958458413403 0.0639792292067016 27 0.915226464322405 0.169547071355190 0.0847735356775951 28 0.879227004989614 0.241545990020773 0.120772995010386 29 0.869943916034871 0.260112167930257 0.130056083965129 30 0.915404878574226 0.169190242851547 0.0845951214257737 31 0.895400966836576 0.209198066326848 0.104599033163424 32 0.840890282342922 0.318219435314155 0.159109717657078 33 0.768565606517241 0.462868786965517 0.231434393482758 34 0.701496506840792 0.597006986318416 0.298503493159208 35 0.85874733779577 0.282505324408458 0.141252662204229 36 0.806516364606116 0.386967270787768 0.193483635393884 37 0.80809268992176 0.383814620156479 0.191907310078239 38 0.731860725370066 0.536278549259869 0.268139274629934 39 0.629834921755365 0.74033015648927 0.370165078244635 40 0.897978497010546 0.204043005978908 0.102021502989454 41 0.998936013630395 0.00212797273920960 0.00106398636960480 42 0.995070508583137 0.00985898283372655 0.00492949141686328 43 0.987532943383717 0.0249341132325664 0.0124670566162832 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.0740740740740741 NOK 5% type I error level 3 0.111111111111111 NOK 10% type I error level 3 0.111111111111111 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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