*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: Fri, 20 Nov 2009 07:01:59 -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/20/t125872576935ckqfpspxu8l5k.htm/, Retrieved Fri, 20 Nov 2009 15:03:01 +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/20/t125872576935ckqfpspxu8l5k.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:

shwws7

Dataseries X:

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6539 2605 6699 2682 6962 2755 6981 2760 7024 2735 6940 2659 6774 2654 6671 2670 6965 2785 6969 2845 6822 2723 6878 2746 6691 2767 6837 2940 7018 2977 7167 2993 7076 2892 7171 2824 7093 2771 6971 2686 7142 2738 7047 2723 6999 2731 6650 2632 6475 2606 6437 2605 6639 2646 6422 2627 6272 2535 6232 2456 6003 2404 5673 2319 6050 2519 5977 2504 5796 2382 5752 2394 5609 2381 5839 2501 6069 2532 6006 2515 5809 2429 5797 2389 5502 2261 5568 2272 5864 2439 5764 2373 5615 2327 5615 2364 5681 2388 5915 2553 6334 2663 6494 2694 6620 2679 6578 2611 6495 2580 6538 2627 6737 2732 6651 2707 6530 2633 6563 2683

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 Voeding-Mannen[t] = -405.961252705834 + 2.67275759582622`Landbouw-Mannen`[t] -101.428995792543M1[t] -236.177988374742M2[t] -128.965513318953M3[t] -123.616818973557M4[t] -2.59336570780475M5[t] + 162.044705787931M6[t] + 139.940583095422M7[t] + 106.359047587325M8[t] + 36.4821454927739M9[t] + 3.39130681389371M10[t] + 68.7931662887606M11[t] -4.30151865203991t + 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) -405.961252705834 396.851738 -1.023 0.311679 0.15584 `Landbouw-Mannen` 2.67275759582622 0.141946 18.8294 0 0 M1 -101.428995792543 96.857076 -1.0472 0.300478 0.150239 M2 -236.177988374742 96.428293 -2.4493 0.018183 0.009092 M3 -128.965513318953 97.289058 -1.3256 0.191521 0.095761 M4 -123.616818973557 97.359274 -1.2697 0.210578 0.105289 M5 -2.59336570780475 96.208323 -0.027 0.978612 0.489306 M6 162.044705787931 95.792379 1.6916 0.097483 0.048741 M7 139.940583095422 96.022357 1.4574 0.151806 0.075903 M8 106.359047587325 96.144766 1.1062 0.274375 0.137188 M9 36.4821454927739 96.035892 0.3799 0.705783 0.352891 M10 3.39130681389371 95.908536 0.0354 0.971946 0.485973 M11 68.7931662887606 95.557346 0.7199 0.47522 0.23761 t -4.30151865203991 1.341897 -3.2056 0.002452 0.001226 Multiple Linear Regression - Regression Statistics Multiple R 0.965428192773583 R-squared 0.932051595402067 Adjusted R-squared 0.912848785406999 F-TEST (value) 48.5372503108371 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 151.063517683038 Sum Squared Residuals 1049728.57323958 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6539 6450.8417699769 88.1582300230973 2 6699 6517.59359362127 181.406406378726 3 6962 6815.61585452034 146.384145479663 4 6981 6830.02681819282 150.973181807175 5 7024 6879.92981291088 144.070187089118 6 6940 6837.13678847178 102.863211528215 7 6774 6797.3673591481 -23.3673591481044 8 6671 6802.24842652119 -131.248426521188 9 6965 7035.43712929461 -70.4371292946119 10 6969 7158.41022771327 -189.410227713265 11 6822 6893.43414184529 -71.434141845293 12 6878 6881.8128816085 -3.81288160849564 13 6691 6832.21027667626 -141.210276676263 14 6837 7155.54682951996 -318.546829519960 15 7018 7357.34981696928 -339.349816969279 16 7167 7401.16111419586 -234.161114195855 17 7076 7247.93453163112 -171.934531631120 18 7171 7226.52356795863 -55.5235679586325 19 7093 7058.46177403529 34.5382259647064 20 6971 6793.39432422993 177.605675770072 21 7142 6858.1992984663 283.800701533700 22 7047 6780.71557719799 266.284422802013 23 6999 6863.19797878742 135.802021212576 24 6650 6525.50029185983 124.499708140173 25 6475 6350.27807992376 124.721920076238 26 6437 6208.5548110937 228.445188906302 27 6639 6421.04882892632 217.951171073679 28 6422 6371.31361029898 50.6863897010209 29 6272 6242.14184609668 29.8581539033204 30 6232 6191.33054887010 40.669451129896 31 6003 6025.94151254259 -22.9415125425911 32 5673 5760.87406273723 -87.8740627372258 33 6050 6221.24716115588 -171.247161155879 34 5977 6143.76343988757 -166.763439887566 35 5796 5878.78735401959 -82.7873540195935 36 5752 5837.76576022871 -85.7657602287076 37 5609 5697.28939703838 -88.2893970383836 38 5839 5878.96979730329 -39.9697973032916 39 6069 6064.73623917765 4.26376082234696 40 6006 6020.34653574196 -14.3465357419633 41 5809 5907.21131711462 -98.2113171146212 42 5797 5960.63756612527 -163.637566125268 43 5502 5592.11895251496 -90.1189525149625 44 5568 5583.63623190891 -15.6362319089144 45 5864 5955.8083296653 -91.8083296653023 46 5764 5742.01397100985 21.9860289901484 47 5615 5680.16746242467 -65.1674624246724 48 5615 5705.96480852944 -90.964808529442 49 5681 5664.38047638469 16.6195236153118 50 5915 5966.33496846178 -51.3349684617762 51 6334 6363.24926040641 -29.2492604064092 52 6494 6447.15192157038 46.848078429622 53 6620 6523.7824922467 96.2175077533024 54 6578 6502.37152857421 75.6284714257895 55 6495 6393.11040175905 101.889598240952 56 6538 6480.84695460274 57.1530453972558 57 6737 6687.3080814179 49.6919185820936 58 6651 6583.09678419133 67.9032158086694 59 6530 6446.41306292302 83.5869370769827 60 6563 6506.95625777353 56.0437422264723 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.120839214481655 0.241678428963309 0.879160785518345 18 0.187282969480263 0.374565938960526 0.812717030519737 19 0.314683493715625 0.62936698743125 0.685316506284375 20 0.201197642855547 0.402395285711095 0.798802357144452 21 0.28541301100098 0.57082602200196 0.71458698899902 22 0.410261120364382 0.820522240728763 0.589738879635618 23 0.306533658255753 0.613067316511507 0.693466341744247 24 0.814736806930472 0.370526386139056 0.185263193069528 25 0.875862423801736 0.248275152396527 0.124137576198264 26 0.967114155259604 0.0657716894807916 0.0328858447403958 27 0.993482390906212 0.0130352181875763 0.00651760909378813 28 0.998509703835144 0.00298059232971279 0.00149029616485639 29 0.999519497318528 0.000961005362944784 0.000480502681472392 30 0.999945575879126 0.000108848241747817 5.44241208739086e-05 31 0.99995903008453 8.19398309385394e-05 4.09699154692697e-05 32 0.99995793919468 8.41216106393557e-05 4.20608053196779e-05 33 0.999951220123937 9.75597521257433e-05 4.87798760628717e-05 34 0.999976800844216 4.63983115672947e-05 2.31991557836474e-05 35 0.9999316253681 0.000136749263802048 6.83746319010241e-05 36 0.999798458373012 0.000403083253975725 0.000201541626987862 37 0.999583254545454 0.000833490909091566 0.000416745454545783 38 0.998688709438622 0.00262258112275645 0.00131129056137822 39 0.999153141440724 0.00169371711855127 0.000846858559275634 40 0.999917000536292 0.000165998927415436 8.29994637077178e-05 41 0.999490593428929 0.00101881314214256 0.000509406571071279 42 0.997273248063142 0.00545350387371527 0.00272675193685764 43 0.995631868676239 0.00873626264752268 0.00436813132376134 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 16 0.592592592592593 NOK 5% type I error level 17 0.62962962962963 NOK 10% type I error level 18 0.666666666666667 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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