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*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: Mon, 01 Dec 2008 12:02:38 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228158454puohtbwv6llgsjy.htm/, Retrieved Mon, 01 Dec 2008 19:07:34 +0000

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/2008/Dec/01/t1228158454puohtbwv6llgsjy.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

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User-defined keywords:

blog

Dataseries X:

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564260 0 491117 0 621769 0 642302 0 611278 0 846462 0 607912 0 547550 0 715309 0 695634 0 779700 0 1303196 0 540356 0 532917 0 680054 0 663715 0 711397 0 801442 0 589042 0 611648 0 852471 0 703403 0 701913 0 1277262 0 552924 0 624650 0 785161 0 683755 0 637168 0 766338 1 590239 1 724734 1 797947 1 734796 1 741821 1 1352663 1 586784 0 619788 0 817280 0 670827 0 741638 0 791051 0 614362 0 684702 0 815746 0 740751 0 787766 0 1403677 0 704144 0 609141 0 770951 0 664689 0 719533 0 799724 0 683953 0 723532 0 705441 0 711204 0 792322 0 1360777 0

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation x[t] = + 1282020.1 + 6650.00000000011y[t] -731329.902777778M1[t] -747061.038888889M2[t] -589100.775M3[t] -660646.311111111M4[t] -643061.247222222M5[t] -529150.783333334M6[t] -714612.719444445M7[t] -674841.255555555M8[t] -557451.791666667M9[t] -619237.127777778M10[t] -577250.463888889M11[t] + 1560.13611111111t + 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) 1282020.1 24394.175515 52.5544 0 0 y 6650.00000000011 19406.964022 0.3427 0.733415 0.366707 M1 -731329.902777778 29554.792572 -24.7449 0 0 M2 -747061.038888889 29511.397559 -25.3143 0 0 M3 -589100.775 29472.080347 -19.9884 0 0 M4 -660646.311111111 29436.857275 -22.4428 0 0 M5 -643061.247222222 29405.743057 -21.8686 0 0 M6 -529150.783333334 29121.225684 -18.1706 0 0 M7 -714612.719444445 29098.164345 -24.5587 0 0 M8 -674841.255555555 29079.282373 -23.2069 0 0 M9 -557451.791666667 29064.587914 -19.1798 0 0 M10 -619237.127777778 29054.087322 -21.3133 0 0 M11 -577250.463888889 29047.785145 -19.8724 0 0 t 1560.13611111111 349.365282 4.4656 5.1e-05 2.6e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.979289983408107 R-squared 0.95900887160345 Adjusted R-squared 0.94742442227399 F-TEST (value) 82.7841569615778 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 45925.2590011078 Sum Squared Residuals 97019953058.6665 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 564260 552250.333333334 12009.6666666659 2 491117 538079.333333333 -46962.3333333332 3 621769 697599.733333333 -75830.7333333333 4 642302 627614.333333334 14687.6666666665 5 611278 646759.533333334 -35481.5333333336 6 846462 762230.133333334 84231.8666666665 7 607912 578328.333333333 29583.6666666666 8 547550 619659.933333333 -72109.9333333329 9 715309 738609.533333333 -23300.5333333332 10 695634 678384.333333333 17249.6666666667 11 779700 721931.133333333 57768.8666666666 12 1303196 1300741.73333333 2454.26666666682 13 540356 570971.966666666 -30615.9666666664 14 532917 556800.966666667 -23883.9666666667 15 680054 716321.366666667 -36267.3666666667 16 663715 646335.966666667 17379.0333333334 17 711397 665481.166666667 45915.8333333334 18 801442 780951.766666667 20490.2333333334 19 589042 597049.966666667 -8007.96666666659 20 611648 638381.566666667 -26733.5666666667 21 852471 757331.166666667 95139.8333333334 22 703403 697105.966666667 6297.03333333335 23 701913 740652.766666667 -38739.7666666666 24 1277262 1319463.36666667 -42201.3666666667 25 552924 589693.6 -36769.5999999998 26 624650 575522.6 49127.4 27 785161 735043 50118 28 683755 665057.6 18697.4000000001 29 637168 684202.8 -47034.7999999999 30 766338 806323.4 -39985.4 31 590239 622421.6 -32182.6 32 724734 663753.2 60980.7999999999 33 797947 782702.8 15244.1999999999 34 734796 722477.6 12318.4000000000 35 741821 766024.4 -24203.3999999999 36 1352663 1344835 7828.00000000005 37 586784 608415.233333333 -21631.2333333332 38 619788 594244.233333333 25543.7666666666 39 817280 753764.633333333 63515.3666666666 40 670827 683779.233333333 -12952.2333333333 41 741638 702924.433333333 38713.5666666667 42 791051 818395.033333333 -27344.0333333333 43 614362 634493.233333333 -20131.2333333333 44 684702 675824.833333333 8877.16666666656 45 815746 794774.433333333 20971.5666666667 46 740751 734549.233333333 6201.76666666665 47 787766 778096.033333333 9669.96666666667 48 1403677 1356906.63333333 46770.3666666665 49 704144 627136.866666666 77007.1333333335 50 609141 612965.866666667 -3824.86666666673 51 770951 772486.266666667 -1535.26666666672 52 664689 702500.866666667 -37811.8666666666 53 719533 721646.066666667 -2113.06666666663 54 799724 837116.666666667 -37392.6666666666 55 683953 653214.866666667 30738.1333333333 56 723532 694546.466666667 28985.5333333332 57 705441 813496.066666667 -108055.066666667 58 711204 753270.866666667 -42066.8666666667 59 792322 796817.666666667 -4495.66666666670 60 1360777 1375628.26666667 -14851.2666666668 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.47526606422472 0.95053212844944 0.52473393577528 18 0.564426375620349 0.871147248759302 0.435573624379651 19 0.468657555289822 0.937315110579643 0.531342444710178 20 0.425140978400744 0.850281956801488 0.574859021599256 21 0.73684702016327 0.52630595967346 0.26315297983673 22 0.653375634121147 0.693248731757707 0.346624365878853 23 0.762619824179694 0.474760351640612 0.237380175820306 24 0.75337609000017 0.49324781999966 0.24662390999983 25 0.760467834014632 0.479064331970735 0.239532165985368 26 0.79008761544124 0.419824769117518 0.209912384558759 27 0.815084944010922 0.369830111978155 0.184915055989078 28 0.75579036463901 0.48841927072198 0.24420963536099 29 0.839892626165206 0.320214747669587 0.160107373834794 30 0.773609656916943 0.452780686166115 0.226390343083058 31 0.753949536906564 0.492100926186873 0.246050463093436 32 0.862458462621098 0.275083074757804 0.137541537378902 33 0.838959409788152 0.322081180423696 0.161040590211848 34 0.79332982395305 0.4133403520939 0.20667017604695 35 0.714653047171019 0.570693905657962 0.285346952828981 36 0.625819569506 0.748360860988 0.374180430494 37 0.82610251765132 0.347794964697361 0.173897482348681 38 0.738673737224489 0.522652525551022 0.261326262775511 39 0.687583642223464 0.624832715553073 0.312416357776536 40 0.582712651110714 0.834574697778571 0.417287348889286 41 0.452870356358376 0.905740712716753 0.547129643641624 42 0.350741990482314 0.701483980964628 0.649258009517686 43 0.42182460863766 0.84364921727532 0.57817539136234 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

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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