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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 21 Dec 2009 06:05:51 -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/Dec/21/t1261401006a0zshta9n2img1c.htm/, Retrieved Mon, 21 Dec 2009 14:10:18 +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/Dec/21/t1261401006a0zshta9n2img1c.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:

Dataseries X:

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581 103.5 597 104.6 587 118.6 536 106.3 524 110.7 537 121.6 536 107 533 107.6 528 125.6 516 113.5 502 129.2 506 130.9 518 104.7 534 115.2 528 124.5 478 112.3 469 127.5 490 120.6 493 117.5 508 117.7 517 120.4 514 125 510 131.6 527 121.1 542 114.2 565 112.1 555 127 499 116.8 511 112 526 129.7 532 113.6 549 115.7 561 119.5 557 125.8 566 129.6 588 128 620 112.8 626 101.6 620 123.9 573 118.8 573 109.1 574 130.6 580 112.4 590 111 593 116.2 597 119.8 595 117.2 612 127.3 628 107.7 629 97.5 621 120.1 569 110.6 567 111.3 573 119.8 584 105.5 589 108.7 591 128.7 595 119.5 594 121.1 611 128.4

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 Prod[t] = + 799.47445598441 -2.26997272111808Werkl[t] -15.4298983271748M1[t] -10.0415966195063M2[t] + 18.0761867894057M3[t] -57.1149074568893M4[t] -58.290902316463M5[t] -25.2285475961726M6[t] -51.937549094269M7[t] -42.6129379524887M8[t] -17.4585723206456M9[t] -24.3548984374369M10[t] -16.9687985934948M11[t] + 1.60916321607065t + 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) 799.47445598441 84.595798 9.4505 0 0 Werkl -2.26997272111808 0.653062 -3.4759 0.001122 0.000561 M1 -15.4298983271748 19.689126 -0.7837 0.437247 0.218623 M2 -10.0415966195063 20.6679 -0.4859 0.629377 0.314688 M3 18.0761867894057 15.609322 1.158 0.252826 0.126413 M4 -57.1149074568893 17.959417 -3.1802 0.002634 0.001317 M5 -58.290902316463 17.552113 -3.321 0.001763 0.000881 M6 -25.2285475961726 15.385714 -1.6397 0.107882 0.053941 M7 -51.937549094269 18.52223 -2.8041 0.007367 0.003683 M8 -42.6129379524887 18.163789 -2.346 0.023339 0.01167 M9 -17.4585723206456 15.609036 -1.1185 0.269164 0.134582 M10 -24.3548984374369 15.813885 -1.5401 0.130389 0.065194 M11 -16.9687985934948 15.263641 -1.1117 0.272038 0.136019 t 1.60916321607065 0.184038 8.7437 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.860766387238483 R-squared 0.74091877339959 Adjusted R-squared 0.667700165882082 F-TEST (value) 10.1192688378078 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.47951073614649e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 24.0872167020129 Sum Squared Residuals 26688.9243886876 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 581 550.711544237585 30.2884557624147 2 597 555.212039168093 41.7879608319066 3 587 553.159367697423 33.8406323025773 4 536 507.498101136951 28.5018988630492 5 524 497.943389520528 26.0566104794718 6 537 507.872204796702 29.1277952032979 7 536 515.913968243 20.0860317569997 8 533 525.48575896818 7.51424103181953 9 528 511.389778835969 16.6102211640312 10 516 533.569285860777 -17.5692858607769 11 502 506.925977199236 -4.92597719923579 12 506 521.6449853829 -15.6449853829003 13 518 567.29753556509 -49.2975355650901 14 534 550.460286917089 -16.4602869170893 15 528 559.076487235674 -31.0764872356738 16 478 513.18822340309 -35.1882234030901 17 469 479.117806398592 -10.1178063985922 18 490 529.452136110668 -39.452136110668 19 493 511.389213264108 -18.3892132641082 20 508 521.868993077736 -13.8689930777356 21 517 542.50359557863 -25.5035955786305 22 514 526.774558160767 -12.7745581607668 23 510 520.7880012614 -10.7880012614002 24 527 563.200676642706 -36.2006766427055 25 542 565.042753307316 -23.0427533073161 26 565 576.807160945403 -11.8071609454033 27 555 572.711514025726 -17.7115140257264 28 499 522.283304750906 -23.2833047509065 29 511 533.61234216877 -22.6123421687703 30 526 528.105342941341 -2.10534294134123 31 532 539.552065469317 -7.55206546931661 32 549 545.71889711282 3.2811028871804 33 561 563.856529620485 -2.85652962048465 34 557 544.26853857672 12.7314614232799 35 566 544.637905296484 21.3620947035158 36 588 566.847823459838 21.1521765401615 37 620 587.530673709729 32.4693262902708 38 626 619.951833109991 6.04816689000898 39 620 599.05838805404 20.9416119459597 40 573 537.053317901518 35.9466820984818 41 573 559.50522165286 13.4947783471394 42 574 545.372326085183 28.6276739148172 43 580 561.585991327506 18.4140086724939 44 590 575.697727494922 14.3022725050776 45 593 590.657398193022 2.34260180697787 46 597 577.198333496276 19.8016665037235 47 595 592.095525631196 2.90447436880373 48 612 587.746762957469 24.2532370425310 49 628 618.417493180279 9.58250681972072 50 629 648.568679859423 -19.568679859423 51 621 626.994242987137 -5.99424298713684 52 569 574.977052807534 -5.97705280753435 53 567 573.821240259249 -6.82124025924866 54 573 589.197990066106 -16.1979900661059 55 584 596.558761696069 -12.5587616960688 56 589 600.228623346342 -11.2286233463419 57 591 581.592697771894 9.40730222810607 58 595 597.18928390546 -2.18928390545971 59 594 602.552590611684 -8.55259061168358 60 611 604.559751557087 6.4402484429131 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00276615110530828 0.00553230221061656 0.997233848894692 18 0.0088351617559298 0.0176703235118596 0.99116483824407 19 0.0113262339583846 0.0226524679167692 0.988673766041615 20 0.0626069488962769 0.125213897792554 0.937393051103723 21 0.154997669756010 0.309995339512020 0.84500233024399 22 0.382506820972940 0.765013641945879 0.61749317902706 23 0.550748673972011 0.898502652055979 0.449251326027989 24 0.625983248459461 0.748033503081078 0.374016751540539 25 0.831996172803434 0.336007654393133 0.168003827196566 26 0.84337821870609 0.313243562587821 0.156621781293910 27 0.883752520257794 0.232494959484413 0.116247479742206 28 0.950361350794665 0.0992772984106707 0.0496386492053354 29 0.972067781698 0.0558644366039987 0.0279322183019994 30 0.98721884875114 0.0255623024977191 0.0127811512488595 31 0.995213219082117 0.00957356183576684 0.00478678091788342 32 0.998007392191113 0.00398521561777478 0.00199260780888739 33 0.99874105383356 0.00251789233288183 0.00125894616644092 34 0.999921531227765 0.000156937544470867 7.84687722354333e-05 35 0.999990069420069 1.98611598630301e-05 9.93057993151506e-06 36 0.999999995338942 9.32211631474562e-09 4.66105815737281e-09 37 0.99999999860192 2.79616176650075e-09 1.39808088325037e-09 38 0.999999991341513 1.73169750771443e-08 8.65848753857217e-09 39 0.999999915551844 1.68896312635276e-07 8.44481563176382e-08 40 0.999999593326704 8.13346592182642e-07 4.06673296091321e-07 41 0.999999005113444 1.98977311308084e-06 9.94886556540421e-07 42 0.999990699265017 1.86014699657421e-05 9.30073498287107e-06 43 0.999996244643348 7.51071330340949e-06 3.75535665170474e-06 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.518518518518518 NOK 5% type I error level 17 0.62962962962963 NOK 10% type I error level 19 0.703703703703704 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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