*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: Sun, 13 Dec 2009 06:23:46 -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/13/t1260710680wouxo6a4s4vqjum.htm/, Retrieved Sun, 13 Dec 2009 14:24:54 +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/13/t1260710680wouxo6a4s4vqjum.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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507 104.5 501 517 519 569 87.4 507 510 517 580 89.9 569 509 510 578 109.8 580 501 509 565 111.7 578 507 501 547 98.6 565 569 507 555 96.9 547 580 569 562 95.1 555 578 580 561 97 562 565 578 555 112.7 561 547 565 544 102.9 555 555 547 537 97.4 544 562 555 543 111.4 537 561 562 594 87.4 543 555 561 611 96.8 594 544 555 613 114.1 611 537 544 611 110.3 613 543 537 594 103.9 611 594 543 595 101.6 594 611 594 591 94.6 595 613 611 589 95.9 591 611 613 584 104.7 589 594 611 573 102.8 584 595 594 567 98.1 573 591 595 569 113.9 567 589 591 621 80.9 569 584 589 629 95.7 621 573 584 628 113.2 629 567 573 612 105.9 628 569 567 595 108.8 612 621 569 597 102.3 595 629 621 593 99 597 628 629 590 100.7 593 612 628 580 115.5 590 595 612 574 100.7 580 597 595 573 109.9 574 593 597 573 114.6 573 590 593 620 85.4 573 580 590 626 100.5 620 574 580 620 114.8 626 573 574 588 116.5 620 573 573 566 112.9 588 620 573 557 102 566 626 620 561 106 557 620 626 549 105.3 561 588 620 532 118.8 549 etc...

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 Y[t] = + 239.710507892753 -1.50323568329146X[t] + 0.913782838019183`Yt-1`[t] -0.311051463965936`Yt-4`[t] + 0.253189547911919`Yt-5`[t] -0.0368144501848631t + 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) 239.710507892753 32.721781 7.3257 0 0 X -1.50323568329146 0.187441 -8.0198 0 0 `Yt-1` 0.913782838019183 0.052815 17.3017 0 0 `Yt-4` -0.311051463965936 0.086816 -3.5829 0.000675 0.000338 `Yt-5` 0.253189547911919 0.082149 3.0821 0.003084 0.001542 t -0.0368144501848631 0.096896 -0.3799 0.705311 0.352655 Multiple Linear Regression - Regression Statistics Multiple R 0.955223117147497 R-squared 0.912451203532981 Adjusted R-squared 0.905275072675029 F-TEST (value) 127.15085909029 F-TEST (DF numerator) 5 F-TEST (DF denominator) 61 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 12.4354714485818 Sum Squared Residuals 9433.09795905813 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 507 510.98253488212 -3.98253488211976 2 569 543.804728796271 25.1952712037293 3 580 595.203085723629 -15.2030857236291 4 578 577.538714557971 0.461285442029296 5 565 568.926361466403 -3.92636146640275 6 547 558.93670409467 -11.9367040946702 7 555 557.283485088649 -2.28348508864914 8 562 570.669945527505 -8.66994552750537 9 561 577.710753080934 -16.7107530809343 10 555 555.466817793586 -0.466817793586271 11 544 557.633192437401 -13.6331924374006 12 537 555.660719162641 -18.6607191626415 13 543 530.265503579591 12.7344964204087 14 594 573.4021617924 20.5978382075997 15 611 607.740285474408 3.25971452559218 16 613 596.624077170337 16.3759228296627 17 611 600.48848837352 10.5115116264807 18 594 593.90032924557 0.0996707544298384 19 595 589.411440676717 5.58855932328347 20 591 604.493178234162 -13.4931782341618 21 589 599.975508067377 -10.9755080673770 22 584 589.664149719786 -5.66414971978602 23 573 583.29929509929 -10.2992950992905 24 567 581.77347254614 -14.7734725461401 25 569 552.112182008119 16.8878179918807 26 621 604.558589006597 16.4414109934032 27 629 631.946212384762 -2.94621238476152 28 628 611.994259937894 16.0057400621059 29 612 619.876042922314 -7.87604292231431 30 595 585.191022551872 9.8089774481275 31 597 590.068376576448 6.9316234235517 32 593 599.156373404425 -6.15637340442491 33 590 597.632560816111 -7.63256081611087 34 580 573.843351859985 6.15664814001493 35 574 581.990271899887 -7.99027189988747 36 573 564.391577086994 8.60842291300633 37 573 556.29616828757 16.7038317124301 38 620 602.504781785419 17.4952182145808 39 626 622.051315209111 3.94868479088863 40 620 604.792841692468 15.2071583075318 41 588 596.464640004661 -8.4646400046608 42 566 557.979004391312 8.02099560868765 43 557 564.257836420647 -7.25783642064696 44 561 553.369479766391 7.63052023360927 45 549 566.474571206025 -17.4745712060251 46 532 533.919747649244 -1.91974764924447 47 526 534.669011252166 -8.66901125216623 48 511 520.816233800263 -9.81623380026258 49 499 499.942490641026 -0.942490641026338 50 555 528.319803824388 26.6801961756118 51 565 559.42905727806 5.5709427219395 52 542 559.199849708766 -17.1998497087659 53 527 523.198771068467 3.8012289315332 54 510 502.677502208911 7.32249779108894 55 514 518.167514143585 -4.16751414358458 56 517 515.387288384594 1.61271161540645 57 508 513.777439871069 -5.77743987106908 58 493 511.516318597328 -18.5163185973281 59 490 480.950065781803 9.04993421819686 60 469 490.578039220301 -21.5780392203006 61 478 464.68881434476 13.3111856552399 62 528 505.17750156253 22.8224984374703 63 534 542.252844590015 -8.25284459001547 64 518 527.91623265154 -9.9162326515398 65 506 506.796008362825 -0.796008362824866 66 502 507.022674226971 -5.02267422697108 67 516 521.790399021296 -5.79039902129627 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.712108896972123 0.575782206055753 0.287891103027877 10 0.561425591631916 0.877148816736167 0.438574408368084 11 0.590602473296887 0.818795053406226 0.409397526703113 12 0.601095590905031 0.797808818189939 0.398904409094969 13 0.666369338388266 0.667261323223467 0.333630661611734 14 0.739050636915397 0.521898726169207 0.260949363084603 15 0.656772457859618 0.686455084280764 0.343227542140382 16 0.690323503057309 0.619352993885382 0.309676496942691 17 0.615209534369939 0.769580931260122 0.384790465630061 18 0.539564108553364 0.920871782893273 0.460435891446636 19 0.488022743577816 0.976045487155632 0.511977256422184 20 0.490096607561469 0.980193215122938 0.509903392438531 21 0.474551951160005 0.94910390232001 0.525448048839995 22 0.438970063053194 0.877940126106389 0.561029936946806 23 0.520611350603148 0.958777298793705 0.479388649396852 24 0.733693551435243 0.532612897129515 0.266306448564757 25 0.691739273074455 0.61652145385109 0.308260726925545 26 0.631746815789238 0.736506368421524 0.368253184210762 27 0.618250031472568 0.763499937054863 0.381749968527432 28 0.573159786577676 0.853680426844648 0.426840213422324 29 0.664957378660158 0.670085242679685 0.335042621339842 30 0.603382589971294 0.793234820057413 0.396617410028706 31 0.533533362882448 0.932933274235104 0.466466637117552 32 0.507259334688283 0.985481330623433 0.492740665311717 33 0.522846499212314 0.954307001575372 0.477153500787686 34 0.455052324761254 0.910104649522507 0.544947675238746 35 0.609404229056974 0.781191541886052 0.390595770943026 36 0.536946672106336 0.926106655787328 0.463053327893664 37 0.487543997463489 0.975087994926977 0.512456002536511 38 0.414657338878849 0.829314677757699 0.585342661121151 39 0.35590251720789 0.71180503441578 0.64409748279211 40 0.438786850798575 0.87757370159715 0.561213149201425 41 0.475733160609389 0.951466321218777 0.524266839390611 42 0.474127301456535 0.94825460291307 0.525872698543465 43 0.440848425928476 0.881696851856953 0.559151574071524 44 0.544885638940199 0.910228722119602 0.455114361059801 45 0.590890964185492 0.818218071629017 0.409109035814508 46 0.594264481990312 0.811471036019375 0.405735518009688 47 0.587583960036525 0.82483207992695 0.412416039963475 48 0.597990766522693 0.804018466954615 0.402009233477307 49 0.520797916219647 0.958404167560707 0.479202083780354 50 0.504283636689072 0.991432726621856 0.495716363310928 51 0.471116535816456 0.942233071632911 0.528883464183544 52 0.460188054665737 0.920376109331475 0.539811945334263 53 0.381525892599445 0.76305178519889 0.618474107400555 54 0.379351644449645 0.758703288899289 0.620648355550355 55 0.293481755092537 0.586963510185075 0.706518244907463 56 0.304691926314094 0.609383852628189 0.695308073685906 57 0.392469866129472 0.784939732258944 0.607530133870528 58 0.273537991619287 0.547075983238575 0.726462008380713 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 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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