*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: Sat, 12 Dec 2009 14:02:49 -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/12/t12606525500g7bm0u8of4tqci.htm/, Retrieved Sat, 12 Dec 2009 22:16:02 +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/12/t12606525500g7bm0u8of4tqci.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:

» Textbox « » Textfile « » CSV «

577992 0 565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 1 610763 1 612613 1 611324 1 594167 1 595454 1 590865 1 589379 1 584428 1 573100 1 567456 1 569028 1 620735 1 628884 1 628232 1 612117 1 595404 1 597141 1 593408 1 590072 1 579799 1 574205 1 572775 1 572942 1 619567 1 625809 1 619916 1 587625 1 565742 1 557274 1 560576 1 548854 1 531673 1 525919 1 511038 1 498662 1 555362 1 564591 1 541657 1 527070 1 509846 1 514258 1 516922 1 507561 1 492622 1 490243 1 469357 1 477580 1 528379 1 533590 1 517945 1 506174 1 501866 1 516141 1 528222 1 532638 1 536322 1 536535 1 523597 1 536214 1 586570 1 596594 1 580523 1

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 Y[t] = + 604335.544025157 + 52211.4327044027X[t] -10737.0504941598M1[t] -31415.9620245583M2[t] -45812.6252770291M3[t] -40860.6218628332M4[t] -36479.4517819706M5[t] -38801.9483677747M6[t] -45494.7782869121M7[t] -50086.4415393831M8[t] -59034.9381251872M9[t] -54820.2680443246M10[t] -10852.1700808625M11[t] -1504.17008086253t + 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) 604335.544025157 13504.06558 44.7521 0 0 X 52211.4327044027 10825.367641 4.8231 1e-05 5e-06 M1 -10737.0504941598 14061.215256 -0.7636 0.448152 0.224076 M2 -31415.9620245583 14623.044119 -2.1484 0.035799 0.017899 M3 -45812.6252770291 14615.876218 -3.1344 0.002682 0.001341 M4 -40860.6218628332 14610.815998 -2.7966 0.006961 0.003481 M5 -36479.4517819706 14607.86565 -2.4972 0.015326 0.007663 M6 -38801.9483677747 14607.026451 -2.6564 0.010143 0.005071 M7 -45494.7782869121 14608.298766 -3.1143 0.002844 0.001422 M8 -50086.4415393831 14611.682042 -3.4278 0.001115 0.000557 M9 -59034.9381251872 14617.174815 -4.0387 0.000157 7.9e-05 M10 -54820.2680443246 14624.774708 -3.7485 0.000407 0.000204 M11 -10852.1700808625 14535.789514 -0.7466 0.45828 0.22914 t -1504.17008086253 175.624874 -8.5647 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.815618618735924 R-squared 0.665233731228697 Adjusted R-squared 0.591471672007901 F-TEST (value) 9.0186437072943 F-TEST (DF numerator) 13 F-TEST (DF denominator) 59 p-value 8.28744184389052e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 25174.8882440813 Sum Squared Residuals 37392724888.0169 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 577992 592094.323450134 -14102.3234501342 2 565464 569911.241838874 -4447.24183887437 3 547344 554010.408505541 -6666.40850554064 4 554788 557458.241838874 -2670.24183887389 5 562325 560335.241838874 1989.75816112615 6 560854 556508.575172207 4345.42482779281 7 555332 548311.575172207 7020.42482779284 8 543599 542215.741838874 1383.25816112601 9 536662 531763.075172207 4898.92482779258 10 542722 534473.575172207 8248.42482779282 11 593530 629148.93575921 -35618.9357592094 12 610763 638496.935759209 -27733.9357592094 13 612613 626255.715184187 -13642.7151841870 14 611324 604072.633572926 7251.3664270741 15 594167 588171.800239593 5995.19976040731 16 595454 591619.633572926 3834.36642707397 17 590865 594496.633572926 -3631.63357292605 18 589379 590669.96690626 -1290.96690625937 19 584428 582472.966906259 1955.03309374061 20 573100 576377.133572926 -3277.13357292601 21 567456 565924.466906259 1531.53309374067 22 569028 568634.966906259 393.03309374062 23 620735 611098.894788859 9636.10521114107 24 628884 620446.894788859 8437.1052111411 25 628232 608205.674213837 20026.3257861634 26 612117 586022.592602576 26094.4073974245 27 595404 570121.759269242 25282.2407307577 28 597141 573569.592602576 23571.4073974244 29 593408 576446.592602576 16961.4073974244 30 590072 572619.925935909 17452.0740640910 31 579799 564422.925935909 15376.0740640910 32 574205 558327.092602576 15877.9073974244 33 572775 547874.425935909 24900.5740640911 34 572942 550584.925935909 22357.0740640910 35 619567 593048.853818509 26518.1461814915 36 625809 602396.853818509 23412.1461814915 37 619916 590155.633243486 29760.3667565138 38 587625 567972.551632225 19652.4483677749 39 565742 552071.718298892 13670.2817011081 40 557274 555519.551632225 1754.44836777478 41 560576 558396.551632225 2179.44836777476 42 548854 554569.884965559 -5715.88496555857 43 531673 546372.884965559 -14699.8849655586 44 525919 540277.051632225 -14358.0516322252 45 511038 529824.384965559 -18786.3849655585 46 498662 532534.884965559 -33872.8849655586 47 555362 574998.812848158 -19636.8128481581 48 564591 584346.812848158 -19755.8128481581 49 541657 572105.592273136 -30448.5922731358 50 527070 549922.510661875 -22852.5106618747 51 509846 534021.677328541 -24175.6773285415 52 514258 537469.510661875 -23211.5106618748 53 516922 540346.510661875 -23424.5106618748 54 507561 536519.843995208 -28958.8439952082 55 492622 528322.843995208 -35700.8439952082 56 490243 522227.010661875 -31984.0106618748 57 469357 511774.343995208 -42417.3439952081 58 477580 514484.843995208 -36904.8439952081 59 528379 556948.771877808 -28569.7718778077 60 533590 566296.771877808 -32706.7718778077 61 517945 554055.551302785 -36110.5513027854 62 506174 531872.469691524 -25698.4696915243 63 501866 515971.636358191 -14105.6363581911 64 516141 519419.469691524 -3278.46969152441 65 528222 522296.469691524 5925.53030847558 66 532638 518469.803024858 14168.1969751422 67 536322 510272.803024858 26049.1969751422 68 536535 504176.969691524 32358.0303084756 69 523597 493724.303024858 29872.6969751423 70 536214 496434.803024858 39779.1969751423 71 586570 538898.730907457 47671.2690925427 72 596594 548246.730907457 48347.2690925427 73 580523 536005.510332435 44517.4896675651 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0149479736485723 0.0298959472971445 0.985052026351428 18 0.00513693621613692 0.0102738724322738 0.994863063783863 19 0.00144391983866729 0.00288783967733458 0.998556080161333 20 0.000358412204707317 0.000716824409414634 0.999641587795293 21 7.46764115827677e-05 0.000149352823165535 0.999925323588417 22 2.16714531832214e-05 4.33429063664427e-05 0.999978328546817 23 3.69890578344136e-06 7.39781156688272e-06 0.999996301094217 24 8.56005445744122e-07 1.71201089148824e-06 0.999999143994554 25 1.89173715788026e-07 3.78347431576052e-07 0.999999810826284 26 1.33817885533315e-07 2.67635771066629e-07 0.999999866182114 27 4.48930169661696e-08 8.97860339323393e-08 0.999999955106983 28 1.73324390767128e-08 3.46648781534256e-08 0.99999998266756 29 1.13972219659738e-08 2.27944439319477e-08 0.999999988602778 30 7.25307987218253e-09 1.45061597443651e-08 0.99999999274692 31 8.11454723278488e-09 1.62290944655698e-08 0.999999991885453 32 2.75193190855175e-09 5.5038638171035e-09 0.999999997248068 33 8.62349769750184e-10 1.72469953950037e-09 0.99999999913765 34 3.45208927578017e-10 6.90417855156033e-10 0.999999999654791 35 1.17657425013385e-10 2.35314850026770e-10 0.999999999882343 36 4.65328715685841e-11 9.30657431371681e-11 0.999999999953467 37 5.77777599073358e-11 1.15555519814672e-10 0.999999999942222 38 9.47722661646543e-09 1.89544532329309e-08 0.999999990522773 39 4.06517749705112e-07 8.13035499410224e-07 0.99999959348225 40 1.72359442126052e-05 3.44718884252103e-05 0.999982764055787 41 0.000112283535831738 0.000224567071663476 0.999887716464168 42 0.000826027031570898 0.00165205406314180 0.99917397296843 43 0.00481973740923462 0.00963947481846924 0.995180262590765 44 0.0112779463897377 0.0225558927794755 0.988722053610262 45 0.0367445059560468 0.0734890119120937 0.963255494043953 46 0.082992583990747 0.165985167981494 0.917007416009253 47 0.093831908348193 0.187663816696386 0.906168091651807 48 0.126116743485449 0.252233486970897 0.873883256514551 49 0.207198727543939 0.414397455087877 0.792801272456061 50 0.430222459594451 0.860444919188902 0.569777540405549 51 0.649163189754325 0.70167362049135 0.350836810245675 52 0.829882268627089 0.340235462745823 0.170117731372911 53 0.952393829075837 0.0952123418483266 0.0476061709241633 54 0.99257685773841 0.0148462845231808 0.00742314226159041 55 0.991986515362186 0.0160269692756283 0.00801348463781416 56 0.995123825288179 0.00975234942364287 0.00487617471182143 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.65 NOK 5% type I error level 31 0.775 NOK 10% type I error level 33 0.825 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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