*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: Thu, 09 Dec 2010 17:00:25 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/09/t1291913937e6m29dxxwetqx9q.htm/, Retrieved Thu, 09 Dec 2010 17:59:00 +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/2010/Dec/09/t1291913937e6m29dxxwetqx9q.htm/}, year = {2010}, } @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 = {2010}, 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 «

9700 0 9081 0 9084 0 9743 0 8587 0 9731 0 9563 0 9998 0 9437 0 10038 0 9918 0 9252 0 9737 0 9035 0 9133 0 9487 0 8700 0 9627 0 8947 0 9283 0 8829 0 9947 0 9628 0 9318 0 9605 0 8640 0 9214 0 9567 0 8547 0 9185 0 9470 0 9123 0 9278 0 10170 0 9434 0 9655 0 9429 0 8739 0 9552 0 9687 1 9019 1 9672 1 9206 1 9069 1 9788 1 10312 1 10105 1 9863 1 9656 1 9295 1 9946 1 9701 1 9049 1 10190 1 9706 1 9765 1 9893 1 9994 1 10433 1 10073 1 10112 1 9266 1 9820 1 10097 1 9115 1 10411 1 9678 1 10408 1 10153 1 10368 1 10581 1 10597 1 10680 1 9738 1 9556 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation births[t] = + 9369.51282051282 + 491.653846153847difference[t] + 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) 9369.51282051282 70.630247 132.6558 0 0 difference 491.653846153847 101.94598 4.8227 8e-06 4e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.491552779078138 R-squared 0.24162413461944 Adjusted R-squared 0.231235424134775 F-TEST (value) 23.2583374978158 F-TEST (DF numerator) 1 F-TEST (DF denominator) 73 p-value 7.52295409400805e-06 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 441.085751666438 Sum Squared Residuals 14202634.7435897 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9700 9369.51282051285 330.487179487148 2 9081 9369.51282051282 -288.51282051282 3 9084 9369.51282051282 -285.51282051282 4 9743 9369.51282051282 373.48717948718 5 8587 9369.51282051282 -782.51282051282 6 9731 9369.51282051282 361.48717948718 7 9563 9369.51282051282 193.48717948718 8 9998 9369.51282051282 628.48717948718 9 9437 9369.51282051282 67.4871794871803 10 10038 9369.51282051282 668.48717948718 11 9918 9369.51282051282 548.48717948718 12 9252 9369.51282051282 -117.51282051282 13 9737 9369.51282051282 367.48717948718 14 9035 9369.51282051282 -334.51282051282 15 9133 9369.51282051282 -236.51282051282 16 9487 9369.51282051282 117.48717948718 17 8700 9369.51282051282 -669.51282051282 18 9627 9369.51282051282 257.48717948718 19 8947 9369.51282051282 -422.51282051282 20 9283 9369.51282051282 -86.5128205128197 21 8829 9369.51282051282 -540.51282051282 22 9947 9369.51282051282 577.48717948718 23 9628 9369.51282051282 258.48717948718 24 9318 9369.51282051282 -51.5128205128197 25 9605 9369.51282051282 235.48717948718 26 8640 9369.51282051282 -729.51282051282 27 9214 9369.51282051282 -155.51282051282 28 9567 9369.51282051282 197.48717948718 29 8547 9369.51282051282 -822.51282051282 30 9185 9369.51282051282 -184.51282051282 31 9470 9369.51282051282 100.48717948718 32 9123 9369.51282051282 -246.51282051282 33 9278 9369.51282051282 -91.5128205128197 34 10170 9369.51282051282 800.48717948718 35 9434 9369.51282051282 64.4871794871803 36 9655 9369.51282051282 285.48717948718 37 9429 9369.51282051282 59.4871794871803 38 8739 9369.51282051282 -630.51282051282 39 9552 9369.51282051282 182.48717948718 40 9687 9861.16666666667 -174.166666666667 41 9019 9861.16666666667 -842.166666666667 42 9672 9861.16666666667 -189.166666666667 43 9206 9861.16666666667 -655.166666666667 44 9069 9861.16666666667 -792.166666666667 45 9788 9861.16666666667 -73.1666666666667 46 10312 9861.16666666667 450.833333333333 47 10105 9861.16666666667 243.833333333333 48 9863 9861.16666666667 1.83333333333333 49 9656 9861.16666666667 -205.166666666667 50 9295 9861.16666666667 -566.166666666667 51 9946 9861.16666666667 84.8333333333334 52 9701 9861.16666666667 -160.166666666667 53 9049 9861.16666666667 -812.166666666667 54 10190 9861.16666666667 328.833333333333 55 9706 9861.16666666667 -155.166666666667 56 9765 9861.16666666667 -96.1666666666667 57 9893 9861.16666666667 31.8333333333334 58 9994 9861.16666666667 132.833333333333 59 10433 9861.16666666667 571.833333333333 60 10073 9861.16666666667 211.833333333333 61 10112 9861.16666666667 250.833333333333 62 9266 9861.16666666667 -595.166666666667 63 9820 9861.16666666667 -41.1666666666667 64 10097 9861.16666666667 235.833333333333 65 9115 9861.16666666667 -746.166666666667 66 10411 9861.16666666667 549.833333333333 67 9678 9861.16666666667 -183.166666666667 68 10408 9861.16666666667 546.833333333333 69 10153 9861.16666666667 291.833333333333 70 10368 9861.16666666667 506.833333333333 71 10581 9861.16666666667 719.833333333333 72 10597 9861.16666666667 735.833333333333 73 10680 9861.16666666667 818.833333333333 74 9738 9861.16666666667 -123.166666666667 75 9556 9861.16666666667 -305.166666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.80709932379453 0.38580135241094 0.19290067620547 6 0.777933210944197 0.444133578111605 0.222066789055803 7 0.685774101959898 0.628451796080204 0.314225898040102 8 0.745587693600533 0.508824612798934 0.254412306399467 9 0.642806795017526 0.714386409964948 0.357193204982474 10 0.699297037069166 0.601405925861669 0.300702962930834 11 0.68720110616407 0.625597787671859 0.31279889383593 12 0.622325882224258 0.755348235551485 0.377674117775742 13 0.560423896917953 0.879152206164093 0.439576103082047 14 0.55923485010623 0.88153029978754 0.44076514989377 15 0.516092029148479 0.967815941703042 0.483907970851521 16 0.431430610494715 0.86286122098943 0.568569389505285 17 0.566649267808118 0.866701464383765 0.433350732191882 18 0.504940545444166 0.990118909111668 0.495059454555834 19 0.506668030572806 0.986663938854388 0.493331969427194 20 0.432442877309352 0.864885754618705 0.567557122690648 21 0.4718511243935 0.943702248787 0.5281488756065 22 0.517532943854912 0.964934112290176 0.482467056145088 23 0.465508256772166 0.931016513544332 0.534491743227834 24 0.394646671229708 0.789293342459416 0.605353328770292 25 0.344045836100425 0.688091672200849 0.655954163899575 26 0.463848972073221 0.927697944146441 0.53615102792678 27 0.401861701459451 0.803723402918902 0.598138298540549 28 0.347906397781719 0.695812795563437 0.652093602218281 29 0.509549496662721 0.980901006674558 0.490450503337279 30 0.453059699261385 0.906119398522769 0.546940300738615 31 0.388237012190303 0.776474024380606 0.611762987809697 32 0.346418477500782 0.692836955001563 0.653581522499219 33 0.290799607280533 0.581599214561065 0.709200392719467 34 0.420471679213593 0.840943358427186 0.579528320786407 35 0.356743122226342 0.713486244452684 0.643256877773658 36 0.325240762000497 0.650481524000993 0.674759237999503 37 0.273536763805492 0.547073527610985 0.726463236194508 38 0.322470570067983 0.644941140135966 0.677529429932017 39 0.269119404425907 0.538238808851814 0.730880595574093 40 0.219722508065967 0.439445016131933 0.780277491934033 41 0.294782320400572 0.589564640801145 0.705217679599428 42 0.254849479028202 0.509698958056403 0.745150520971798 43 0.279338120846487 0.558676241692974 0.720661879153513 44 0.364782464070664 0.729564928141328 0.635217535929336 45 0.332316602138573 0.664633204277145 0.667683397861427 46 0.394675461287209 0.789350922574418 0.605324538712791 47 0.372124218294671 0.744248436589342 0.627875781705329 48 0.315798146693745 0.631596293387491 0.684201853306255 49 0.270206687325506 0.540413374651012 0.729793312674494 50 0.307492900974226 0.614985801948452 0.692507099025774 51 0.258364084211714 0.516728168423429 0.741635915788285 52 0.216685216549835 0.433370433099671 0.783314783450164 53 0.394280336486075 0.78856067297215 0.605719663513925 54 0.366433188771369 0.732866377542738 0.633566811228631 55 0.323667938749357 0.647335877498714 0.676332061250643 56 0.276996032151893 0.553992064303785 0.723003967848107 57 0.225199305527726 0.450398611055452 0.774800694472274 58 0.177751495710404 0.355502991420808 0.822248504289596 59 0.188998896290797 0.377997792581594 0.811001103709203 60 0.144275984015049 0.288551968030097 0.855724015984951 61 0.107664788303808 0.215329576607616 0.892335211696192 62 0.180606903186614 0.361213806373228 0.819393096813386 63 0.141227788208926 0.282455576417853 0.858772211791074 64 0.0991367708428687 0.198273541685737 0.900863229157131 65 0.362849271215506 0.725698542431012 0.637150728784494 66 0.308334384115445 0.61666876823089 0.691665615884555 67 0.343867447860136 0.687734895720272 0.656132552139864 68 0.265130041238933 0.530260082477866 0.734869958761067 69 0.172702615392186 0.345405230784371 0.827297384607814 70 0.103258319681705 0.20651663936341 0.896741680318295 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 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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