lin regr wlh dummies+trend

*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: Fri, 25 Dec 2009 12:25:37 -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/25/t1261769202zh8k7znsmh6t1en.htm/, Retrieved Fri, 25 Dec 2009 20:26:55 +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/25/t1261769202zh8k7znsmh6t1en.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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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 0 565742 0 557274 0 560576 0 548854 0 531673 0 525919 0 511038 0 498662 0 555362 0 564591 0 541657 0 527070 0 509846 0 514258 0 516922 0 507561 0 492622 0 490243 0 469357 0 477580 0 528379 0 533590 0 517945 0 506174 0 501866 0 516141 0 528222 0 532638 0 536322 0 536535 0 523597 0 536214 0 586570 0 596594 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation wlh[t] = + 577655.916666666 + 57290.8333333334dummies[t] -20542.0875000001M1[t] -23997.8916666666M2[t] -39158.2625M3[t] -36213.0333333333M4[t] -33971.4041666667M5[t] -37972.5749999999M6[t] -46407.9458333334M7[t] -51079.7166666667M8[t] -61938.8875M9[t] -59601.6583333333M10[t] -8067.62916666667M11[t] -296.629166666666t + 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) 577655.916666666 17813.641677 32.4277 0 0 dummies 57290.8333333334 10881.413528 5.265 4e-06 2e-06 M1 -20542.0875000001 13196.751749 -1.5566 0.126419 0.06321 M2 -23997.8916666666 13430.209516 -1.7869 0.080551 0.040275 M3 -39158.2625 13360.231258 -2.931 0.005247 0.002624 M4 -36213.0333333333 13297.306976 -2.7233 0.009102 0.004551 M5 -33971.4041666667 13241.537234 -2.5655 0.013627 0.006813 M6 -37972.5749999999 13193.012762 -2.8782 0.006048 0.003024 M7 -46407.9458333334 13151.813757 -3.5286 0.00096 0.00048 M8 -51079.7166666667 13118.009239 -3.8939 0.000317 0.000159 M9 -61938.8875 13091.656489 -4.7312 2.2e-05 1.1e-05 M10 -59601.6583333333 13072.800572 -4.5592 3.8e-05 1.9e-05 M11 -8067.62916666667 13061.473956 -0.6177 0.539841 0.269921 t -296.629166666666 314.119351 -0.9443 0.34994 0.17497 Multiple Linear Regression - Regression Statistics Multiple R 0.902455534317694 R-squared 0.814425991420635 Adjusted R-squared 0.761981162909076 F-TEST (value) 15.5291954332757 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.12287956710588e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 20646.0305467409 Sum Squared Residuals 19607894557.5 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 612613 614108.033333334 -1495.03333333374 2 611324 610355.6 968.40000000007 3 594167 594898.6 -731.59999999998 4 595454 597547.2 -2093.19999999998 5 590865 599492.2 -8627.19999999995 6 589379 595194.4 -5815.39999999997 7 584428 586462.4 -2034.39999999995 8 573100 581494 -8394.00000000013 9 567456 570338.2 -2882.19999999991 10 569028 572378.8 -3350.79999999999 11 620735 623616.2 -2881.19999999998 12 628884 631387.2 -2503.19999999997 13 628232 610548.483333333 17683.5166666668 14 612117 606796.05 5320.94999999996 15 595404 591339.05 4064.94999999999 16 597141 593987.65 3153.35000000001 17 593408 595932.65 -2524.65000000001 18 590072 591634.85 -1562.85000000000 19 579799 582902.85 -3103.85 20 574205 577934.45 -3729.44999999997 21 572775 566778.65 5996.34999999998 22 572942 568819.25 4122.74999999999 23 619567 620056.65 -489.65 24 625809 627827.65 -2018.65000000001 25 619916 606988.933333333 12927.0666666668 26 587625 545945.666666667 41679.3333333333 27 565742 530488.666666667 35253.3333333333 28 557274 533137.266666667 24136.7333333333 29 560576 535082.266666667 25493.7333333333 30 548854 530784.466666667 18069.5333333333 31 531673 522052.466666667 9620.53333333333 32 525919 517084.066666667 8834.93333333337 33 511038 505928.266666667 5109.73333333333 34 498662 507968.866666667 -9306.86666666665 35 555362 559206.266666667 -3844.26666666665 36 564591 566977.266666667 -2386.26666666667 37 541657 546138.55 -4481.54999999989 38 527070 542386.116666667 -15316.1166666667 39 509846 526929.116666667 -17083.1166666667 40 514258 529577.716666667 -15319.7166666667 41 516922 531522.716666667 -14600.7166666667 42 507561 527224.916666667 -19663.9166666667 43 492622 518492.916666667 -25870.9166666667 44 490243 513524.516666667 -23281.5166666666 45 469357 502368.716666667 -33011.7166666667 46 477580 504409.316666667 -26829.3166666667 47 528379 555646.716666667 -27267.7166666667 48 533590 563417.716666667 -29827.7166666667 49 517945 542579 -24633.9999999999 50 506174 538826.566666667 -32652.5666666667 51 501866 523369.566666667 -21503.5666666667 52 516141 526018.166666667 -9877.1666666667 53 528222 527963.166666667 258.833333333305 54 532638 523665.366666667 8972.6333333333 55 536322 514933.366666667 21388.6333333333 56 536535 509964.966666667 26570.0333333334 57 523597 498809.166666667 24787.8333333333 58 536214 500849.766666667 35364.2333333333 59 586570 552087.166666667 34482.8333333333 60 596594 559858.166666667 36735.8333333333 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0113483427669974 0.0226966855339947 0.988651657233003 18 0.00208209384444360 0.00416418768888719 0.997917906155556 19 0.000646047919944538 0.00129209583988908 0.999353952080055 20 0.000104582434019131 0.000209164868038263 0.99989541756598 21 1.66721288989463e-05 3.33442577978926e-05 0.999983327871101 22 2.27546858547463e-06 4.55093717094926e-06 0.999997724531414 23 3.72080303162505e-07 7.4416060632501e-07 0.999999627919697 24 8.11208056561786e-08 1.62241611312357e-07 0.999999918879194 25 1.22236894187856e-08 2.44473788375712e-08 0.99999998777631 26 3.77228028922556e-09 7.54456057845113e-09 0.99999999622772 27 1.71578426194748e-09 3.43156852389495e-09 0.999999998284216 28 5.11297931069475e-09 1.02259586213895e-08 0.99999999488702 29 1.76335439391028e-09 3.52670878782055e-09 0.999999998236646 30 2.75310143868448e-09 5.50620287736895e-09 0.999999997246899 31 3.37360729336774e-08 6.74721458673548e-08 0.999999966263927 32 4.50100086504512e-08 9.00200173009024e-08 0.999999954989991 33 7.30134014386348e-07 1.46026802877270e-06 0.999999269865986 34 2.20040296194333e-05 4.40080592388665e-05 0.99997799597038 35 4.44560452339164e-05 8.89120904678329e-05 0.999955543954766 36 8.16763000083316e-05 0.000163352600016663 0.999918323699992 37 0.00164731776466357 0.00329463552932715 0.998352682235336 38 0.0452617333562613 0.0905234667125226 0.954738266643739 39 0.207581375184809 0.415162750369618 0.792418624815191 40 0.464882348942237 0.929764697884473 0.535117651057763 41 0.773567283841148 0.452865432317705 0.226432716158852 42 0.949956805587168 0.100086388825664 0.050043194412832 43 0.94514413625989 0.109711727480218 0.0548558637401089 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.740740740740741 NOK 5% type I error level 21 0.777777777777778 NOK 10% type I error level 22 0.814814814814815 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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