lin regr wlh seasonal dummies

*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: Wed, 30 Dec 2009 14:16:38 -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/30/t12622078589rlqnhapuvsv6yx.htm/, Retrieved Wed, 30 Dec 2009 22:17:49 +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/30/t12622078589rlqnhapuvsv6yx.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 0 611324 0 594167 0 595454 0 590865 0 589379 0 584428 0 573100 0 567456 0 569028 0 620735 0 628884 0 628232 0 612117 0 595404 0 597141 0 593408 0 590072 0 579799 0 574205 0 572775 0 572942 0 619567 0 625809 0 619916 0 587625 0 565742 0 557274 0 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

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 wlh[t] = + 630954.108333333 -68434.1805555556dummies[t] -19507.8361111112M1[t] -34718.4361111111M2[t] -50175.4361111111M3[t] -47526.8361111111M4[t] -31895M5[t] -36192.8000000000M6[t] -44924.800M7[t] -49893.2M8[t] -61049M9[t] -59008.4M10[t] -7771M11[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) 630954.108333333 8652.025238 72.9256 0 0 dummies -68434.1805555556 4806.680688 -14.2373 0 0 M1 -19507.8361111112 11576.020022 -1.6852 0.098581 0.04929 M2 -34718.4361111111 11576.020022 -2.9992 0.004319 0.002159 M3 -50175.4361111111 11576.020022 -4.3344 7.7e-05 3.8e-05 M4 -47526.8361111111 11576.020022 -4.1056 0.00016 8e-05 M5 -31895 11536.03365 -2.7648 0.008111 0.004056 M6 -36192.8000000000 11536.03365 -3.1374 0.002941 0.00147 M7 -44924.800 11536.03365 -3.8943 0.00031 0.000155 M8 -49893.2 11536.03365 -4.325 7.9e-05 3.9e-05 M9 -61049 11536.03365 -5.292 3e-06 2e-06 M10 -59008.4 11536.03365 -5.1151 6e-06 3e-06 M11 -7771 11536.03365 -0.6736 0.503847 0.251924 Multiple Linear Regression - Regression Statistics Multiple R 0.923043008017838 R-squared 0.852008394650618 Adjusted R-squared 0.814223303923116 F-TEST (value) 22.5487984346822 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.55431223447522e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18240.0707498689 Sum Squared Residuals 15636908505.1306 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 612613 611446.272222223 1166.7277777775 2 611324 596235.672222222 15088.3277777778 3 594167 580778.672222222 13388.3277777778 4 595454 583427.272222222 12026.7277777778 5 590865 599059.108333333 -8194.10833333333 6 589379 594761.308333333 -5382.30833333328 7 584428 586029.308333333 -1601.30833333331 8 573100 581060.908333333 -7960.90833333338 9 567456 569905.108333333 -2449.10833333343 10 569028 571945.708333333 -2917.70833333334 11 620735 623183.108333333 -2448.1083333333 12 628884 630954.108333333 -2070.10833333331 13 628232 611446.272222222 16785.7277777779 14 612117 596235.672222222 15881.3277777778 15 595404 580778.672222222 14625.3277777778 16 597141 583427.272222222 13713.7277777778 17 593408 599059.108333333 -5651.10833333331 18 590072 594761.308333333 -4689.30833333333 19 579799 586029.308333333 -6230.30833333334 20 574205 581060.908333333 -6855.90833333332 21 572775 569905.108333333 2869.89166666669 22 572942 571945.708333333 996.29166666667 23 619567 623183.108333333 -3616.10833333333 24 625809 630954.108333333 -5145.10833333333 25 619916 611446.272222222 8469.72777777785 26 587625 596235.672222222 -8610.67222222224 27 565742 580778.672222222 -15036.6722222222 28 557274 583427.272222222 -26153.2722222222 29 560576 530624.927777778 29951.0722222222 30 548854 526327.127777778 22526.8722222222 31 531673 517595.127777778 14077.8722222222 32 525919 512626.727777778 13292.2722222222 33 511038 501470.927777778 9567.07222222224 34 498662 503511.527777778 -4849.52777777778 35 555362 554748.927777778 613.072222222213 36 564591 562519.927777778 2071.07222222221 37 541657 543012.091666667 -1355.09166666660 38 527070 527801.491666667 -731.491666666687 39 509846 512344.491666667 -2498.49166666668 40 514258 514993.091666667 -735.091666666687 41 516922 530624.927777778 -13702.9277777778 42 507561 526327.127777778 -18766.1277777778 43 492622 517595.127777778 -24973.1277777778 44 490243 512626.727777778 -22383.7277777778 45 469357 501470.927777778 -32113.9277777778 46 477580 503511.527777778 -25931.5277777778 47 528379 554748.927777778 -26369.9277777778 48 533590 562519.927777778 -28929.9277777778 49 517945 543012.091666667 -25067.0916666666 50 506174 527801.491666667 -21627.4916666667 51 501866 512344.491666667 -10478.4916666667 52 516141 514993.091666667 1147.90833333331 53 528222 530624.927777778 -2402.92777777778 54 532638 526327.127777778 6310.87222222221 55 536322 517595.127777778 18726.8722222222 56 536535 512626.727777778 23908.2722222222 57 523597 501470.927777778 22126.0722222223 58 536214 503511.527777778 32702.4722222222 59 586570 554748.927777778 31821.0722222222 60 596594 562519.927777778 34074.0722222222 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0409428612015161 0.0818857224030322 0.959057138798484 17 0.0107415186502737 0.0214830373005474 0.989258481349726 18 0.00243677737761075 0.00487355475522149 0.99756322262239 19 0.000630162961181439 0.00126032592236288 0.999369837038819 20 0.000126545195588692 0.000253090391177385 0.999873454804411 21 3.34314424506887e-05 6.68628849013774e-05 0.99996656855755 22 7.30020390743716e-06 1.46004078148743e-05 0.999992699796093 23 1.25468483444977e-06 2.50936966889954e-06 0.999998745315166 24 2.3206049933155e-07 4.641209986631e-07 0.9999997679395 25 4.49171302414181e-08 8.98342604828362e-08 0.99999995508287 26 1.09875315597915e-05 2.19750631195831e-05 0.99998901246844 27 0.000202502317809450 0.000405004635618899 0.99979749768219 28 0.00281339008131855 0.00562678016263711 0.997186609918681 29 0.00194603633018517 0.00389207266037034 0.998053963669815 30 0.00121322048090854 0.00242644096181707 0.998786779519091 31 0.000728674619243659 0.00145734923848732 0.999271325380756 32 0.000333886285413937 0.000667772570827875 0.999666113714586 33 0.000216804746093083 0.000433609492186166 0.999783195253907 34 0.000245286015568489 0.000490572031136978 0.999754713984431 35 0.000126174751877545 0.000252349503755089 0.999873825248123 36 5.35033894459416e-05 0.000107006778891883 0.999946496610554 37 6.49755310017573e-05 0.000129951062003515 0.999935024468998 38 4.93115351426147e-05 9.86230702852294e-05 0.999950688464857 39 2.50118885175406e-05 5.00237770350811e-05 0.999974988111482 40 8.62411300601944e-06 1.72482260120389e-05 0.999991375886994 41 6.43377505467588e-06 1.28675501093518e-05 0.999993566224945 42 6.61857254881832e-06 1.32371450976366e-05 0.999993381427451 43 1.39640575415495e-05 2.79281150830989e-05 0.999986035942458 44 2.0647713826158e-05 4.1295427652316e-05 0.999979352286174 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 27 0.93103448275862 NOK 5% type I error level 28 0.96551724137931 NOK 10% type I error level 29 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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