dummie lineaire 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, 19 Dec 2008 03:47:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/19/t1229683786vhp733g7dy1dqe7.htm/, Retrieved Fri, 19 Dec 2008 11:49:47 +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/2008/Dec/19/t1229683786vhp733g7dy1dqe7.htm/}, year = {2008}, } @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 = {2008}, 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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565464 0 547344 0 554788 0 562325 0 560854 0 555332 0 543599 0 536662 0 542722 0 593530 0 610763 0 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

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 9 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 602426.375757576 -74774.9393939395X[t] -14776.5267676769M1[t] -33316.9323232323M2[t] -32355.5378787879M3[t] -16685.3555555555M4[t] -22481.5611111111M5[t] -33375.7666666666M6[t] -41054.3722222222M7[t] -51330.9777777778M8[t] -50922.7833333333M9[t] + 84.0111111111166M10[t] + 8975.80555555557M11[t] + 321.005555555559t + 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) 602426.375757576 10466.936469 57.5552 0 0 X -74774.9393939395 9127.602355 -8.1922 0 0 M1 -14776.5267676769 11836.347374 -1.2484 0.2182 0.1091 M2 -33316.9323232323 11812.12688 -2.8206 0.007052 0.003526 M3 -32355.5378787879 11793.254328 -2.7436 0.008635 0.004318 M4 -16685.3555555555 11897.047615 -1.4025 0.167485 0.083743 M5 -22481.5611111111 11856.859297 -1.8961 0.064241 0.03212 M6 -33375.7666666666 11821.918913 -2.8232 0.007003 0.003501 M7 -41054.3722222222 11792.27311 -3.4815 0.001104 0.000552 M8 -51330.9777777778 11767.961904 -4.3619 7.2e-05 3.6e-05 M9 -50922.7833333333 11749.018409 -4.3342 7.9e-05 3.9e-05 M10 84.0111111111166 11735.46862 0.0072 0.994319 0.49716 M11 8975.80555555557 11727.331232 0.7654 0.447958 0.223979 t 321.005555555559 252.273602 1.2725 0.209608 0.104804 Multiple Linear Regression - Regression Statistics Multiple R 0.913774933820026 R-squared 0.834984629677793 Adjusted R-squared 0.788349851108473 F-TEST (value) 17.904762396087 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 8.59312621059871e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18538.2480190642 Sum Squared Residuals 15808665422.3516 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 565464 587970.854545455 -22506.8545454552 2 547344 569751.454545454 -22407.4545454545 3 554788 571033.854545454 -16245.8545454545 4 562325 587025.042424242 -24700.0424242424 5 560854 581549.842424242 -20695.8424242424 6 555332 570976.642424242 -15644.6424242424 7 543599 563619.042424242 -20020.0424242424 8 536662 553663.442424242 -17001.4424242424 9 542722 554392.642424242 -11670.6424242424 10 593530 605720.442424242 -12190.4424242424 11 610763 614933.242424242 -4170.24242424238 12 612613 606278.442424242 6334.55757575763 13 611324 591822.921212121 19501.078787879 14 594167 573603.521212121 20563.4787878788 15 595454 574885.921212121 20568.0787878788 16 590865 590877.109090909 -12.1090909090864 17 589379 585401.909090909 3977.09090909092 18 584428 574828.709090909 9599.29090909092 19 573100 567471.109090909 5628.89090909092 20 567456 557515.509090909 9940.49090909092 21 569028 558244.709090909 10783.2909090909 22 620735 609572.509090909 11162.4909090909 23 628884 618785.309090909 10098.6909090909 24 628232 610130.509090909 18101.4909090909 25 612117 595674.987878788 16442.0121212123 26 595404 577455.587878788 17948.4121212121 27 597141 578737.987878788 18403.0121212121 28 593408 594729.175757576 -1321.17575757579 29 590072 589253.975757576 818.02424242421 30 579799 578680.775757576 1118.22424242421 31 574205 571323.175757576 2881.82424242421 32 572775 561367.575757576 11407.4242424242 33 572942 562096.775757576 10845.2242424242 34 619567 613424.575757576 6142.42424242422 35 625809 622637.375757576 3171.62424242422 36 619916 613982.575757576 5933.42424242422 37 587625 599527.054545454 -11902.0545454544 38 565742 581307.654545455 -15565.6545454546 39 557274 582590.054545455 -25316.0545454546 40 560576 523806.303030303 36769.696969697 41 548854 518331.103030303 30522.896969697 42 531673 507757.903030303 23915.096969697 43 525919 500400.303030303 25518.696969697 44 511038 490444.703030303 20593.296969697 45 498662 491173.903030303 7488.09696969698 46 555362 542501.703030303 12860.296969697 47 564591 551714.503030303 12876.4969696970 48 541657 543059.703030303 -1402.70303030301 49 527070 528604.181818182 -1534.18181818165 50 509846 510384.781818182 -538.781818181834 51 514258 511667.181818182 2590.81818181816 52 516922 527658.36969697 -10736.3696969697 53 507561 522183.16969697 -14622.1696969697 54 492622 511609.96969697 -18987.9696969697 55 490243 504252.36969697 -14009.3696969697 56 469357 494296.76969697 -24939.7696969697 57 477580 495025.96969697 -17445.9696969697 58 528379 546353.76969697 -17974.7696969697 59 533590 555566.56969697 -21976.5696969697 60 517945 546911.76969697 -28966.7696969697 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.291269880995930 0.582539761991861 0.70873011900407 18 0.217435613802869 0.434871227605738 0.782564386197131 19 0.183332297155832 0.366664594311665 0.816667702844168 20 0.141643463344383 0.283286926688765 0.858356536655617 21 0.143640395561342 0.287280791122684 0.856359604438658 22 0.158873820464574 0.317747640929147 0.841126179535426 23 0.369210958666529 0.738421917333059 0.63078904133347 24 0.509558168118161 0.980883663763678 0.490441831881839 25 0.71707194962282 0.565856100754361 0.282928050377180 26 0.754104919534878 0.491790160930244 0.245895080465122 27 0.768704876649776 0.462590246700448 0.231295123350224 28 0.908072759377627 0.183854481244745 0.0919272406223726 29 0.951339998060883 0.0973200038782336 0.0486600019391168 30 0.969103910325546 0.0617921793489082 0.0308960896744541 31 0.976456966545829 0.0470860669083422 0.0235430334541711 32 0.962943792526717 0.074112414946566 0.037056207473283 33 0.954328449651604 0.0913431006967915 0.0456715503483957 34 0.93590653406394 0.128186931872120 0.0640934659360598 35 0.922361448231847 0.155277103536305 0.0776385517681527 36 0.977089976304322 0.0458200473913567 0.0229100236956783 37 0.988962755995803 0.0220744880083941 0.0110372440041971 38 0.99245200778423 0.0150959844315418 0.0075479922157709 39 0.99133067318857 0.0173386536228613 0.00866932681143063 40 0.986534019837316 0.0269319603253689 0.0134659801626844 41 0.976945335886239 0.046109328227522 0.023054664113761 42 0.95720278494484 0.0855944301103198 0.0427972150551599 43 0.901835844664526 0.196328310670948 0.0981641553354742 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 7 0.259259259259259 NOK 10% type I error level 12 0.444444444444444 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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