Q3 Monthly Dummies and Linear 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: Mon, 01 Dec 2008 11:59:20 -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/01/t1228158031cdnk49djvkmey5i.htm/, Retrieved Mon, 01 Dec 2008 19:00:31 +0000

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/01/t1228158031cdnk49djvkmey5i.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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12192.5 0 11268.8 0 9097.4 0 12639.8 0 13040.1 0 11687.3 0 11191.7 0 11391.9 0 11793.1 0 13933.2 0 12778.1 0 11810.3 0 13698.4 0 11956.6 0 10723.8 0 13938.9 0 13979.8 0 13807.4 0 12973.9 0 12509.8 0 12934.1 0 14908.3 0 13772.1 0 13012.6 0 14049.9 0 11816.5 0 11593.2 0 14466.2 0 13615.9 0 14733.9 0 13880.7 0 13527.5 0 13584 0 16170.2 0 13260.6 0 14741.9 0 15486.5 0 13154.5 0 12621.2 0 15031.6 0 15452.4 0 15428 0 13105.9 0 14716.8 1 14180 1 16202.2 1 14392.4 1 15140.6 1 15960.1 1 14351.3 1 13230.2 1 15202.1 1 17157.3 1 16159.1 1 13405.7 1 17224.7 1 17338.4 1 17370.6 1 18817.8 1 16593.2 1 17979.5 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 11299.1094197952 + 7.00716723549491x[t] + 1046.03710466439M1[t] -927.165312855518M2[t] -2065.70663822526M3[t] + 654.692036405005M4[t] + 965.910711035267M5[t] + 597.789385665529M6[t] -935.93193970421M7[t] -56.9346985210472M8[t] -47.3160238907847M9[t] + 1621.50265073948M10[t] + 426.641325369738M11[t] + 82.1613253697383t + 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) 11299.1094197952 406.218187 27.8154 0 0 x 7.00716723549491 349.337996 0.0201 0.984082 0.492041 M1 1046.03710466439 454.500279 2.3015 0.025843 0.012921 M2 -927.165312855518 476.877883 -1.9442 0.057866 0.028933 M3 -2065.70663822526 476.307928 -4.3369 7.6e-05 3.8e-05 M4 654.692036405005 475.906784 1.3757 0.175444 0.087722 M5 965.910711035267 475.674878 2.0306 0.047974 0.023987 M6 597.789385665529 475.612459 1.2569 0.215006 0.107503 M7 -935.93193970421 475.719592 -1.9674 0.055054 0.027527 M8 -56.9346985210472 475.023262 -0.1199 0.905108 0.452554 M9 -47.3160238907847 474.428663 -0.0997 0.920981 0.46049 M10 1621.50265073948 474.003492 3.4209 0.001301 0.000651 M11 426.641325369738 473.748207 0.9006 0.372411 0.186205 t 82.1613253697383 8.98048 9.1489 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.93959849877296 R-squared 0.8828453388964 Adjusted R-squared 0.850440858165617 F-TEST (value) 27.2445451674136 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 748.92709043569 Sum Squared Residuals 26361913.979058 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12192.5 12427.3078498293 -234.807849829343 2 11268.8 10536.2667576792 732.533242320818 3 9097.4 9479.88675767918 -382.486757679182 4 12639.8 12282.4467576792 357.353242320818 5 13040.1 12675.8267576792 364.273242320819 6 11687.3 12389.8667576792 -702.566757679182 7 11191.7 10938.3067576792 253.393242320819 8 11391.9 11899.4653242321 -507.565324232083 9 11793.1 11991.2453242321 -198.145324232082 10 13933.2 13742.2253242321 190.974675767919 11 12778.1 12629.5253242321 148.574675767918 12 11810.3 12285.0453242321 -474.745324232083 13 13698.4 13413.2437542662 285.156245733786 14 11956.6 11522.2026621160 434.39733788396 15 10723.8 10465.8226621160 257.977337883958 16 13938.9 13268.3826621160 670.517337883959 17 13979.8 13661.7626621160 318.037337883959 18 13807.4 13375.8026621160 431.597337883959 19 12973.9 11924.2426621160 1049.65733788396 20 12509.8 12885.4012286689 -375.601228668943 21 12934.1 12977.1812286689 -43.0812286689418 22 14908.3 14728.1612286689 180.138771331057 23 13772.1 13615.4612286689 156.638771331059 24 13012.6 13270.9812286689 -258.381228668942 25 14049.9 14399.1796587031 -349.279658703074 26 11816.5 12508.1385665529 -691.638566552901 27 11593.2 11451.7585665529 141.441433447099 28 14466.2 14254.3185665529 211.8814334471 29 13615.9 14647.6985665529 -1031.7985665529 30 14733.9 14361.7385665529 372.161433447099 31 13880.7 12910.1785665529 970.5214334471 32 13527.5 13871.3371331058 -343.837133105801 33 13584 13963.1171331058 -379.117133105802 34 16170.2 15714.0971331058 456.102866894198 35 13260.6 14601.3971331058 -1340.79713310580 36 14741.9 14256.9171331058 484.982866894197 37 15486.5 15385.1155631399 101.384436860067 38 13154.5 13494.0744709898 -339.574470989761 39 12621.2 12437.6944709898 183.505529010240 40 15031.6 15240.2544709898 -208.654470989760 41 15452.4 15633.6344709898 -181.234470989760 42 15428 15347.6744709898 80.3255290102399 43 13105.9 13896.1144709898 -790.214470989761 44 14716.8 14864.2802047782 -147.480204778157 45 14180 14956.0602047782 -776.060204778158 46 16202.2 16707.0402047782 -504.840204778156 47 14392.4 15594.3402047782 -1201.94020477816 48 15140.6 15249.8602047782 -109.260204778157 49 15960.1 16378.0586348123 -417.958634812288 50 14351.3 14487.0175426621 -135.717542662116 51 13230.2 13430.6375426621 -200.437542662115 52 15202.1 16233.1975426621 -1031.09754266212 53 17157.3 16626.5775426621 530.722457337883 54 16159.1 16340.6175426621 -181.517542662115 55 13405.7 14889.0575426621 -1483.35754266212 56 17224.7 15850.2161092150 1374.48389078498 57 17338.4 15941.9961092150 1396.40389078498 58 17370.6 17692.9761092150 -322.376109215018 59 18817.8 16580.2761092150 2237.52389078498 60 16593.2 16235.7961092150 357.403890784984 61 17979.5 17363.9945392491 615.505460750852 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0662761513527165 0.132552302705433 0.933723848647284 18 0.076178075808031 0.152356151616062 0.923821924191969 19 0.0504963420663837 0.100992684132767 0.949503657933616 20 0.0229111196721132 0.0458222393442264 0.977088880327887 21 0.00949749618991345 0.0189949923798269 0.990502503810087 22 0.00475177993650222 0.00950355987300444 0.995248220063498 23 0.00223821910311672 0.00447643820623343 0.997761780896883 24 0.00075702873566451 0.00151405747132902 0.999242971264335 25 0.00112193537305074 0.00224387074610148 0.99887806462695 26 0.0110842989969933 0.0221685979939866 0.988915701003007 27 0.00569316812682057 0.0113863362536411 0.99430683187318 28 0.00442644519293138 0.00885289038586277 0.995573554807069 29 0.0116953622870498 0.0233907245740995 0.98830463771295 30 0.0105982307726674 0.0211964615453349 0.989401769227333 31 0.0893876040153979 0.178775208030796 0.910612395984602 32 0.0617823272664603 0.123564654532921 0.93821767273354 33 0.039244899752331 0.078489799504662 0.960755100247669 34 0.0479995596918256 0.0959991193836511 0.952000440308174 35 0.190030213120053 0.380060426240107 0.809969786879946 36 0.210299681561760 0.420599363123519 0.78970031843824 37 0.160733038120358 0.321466076240716 0.839266961879642 38 0.119286192726631 0.238572385453262 0.88071380727337 39 0.0751012439432984 0.150202487886597 0.924898756056702 40 0.0575824135885074 0.115164827177015 0.942417586411493 41 0.0492823560427836 0.0985647120855671 0.950717643957216 42 0.0263139011772264 0.0526278023544529 0.973686098822774 43 0.0266388490337116 0.0532776980674232 0.973361150966288 44 0.0107824422619315 0.0215648845238630 0.989217557738069 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.178571428571429 NOK 5% type I error level 12 0.428571428571429 NOK 10% type I error level 17 0.607142857142857 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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