regressie, monthly dummies & no linear trend

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 28 Apr 2008 12:41:55 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/28/t12094087850quu379ctjbhoch.htm/, Retrieved Mon, 28 Apr 2008 20:53:17 +0200

User-defined keywords:

Dataseries X:

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56421 53152 53536 52408 41454 38271 35306 26414 31917 38030 27534 18387 50556 43901 48572 43899 37532 40357 35489 29027 34485 42598 30306 26451 47460 50104 61465 53726 39477 43895 31481 29896 33842 39120 33702 25094 51442 45594 52518 48564 41745 49585 32747 33379 35645 37034 35681 20972 58552 54955 65540 51570 51145 46641 35704 33253 35193 41668 34865 21210 56126 49231 59723 48103 47472 50497 40059 34149 36860 46356 36577

Text written by user:

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 aantal[t] = + 22422.8 + 31003.3666666667M1[t] + 27066.7M2[t] + 34469.5333333333M3[t] + 27288.8666666667M4[t] + 20714.7M5[t] + 22451.5333333334M6[t] + 12708.2M7[t] + 8596.86666666668M8[t] + 12234.2M9[t] + 18378.2000000000M10[t] + 10688.0333333334M11[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) 22422.8 1814.592704 12.3569 0 0 M1 31003.3666666667 2456.970136 12.6185 0 0 M2 27066.7 2456.970136 11.0163 0 0 M3 34469.5333333333 2456.970136 14.0293 0 0 M4 27288.8666666667 2456.970136 11.1067 0 0 M5 20714.7 2456.970136 8.431 0 0 M6 22451.5333333334 2456.970136 9.1379 0 0 M7 12708.2 2456.970136 5.1723 3e-06 1e-06 M8 8596.86666666668 2456.970136 3.499 0.000895 0.000448 M9 12234.2 2456.970136 4.9794 6e-06 3e-06 M10 18378.2000000000 2456.970136 7.48 0 0 M11 10688.0333333334 2456.970136 4.3501 5.5e-05 2.7e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.933426029264076 R-squared 0.8712841521077 Adjusted R-squared 0.847286282161677 F-TEST (value) 36.3067286416444 F-TEST (DF numerator) 11 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4057.5526371681 Sum Squared Residuals 971360270.799998 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 56421 53426.1666666666 2994.83333333337 2 53152 49489.5000000001 3662.4999999999 3 53536 56892.3333333333 -3356.33333333331 4 52408 49711.6666666666 2696.33333333335 5 41454 43137.5 -1683.49999999997 6 38271 44874.3333333333 -6603.3333333333 7 35306 35131.0000000000 174.999999999959 8 26414 31019.6666666666 -4605.66666666665 9 31917 34657 -2739.99999999999 10 38030 40801 -2770.99999999998 11 27534 33110.8333333333 -5576.83333333333 12 18387 22422.8 -4035.8 13 50556 53426.1666666667 -2870.16666666668 14 43901 49489.5 -5588.49999999998 15 48572 56892.3333333333 -8320.33333333334 16 43899 49711.6666666667 -5812.66666666667 17 37532 43137.5 -5605.50000000001 18 40357 44874.3333333333 -4517.33333333334 19 35489 35131 358.000000000006 20 29027 31019.6666666667 -1992.66666666667 21 34485 34657 -172.000000000003 22 42598 40801 1796.99999999999 23 30306 33110.8333333333 -2804.83333333333 24 26451 22422.8 4028.20000000001 25 47460 53426.1666666667 -5966.16666666668 26 50104 49489.5 614.50000000002 27 61465 56892.3333333333 4572.66666666666 28 53726 49711.6666666667 4014.33333333333 29 39477 43137.5 -3660.50000000001 30 43895 44874.3333333333 -979.33333333334 31 31481 35131 -3649.99999999999 32 29896 31019.6666666667 -1123.66666666667 33 33842 34657 -815.000000000004 34 39120 40801 -1681.00000000001 35 33702 33110.8333333333 591.166666666666 36 25094 22422.8 2671.20000000001 37 51442 53426.1666666667 -1984.16666666668 38 45594 49489.5 -3895.49999999998 39 52518 56892.3333333333 -4374.33333333334 40 48564 49711.6666666667 -1147.66666666667 41 41745 43137.5 -1392.50000000001 42 49585 44874.3333333333 4710.66666666666 43 32747 35131 -2383.99999999999 44 33379 31019.6666666667 2359.33333333333 45 35645 34657 987.999999999997 46 37034 40801 -3767.00000000001 47 35681 33110.8333333333 2570.16666666667 48 20972 22422.8 -1450.79999999999 49 58552 53426.1666666667 5125.83333333332 50 54955 49489.5 5465.50000000002 51 65540 56892.3333333333 8647.66666666666 52 51570 49711.6666666667 1858.33333333333 53 51145 43137.5 8007.49999999999 54 46641 44874.3333333333 1766.66666666666 55 35704 35131 573.000000000006 56 33253 31019.6666666667 2233.33333333333 57 35193 34657 535.999999999997 58 41668 40801 866.999999999994 59 34865 33110.8333333333 1754.16666666667 60 21210 22422.8 -1212.79999999999 61 56126 53426.1666666667 2699.83333333332 62 49231 49489.5 -258.499999999979 63 59723 56892.3333333333 2830.66666666666 64 48103 49711.6666666667 -1608.66666666667 65 47472 43137.5 4334.49999999999 66 50497 44874.3333333333 5622.66666666666 67 40059 35131 4928 68 34149 31019.6666666667 3129.33333333333 69 36860 34657 2203.00000000000 70 46356 40801 5554.99999999999 71 36577 33110.8333333333 3466.16666666667 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.816700130322775 0.366599739354449 0.183299869677225 16 0.883118824373383 0.233762351253233 0.116881175626617 17 0.861520906992403 0.276958186015194 0.138479093007597 18 0.827270847527724 0.345458304944552 0.172729152472276 19 0.740798358923595 0.51840328215281 0.259201641076405 20 0.674357745145147 0.651284509709706 0.325642254854853 21 0.591347792278216 0.817304415443569 0.408652207721784 22 0.551604713370044 0.896790573259912 0.448395286629956 23 0.50369642201806 0.99260715596388 0.49630357798194 24 0.598724155787247 0.802551688425506 0.401275844212753 25 0.702101509282103 0.595796981435794 0.297898490717897 26 0.624974340958459 0.750051318083082 0.375025659041541 27 0.794063512716824 0.411872974566352 0.205936487283176 28 0.803088050978035 0.393823898043931 0.196911949021965 29 0.812134690182405 0.375730619635189 0.187865309817595 30 0.81888323599845 0.362233528003098 0.181116764001549 31 0.814891173261137 0.370217653477725 0.185108826738863 32 0.783968764462423 0.432062471075153 0.216031235537577 33 0.726205534644679 0.547588930710642 0.273794465355321 34 0.668890279391631 0.662219441216738 0.331109720608369 35 0.641523116897778 0.716953766204444 0.358476883102222 36 0.607602006552799 0.784795986894401 0.392397993447201 37 0.603302808012925 0.79339438397415 0.396697191987075 38 0.64723443785853 0.705531124282941 0.352765562141470 39 0.834204399450629 0.331591201098742 0.165795600549371 40 0.782152839056999 0.435694321886003 0.217847160943001 41 0.87664295707781 0.246714085844379 0.123357042922190 42 0.898004444156067 0.203991111687866 0.101995555843933 43 0.912223962204203 0.175552075591593 0.0877760377957966 44 0.887118345445886 0.225763309108229 0.112881654554114 45 0.839695244651818 0.320609510696364 0.160304755348182 46 0.925112158358492 0.149775683283017 0.0748878416415083 47 0.897606649939069 0.204786700121863 0.102393350060931 48 0.84703095857443 0.305938082851141 0.152969041425571 49 0.833219794896669 0.333560410206663 0.166780205103331 50 0.88438999762356 0.231220004752881 0.115610002376440 51 0.949688937615112 0.100622124769776 0.0503110623848882 52 0.934942197565549 0.130115604868903 0.0650578024344515 53 0.9416498337782 0.116700332443599 0.0583501662217996 54 0.931574120754655 0.136851758490689 0.0684258792453447 55 0.936969775875921 0.126060448248158 0.0630302241240791 56 0.85257007223166 0.294859855536682 0.147429927768341 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 = 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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