regressiemodel

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

Title produced by software: Multiple Regression

Date of computation: Wed, 07 May 2008 09:01:33 -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/May/07/t1210172647k1xc3wbfj8rxtfd.htm/, Retrieved Wed, 07 May 2008 17:04:19 +0200

User-defined keywords:

poging1

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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation registraties[t] = + 18935.8222222222 + 31487.6691358025M1[t] + 27454.1419753086M2[t] + 34760.1148148148M3[t] + 27482.587654321M4[t] + 20811.5604938272M5[t] + 22451.5333333334M6[t] + 12611.3395061728M7[t] + 8403.14567901236M8[t] + 11943.6185185185M9[t] + 17990.7580246914M10[t] + 10203.7308641976M11[t] + 96.8604938271604t + 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) 18935.8222222222 1714.889383 11.042 0 0 M1 31487.6691358025 2102.756003 14.9745 0 0 M2 27454.1419753086 2101.872884 13.0618 0 0 M3 34760.1148148148 2101.185757 16.5431 0 0 M4 27482.587654321 2100.694814 13.0826 0 0 M5 20811.5604938272 2100.400193 9.9084 0 0 M6 22451.5333333334 2100.301977 10.6897 0 0 M7 12611.3395061728 2100.400193 6.0043 0 0 M8 8403.14567901236 2100.694814 4.0002 0.000182 9.1e-05 M9 11943.6185185185 2101.185757 5.6842 0 0 M10 17990.7580246914 2101.872884 8.5594 0 0 M11 10203.7308641976 2102.756003 4.8526 1e-05 5e-06 t 96.8604938271604 20.31198 4.7686 1.3e-05 6e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.952646944818744 R-squared 0.907536201472488 Adjusted R-squared 0.88840576039783 F-TEST (value) 47.4393767467658 F-TEST (DF numerator) 12 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3468.53455910986 Sum Squared Residuals 697782455.288888 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 56421 50520.3518518518 5900.6481481482 2 53152 46583.6851851853 6568.3148148147 3 53536 53986.5185185185 -450.518518518497 4 52408 46805.8518518518 5602.14814814817 5 41454 40231.6851851852 1222.31481481484 6 38271 41968.5185185185 -3697.51851851849 7 35306 32225.1851851852 3080.81481481477 8 26414 28113.8518518518 -1699.85185185184 9 31917 31751.1851851852 165.814814814821 10 38030 37895.1851851852 134.814814814837 11 27534 30205.0185185185 -2671.01851851852 12 18387 20098.1481481481 -1711.14814814815 13 50556 51682.6777777778 -1126.67777777779 14 43901 47746.0111111111 -3845.01111111109 15 48572 55148.8444444444 -6576.84444444445 16 43899 47968.1777777778 -4069.17777777778 17 37532 41394.0111111111 -3862.01111111112 18 40357 43130.8444444445 -2773.84444444445 19 35489 33387.5111111111 2101.48888888889 20 29027 29276.1777777778 -249.177777777783 21 34485 32913.5111111111 1571.48888888889 22 42598 39057.5111111111 3540.48888888888 23 30306 31367.3444444444 -1061.34444444445 24 26451 21260.4740740741 5190.52592592594 25 47460 52845.0037037037 -5385.00370370372 26 50104 48908.337037037 1195.66296296298 27 61465 56311.1703703704 5153.82962962962 28 53726 49130.5037037037 4595.49629629629 29 39477 42556.337037037 -3079.33703703704 30 43895 44293.1703703704 -398.170370370378 31 31481 34549.8370370370 -3068.83703703703 32 29896 30438.5037037037 -542.503703703708 33 33842 34075.8370370370 -233.837037037040 34 39120 40219.837037037 -1099.83703703704 35 33702 32529.6703703704 1172.32962962963 36 25094 22422.8 2671.20000000001 37 51442 54007.3296296296 -2565.32962962964 38 45594 50070.662962963 -4476.66296296294 39 52518 57473.4962962963 -4955.4962962963 40 48564 50292.8296296296 -1728.82962962963 41 41745 43718.662962963 -1973.66296296297 42 49585 45455.4962962963 4129.5037037037 43 32747 35712.1629629630 -2965.16296296296 44 33379 31600.8296296296 1778.17037037037 45 35645 35238.1629629630 406.837037037037 46 37034 41382.162962963 -4348.16296296297 47 35681 33691.9962962963 1989.00370370371 48 20972 23585.1259259259 -2613.12592592592 49 58552 55169.6555555556 3382.34444444443 50 54955 51232.9888888889 3722.01111111113 51 65540 58635.8222222222 6904.17777777777 52 51570 51455.1555555556 114.844444444442 53 51145 44880.9888888889 6264.01111111111 54 46641 46617.8222222222 23.1777777777726 55 35704 36874.4888888889 -1170.48888888888 56 33253 32763.1555555556 489.844444444443 57 35193 36400.4888888889 -1207.48888888889 58 41668 42544.4888888889 -876.488888888891 59 34865 34854.3222222222 10.6777777777801 60 21210 24747.4518518518 -3537.45185185184 61 56126 56331.9814814815 -205.981481481489 62 49231 52395.3148148148 -3164.31481481479 63 59723 59798.1481481482 -75.148148148152 64 48103 52617.4814814815 -4514.48148148148 65 47472 46043.3148148148 1428.68518518518 66 50497 47780.1481481482 2716.85185185185 67 40059 38036.8148148148 2022.18518518519 68 34149 33925.4814814815 223.518518518516 69 36860 37562.8148148148 -702.814814814815 70 46356 43706.8148148148 2649.18518518518 71 36577 36016.6481481481 560.351851851855 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.103677820602556 0.207355641205112 0.896322179397444 17 0.0921982834404402 0.184396566880880 0.90780171655956 18 0.442058442310998 0.884116884621996 0.557941557689002 19 0.460925178565330 0.921850357130659 0.53907482143467 20 0.549351395214822 0.901297209570356 0.450648604785178 21 0.574099166629647 0.851801666740705 0.425900833370353 22 0.669316228868049 0.661367542263903 0.330683771131951 23 0.641020586714981 0.717958826570038 0.358979413285019 24 0.818290023481946 0.363419953036109 0.181709976518054 25 0.829960869135443 0.340078261729114 0.170039130864557 26 0.802877378106639 0.394245243786722 0.197122621893361 27 0.942789617780222 0.114420764439557 0.0572103822197784 28 0.967782971437918 0.0644340571241633 0.0322170285620817 29 0.959083583265748 0.0818328334685047 0.0409164167342523 30 0.947085401109073 0.105829197781855 0.0529145988909275 31 0.938102884553635 0.123794230892729 0.0618971154463646 32 0.909532759328414 0.180934481343172 0.0904672406715862 33 0.870271314434697 0.259457371130606 0.129728685565303 34 0.824256333041598 0.351487333916803 0.175743666958402 35 0.788790830320734 0.422418339358532 0.211209169679266 36 0.813829124987639 0.372341750024723 0.186170875012361 37 0.777184505631736 0.445630988736527 0.222815494368264 38 0.780832969807531 0.438334060384938 0.219167030192469 39 0.88047384776566 0.239052304468679 0.119526152234340 40 0.834494324355582 0.331011351288836 0.165505675644418 41 0.880311775391213 0.239376449217575 0.119688224608787 42 0.896824267090981 0.206351465818038 0.103175732909019 43 0.894955474522744 0.210089050954513 0.105044525477256 44 0.858037734996396 0.283924530007208 0.141962265003604 45 0.797761542562943 0.404476914874114 0.202238457437057 46 0.893220311460625 0.213559377078751 0.106779688539376 47 0.849912023868411 0.300175952263177 0.150087976131589 48 0.789851620903545 0.420296758192909 0.210148379096455 49 0.749100875289016 0.501798249421967 0.250899124710984 50 0.803940346937344 0.392119306125312 0.196059653062656 51 0.917467531910788 0.165064936178424 0.0825324680892118 52 0.939126404807528 0.121747190384944 0.060873595192472 53 0.994105033809123 0.0117899323817539 0.00589496619087696 54 0.981905921617886 0.0361881567642288 0.0180940783821144 55 0.962122003444933 0.0757559931101333 0.0378779965550666 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 2 0.05 NOK 10% type I error level 5 0.125 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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