Paper Multiple regression (vertragende factor)

*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: Sat, 04 Dec 2010 14:53:18 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/04/t1291474996ed1vc4klio79mzj.htm/, Retrieved Sat, 04 Dec 2010 16:03:31 +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/2010/Dec/04/t1291474996ed1vc4klio79mzj.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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User-defined keywords:

Dataseries X:

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2,16 196,2 2,04 2,26 1,95 1,79 2,75 196,2 2,16 2,04 2,26 1,95 2,79 196,2 2,75 2,16 2,04 2,26 2,88 197 2,79 2,75 2,16 2,04 3,36 197,7 2,88 2,79 2,75 2,16 2,97 198 3,36 2,88 2,79 2,75 3,1 198,2 2,97 3,36 2,88 2,79 2,49 198,5 3,1 2,97 3,36 2,88 2,2 198,6 2,49 3,1 2,97 3,36 2,25 199,5 2,2 2,49 3,1 2,97 2,09 200 2,25 2,2 2,49 3,1 2,79 201,3 2,09 2,25 2,2 2,49 3,14 202,2 2,79 2,09 2,25 2,2 2,93 202,9 3,14 2,79 2,09 2,25 2,65 203,5 2,93 3,14 2,79 2,09 2,67 203,5 2,65 2,93 3,14 2,79 2,26 204 2,67 2,65 2,93 3,14 2,35 204,1 2,26 2,67 2,65 2,93 2,13 204,3 2,35 2,26 2,67 2,65 2,18 204,5 2,13 2,35 2,26 2,67 2,9 204,8 2,18 2,13 2,35 2,26 2,63 205,1 2,9 2,18 2,13 2,35 2,67 205,7 2,63 2,9 2,18 2,13 1,81 206,5 2,67 2,63 2,9 2,18 1,33 206,9 1,81 2,67 2,63 2,9 0,88 207,1 1,33 1,81 2,67 2,63 1,28 207,8 0,88 1,33 1,81 2,67 1,26 208 1,28 0,88 1,33 1,81 1,26 208,5 1,26 1,28 0,88 1,33 1,29 208,6 1,26 1,26 1,28 0,88 1,1 209 1,29 1,26 1,26 1,28 1,37 209,1 1,1 1,29 1,26 1,26 1,21 209,7 1,37 1,1 1,29 1,26 etc...

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 10 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 23.8465823459796 -0.120204819900504X[t] + 0.848503057329008Y1[t] -0.0494116230941216Y2[t] -0.0372156025966219Y3[t] + 0.111759361951538Y4[t] + 0.00711983032512751M1[t] + 0.090252044197324M2[t] + 0.0890447094819704M3[t] + 0.0592811754111258M4[t] + 0.0193491456647841M5[t] -0.052730500361094M6[t] -0.0528329084191568M7[t] -0.110932119089967M8[t] -0.0479723801614877M9[t] -0.0284545974149302M10[t] -0.0238767337808014M11[t] + 0.0487671735937128t + 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) 23.8465823459796 18.02241 1.3232 0.1918 0.0959 X -0.120204819900504 0.091846 -1.3088 0.196598 0.098299 Y1 0.848503057329008 0.140846 6.0243 0 0 Y2 -0.0494116230941216 0.183996 -0.2685 0.789383 0.394691 Y3 -0.0372156025966219 0.187414 -0.1986 0.843401 0.4217 Y4 0.111759361951538 0.145693 0.7671 0.446636 0.223318 M1 0.00711983032512751 0.241316 0.0295 0.97658 0.48829 M2 0.090252044197324 0.241418 0.3738 0.710103 0.355052 M3 0.0890447094819704 0.24148 0.3687 0.713874 0.356937 M4 0.0592811754111258 0.241086 0.2459 0.806772 0.403386 M5 0.0193491456647841 0.24128 0.0802 0.936403 0.468202 M6 -0.052730500361094 0.241588 -0.2183 0.82811 0.414055 M7 -0.0528329084191568 0.242444 -0.2179 0.82838 0.41419 M8 -0.110932119089967 0.244087 -0.4545 0.651452 0.325726 M9 -0.0479723801614877 0.255583 -0.1877 0.851873 0.425937 M10 -0.0284545974149302 0.255613 -0.1113 0.911809 0.455904 M11 -0.0238767337808014 0.254794 -0.0937 0.925714 0.462857 t 0.0487671735937128 0.036726 1.3279 0.19025 0.095125 Multiple Linear Regression - Regression Statistics Multiple R 0.850761679392294 R-squared 0.723795435122397 Adjusted R-squared 0.629885883064012 F-TEST (value) 7.70736756014342 F-TEST (DF numerator) 17 F-TEST (DF denominator) 50 p-value 7.36950378499301e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.397227911713991 Sum Squared Residuals 7.88950069223292 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2.16 2.06503848700781 0.0949615129921882 2 2.75 2.31597345954120 0.434026540458797 3 2.79 2.90105354224862 -0.111053542248617 4 2.88 2.79962765857777 0.0803723414222256 5 3.36 2.79016215663282 0.569837843367182 6 2.97 3.19807205911749 -0.228072059117494 7 3.1 2.86918305947392 0.230816940526081 8 2.49 2.94556036021541 -0.455560360215408 9 2.2 2.58941499352404 -0.389414993524039 10 2.25 2.28516663591720 -0.0351666359171965 11 2.09 2.37239402139617 -0.282394021396171 12 2.79 2.09315990653526 0.696840093464738 13 3.14 2.60844957727324 0.53155042272676 14 2.93 2.9301359892211 -0.000135989221098943 15 2.65 2.66616080630724 -0.0161608063072401 16 2.67 2.52316612308501 0.146833876914990 17 2.26 2.54963522582339 -0.289635225823392 18 2.35 2.15237868815163 0.197621311848368 19 2.13 2.24158959693702 -0.111589596937017 20 2.18 2.03459246149261 0.145407538507387 21 2.9 2.11438289535798 0.785617104642017 22 2.63 2.77330380099718 -0.143303800997180 23 2.67 2.46340591241895 0.20659408758105 24 1.81 2.46595995862964 -0.655959958629642 25 1.33 1.83259089366776 -0.502590893667762 26 0.88 1.54399819366581 -0.663998193665813 27 1.28 1.18578165461210 0.0942183453879027 28 1.26 1.46413122144688 -0.204131221446880 29 1.26 1.33923177239151 -0.0792317723915122 30 1.29 1.23970909651434 0.0502909034856609 31 1.1 1.31119508264220 -0.211195082642204 32 1.37 1.12490944675069 0.245090553249308 33 1.21 1.40188103312140 -0.191881033121398 34 1.74 1.31946762541547 0.420532374584535 35 1.76 1.78712216926081 -0.0271221692608111 36 1.48 1.87465701969435 -0.394657019694346 37 1.04 1.55820531189032 -0.518205311890321 38 1.62 1.31696386643990 0.303036133560099 39 1.49 1.85499070272643 -0.364990702726434 40 1.79 1.68405100122787 0.105948998772129 41 1.8 1.85906044053136 -0.059060440531364 42 1.58 1.87502700603360 -0.295027006033602 43 1.86 1.65073117494299 0.20926882505701 44 1.74 1.86290379360797 -0.122903793607965 45 1.59 1.83221866500494 -0.242218665004945 46 1.26 1.70808868319061 -0.448088683190613 47 1.13 1.48853650265187 -0.358536502651873 48 1.92 1.39924965519973 0.520750344800267 49 2.61 2.10335386599478 0.506646134005219 50 2.26 2.64145828175645 -0.381458281756449 51 2.41 2.25391657757943 0.156083422420573 52 2.26 2.41999846398438 -0.159998463984383 53 2.03 2.34822438045351 -0.318224380453514 54 2.86 2.05640838525711 0.80359161474289 55 2.55 2.79495967840951 -0.244959678409507 56 2.27 2.44933476671669 -0.179334766716689 57 2.26 2.22210241299163 0.0378975870083654 58 2.57 2.36397325447955 0.206026745520455 59 3.07 2.60854139427220 0.461458605727804 60 2.76 2.92697345994102 -0.166973459941018 61 2.51 2.62236186416608 -0.112361864166084 62 2.87 2.56147020937554 0.308529790624465 63 3.14 2.89809671652618 0.241903283473816 64 3.11 3.07902553167808 0.0309744683219196 65 3.16 2.9836860241674 0.1763139758326 66 2.47 2.99840476492582 -0.528404764925823 67 2.57 2.44234140759436 0.127658592405638 68 2.89 2.52269917121663 0.367300828783367 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.239305515310514 0.478611030621028 0.760694484689486 22 0.709995942185439 0.580008115629123 0.290004057814561 23 0.745708566472104 0.508582867055793 0.254291433527896 24 0.905363294328874 0.189273411342251 0.0946367056711256 25 0.88432928617743 0.231341427645139 0.115670713822570 26 0.824948768809542 0.350102462380916 0.175051231190458 27 0.767485798428946 0.465028403142107 0.232514201571054 28 0.761279145797394 0.477441708405212 0.238720854202606 29 0.741609104677522 0.516781790644956 0.258390895322478 30 0.65189598759817 0.696208024803661 0.348104012401830 31 0.592252742041663 0.815494515916674 0.407747257958337 32 0.531849539366352 0.936300921267296 0.468150460633648 33 0.488276870929098 0.976553741858196 0.511723129070902 34 0.547491060478786 0.905017879042428 0.452508939521214 35 0.565814582274851 0.868370835450298 0.434185417725149 36 0.485876386945527 0.971752773891054 0.514123613054473 37 0.409018949394446 0.818037898788892 0.590981050605554 38 0.529152764569511 0.941694470860978 0.470847235430489 39 0.481861936727357 0.963723873454713 0.518138063272643 40 0.421423883915846 0.84284776783169 0.578576116084154 41 0.331521717501641 0.663043435003282 0.668478282498359 42 0.242426037082259 0.484852074164519 0.75757396291774 43 0.238984083608754 0.477968167217507 0.761015916391246 44 0.176323190738659 0.352646381477319 0.82367680926134 45 0.104874854107923 0.209749708215846 0.895125145892077 46 0.0658968520463098 0.131793704092620 0.93410314795369 47 0.160526165645966 0.321052331291931 0.839473834354034 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 = 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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