metallurgie

*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, 20 Dec 2008 02:26:47 -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/20/t12297653866nb4id422fg0k40.htm/, Retrieved Sat, 20 Dec 2008 10:29:46 +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/20/t12297653866nb4id422fg0k40.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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99.9 11554.5 98.6 13182.1 107.2 14800.1 95.7 12150.7 93.7 14478.2 106.7 13253.9 86.7 12036.8 95.3 12653.2 99.3 14035.4 101.8 14571.4 96 15400.9 91.7 14283.2 95.3 14485.3 96.6 14196.3 107.2 15559.1 108 13767.4 98.4 14634 103.1 14381.1 81.1 12509.9 96.6 12122.3 103.7 13122.3 106.6 13908.7 97.6 13456.5 87.6 12441.6 99.4 12953 98.5 13057.2 105.2 14350.1 104.6 13830.2 97.5 13755.5 108.9 13574.4 86.8 12802.6 88.9 11737.3 110.3 13850.2 114.8 15081.8 94.6 13653.3 92 14019.1 93.8 13962 93.8 13768.7 107.6 14747.1 101 13858.1 95.4 13188 96.5 13693.1 89.2 12970 87.1 11392.8 110.5 13985.2 110.8 14994.7 104.2 13584.7 88.9 14257.8 89.8 13553.4 90 14007.3 93.9 16535.8 91.3 14721.4 87.8 13664.6 99.7 16405.9 73.5 13829.4 79.2 13735.6 96.9 15870.5 95.2 15962.4 95.6 15744.1 89.7 16083.7 92.8 14863.9 88 15533.1 101.1 17473.1 92.7 15925.5 95.8 15573.7 103.8 17495 81.8 14155.8 87.1 14913.9 105.9 17250.4 108.1 15879.8 102.6 17647.8 93.7 17749.9

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation metallurgie[t] = + 92.9526439898678 + 8.54442296827058e-05Invoer[t] + 3.72544946376561M1[t] + 2.86113152163797M2[t] + 12.2588395462256M3[t] + 7.65949447462836M4[t] + 3.61414372741981M5[t] + 12.0003036185750M6[t] -7.69738175649247M7[t] -1.73633284616141M8[t] + 13.5851964905219M9[t] + 15.4221288822887M10[t] + 7.73791217261122M11[t] -0.0861362210965826t + 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) 92.9526439898678 9.189101 10.1155 0 0 Invoer 8.54442296827058e-05 0.000681 0.1255 0.900525 0.450263 M1 3.72544946376561 2.882194 1.2926 0.201284 0.100642 M2 2.86113152163797 2.844289 1.0059 0.318632 0.159316 M3 12.2588395462256 2.931559 4.1817 9.9e-05 5e-05 M4 7.65949447462836 2.83917 2.6978 0.009125 0.004563 M5 3.61414372741981 2.82918 1.2775 0.206532 0.103266 M6 12.0003036185750 2.824818 4.2482 7.9e-05 4e-05 M7 -7.69738175649247 3.008944 -2.5582 0.013157 0.006578 M8 -1.73633284616141 3.094438 -0.5611 0.576881 0.288441 M9 13.5851964905219 2.816205 4.8239 1.1e-05 5e-06 M10 15.4221288822887 2.825188 5.4588 1e-06 1e-06 M11 7.73791217261122 2.816939 2.7469 0.008001 0.004 t -0.0861362210965826 0.039747 -2.1671 0.034346 0.017173 Multiple Linear Regression - Regression Statistics Multiple R 0.844922695509908 R-squared 0.713894361387728 Adjusted R-squared 0.649767235491874 F-TEST (value) 11.1324864698775 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 2.00326422117314e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.87563260938023 Sum Squared Residuals 1378.76401381581 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 97.5792225844055 2.32077741559453 2 98.6 96.767837449413 1.83216255058700 3 107.2 106.217658016531 0.982341983469345 4 95.7 101.305800781715 -5.60580078171548 5 93.7 97.3731852579969 -3.67318525799684 6 106.7 105.568599557655 1.13140044234510 7 86.7 85.680783789544 1.01921621045597 8 95.3 91.608364301955 3.69163569804506 9 99.3 106.961858431809 -7.66185843180914 10 101.8 108.758452709589 -6.95845270958922 11 96 101.058975767337 -5.058975767337 12 91.7 93.1394263581128 -1.43942635811282 13 95.3 96.7960078796007 -1.49600787960073 14 96.6 95.8208603339982 0.779139666001797 15 107.2 105.248875533701 1.95112446629916 16 108 100.410303814685 7.58969618531548 17 98.4 96.3528628158224 2.04713718417759 18 103.1 104.631277640194 -1.53127764019425 19 81.1 84.687572801448 -3.58757280144793 20 96.6 90.5293673072574 6.0706326927426 21 103.7 105.850204652527 -2.15020465252687 22 106.6 107.668194165420 -1.06819416541951 23 97.6 99.859203353983 -2.25920335398295 24 87.6 91.9484376115702 -4.34843761157017 25 99.4 95.631447033299 3.76855296670108 26 98.5 94.6898961588076 3.81010384119236 27 105.2 104.111938806855 1.08806119314454 28 104.6 99.3820350591496 5.2179649408504 29 97.5 95.2441654068872 2.25583459311283 30 108.9 103.528715126950 5.37128487304979 31 86.8 83.678947674317 3.12105232568293 32 88.9 89.4628366256706 -0.562836625670561 33 110.3 104.878764854154 5.42123514584608 34 114.8 106.734794138101 8.0652058618987 35 94.6 98.8423841252255 -4.24238412522552 36 92 91.0495912307356 0.950408769264363 37 93.8 94.6840256078898 -0.884025607889789 38 93.8 93.7170550750679 0.0829449249321074 39 107.6 103.112225512880 4.48777448711949 40 101 98.3507842999988 2.64921570000124 41 95.4 94.1620411533832 1.23795884661676 42 96.5 102.505222703855 -6.00522270385456 43 89.2 82.659616385207 6.54038361479304 44 87.1 88.3997664353859 -1.29976643538589 45 110.5 103.856665172002 6.6433348279979 46 110.8 105.693717292537 5.10628270746305 47 104.2 97.8028879979103 6.39711200208971 48 88.9 90.0363521152019 -1.13635211520190 49 89.8 93.6154784424824 -3.81547844248245 50 90 92.7038074151112 -2.70380741511119 51 93.9 102.231424953355 -8.33142495335496 52 91.3 97.3909136503248 -6.09091365032485 53 87.8 93.169129220091 -5.36912922009104 54 99.7 101.703381156979 -2.00338115697881 55 73.5 81.6994125030373 -8.19941250303729 56 79.2 87.5663105235275 -8.36631052352753 57 96.9 102.984118525064 -6.0841185250639 58 95.2 104.742767020442 -9.5427670204419 59 95.6 96.9537616143281 -1.35376161432814 60 89.7 89.1587300810206 0.541269918979431 61 92.8 92.6938184523226 0.106181547677361 62 88 91.800543567602 -3.80054356760207 63 101.1 101.277877176678 -0.177877176677580 64 92.7 96.4601623941268 -3.76016239412679 65 95.8 92.2986161458193 3.50138385418070 66 103.8 100.762803814367 3.03719618563274 67 81.8 80.6936668464467 1.10633315355327 68 87.1 86.6333548062037 0.466645193796322 69 105.9 102.068388364444 3.83161163555592 70 108.1 103.702074673911 4.39792532608888 71 102.6 96.0827871412161 6.51721285878389 72 93.7 88.2674626033589 5.4325373966411 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.627757001540149 0.744485996919702 0.372242998459851 18 0.549041818404455 0.90191636319109 0.450958181595545 19 0.548278899752422 0.903442200495157 0.451721100247578 20 0.424798915903103 0.849597831806205 0.575201084096897 21 0.331485932727532 0.662971865455063 0.668514067272468 22 0.251230404846646 0.502460809693293 0.748769595153354 23 0.195100147314948 0.390200294629895 0.804899852685052 24 0.208325106248194 0.416650212496388 0.791674893751806 25 0.141628241696347 0.283256483392695 0.858371758303653 26 0.0942061275674577 0.188412255134915 0.905793872432542 27 0.0678426483941449 0.135685296788290 0.932157351605855 28 0.0473732605037592 0.0947465210075184 0.95262673949624 29 0.027704361164101 0.055408722328202 0.972295638835899 30 0.0215664281724567 0.0431328563449134 0.978433571827543 31 0.0125218192469004 0.0250436384938007 0.9874781807531 32 0.02311645289664 0.04623290579328 0.97688354710336 33 0.0326290257332759 0.0652580514665518 0.967370974266724 34 0.0574744281757358 0.114948856351472 0.942525571824264 35 0.056729525140751 0.113459050281502 0.94327047485925 36 0.0359239951611047 0.0718479903222093 0.964076004838895 37 0.0388899262394774 0.0777798524789547 0.961110073760523 38 0.0347209042147904 0.0694418084295807 0.96527909578521 39 0.0337609290825176 0.0675218581650351 0.966239070917482 40 0.0348658524910555 0.069731704982111 0.965134147508945 41 0.0238018258621795 0.0476036517243591 0.97619817413782 42 0.0464041730504005 0.092808346100801 0.9535958269496 43 0.124152795543628 0.248305591087256 0.875847204456372 44 0.112224817371336 0.224449634742672 0.887775182628664 45 0.197021332660211 0.394042665320422 0.802978667339789 46 0.880763069916556 0.238473860166887 0.119236930083444 47 0.952991731512918 0.0940165369741641 0.0470082684870821 48 0.935971093046607 0.128057813906786 0.0640289069533928 49 0.925892805438253 0.148214389123493 0.0741071945617467 50 0.98027945196144 0.0394410960771193 0.0197205480385596 51 0.9728313526313 0.0543372947373999 0.0271686473687000 52 0.990651438700622 0.0186971225987564 0.0093485612993782 53 0.983475017589042 0.0330499648219153 0.0165249824109577 54 0.983821468501624 0.0323570629967528 0.0161785314983764 55 0.973258773160998 0.0534824536780036 0.0267412268390018 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 8 0.205128205128205 NOK 10% type I error level 20 0.512820512820513 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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