Regression SWS

*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: Tue, 14 Dec 2010 18:51:23 +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/14/t1292352567boxnpmiu1ugwz9b.htm/, Retrieved Tue, 14 Dec 2010 19:49:37 +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/14/t1292352567boxnpmiu1ugwz9b.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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6654000 5712000 -999.0 3.3 38.6 645.0 3 5 3 1000 6600 6.3 8.3 4.5 42.0 3 1 3 3385 44500 -999.0 12.5 14.0 60.0 1 1 1 .920 5700 -999.0 16.5 -999.0 25.0 5 2 3 2547000 4603000 2.1 3.9 69.0 624.0 3 5 4 10550 179500 9.1 9.8 27.0 180.0 4 4 4 .023 .300 15.8 19.7 19.0 35.0 1 1 1 160000 169000 5.2 6.2 30.4 392.0 4 5 4 3300 25600 10.9 14.5 28.0 63.0 1 2 1 52160 440000 8.3 9.7 50.0 230.0 1 1 1 .425 6400 11.0 12.5 7.0 112.0 5 4 4 465000 423000 3.2 3.9 30.0 281.0 5 5 5 .550 2400 7.6 10.3 -999.0 -999.0 2 1 2 187100 419000 -999.0 3.1 40.0 365.0 5 5 5 .075 1200 6.3 8.4 3.5 42.0 1 1 1 3000 25000 8.6 8.6 50.0 28.0 2 2 2 .785 3500 6.6 10.7 6.0 42.0 2 2 2 .200 5000 9.5 10.7 10.4 120.0 2 2 2 1410 17500 4.8 6.1 34.0 -999.0 1 2 1 60000 81000 12.0 18.1 7.0 -999.0 1 1 1 529000 680000 -999.0 -999.0 28.0 400.0 5 5 5 27660 115000 3.3 3.8 20.0 148.0 5 5 5 .120 1000 11.0 14.4 3.9 16.0 3 1 2 207000 406000 -999.0 12.0 39.3 252.0 1 4 1 85000 325000 4.7 6.2 41.0 310.0 1 3 1 36330 119500 -999.0 13.0 16.2 63.0 1 1 1 .10 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation SWS[t] = -206.108738872165 -0.000232932176205793bowgth[t] + 0.000184784917571019brwght[t] + 0.782621969799936TS[t] + 0.205789801600120LIFESPAN[t] -0.200024940166107DRAAGTIJD[t] -10.4093369423387PRED[t] -93.0029961022486Exposure[t] + 115.585648380122OverallD[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) -206.108738872165 110.076253 -1.8724 0.06667 0.033335 bowgth -0.000232932176205793 0.000151 -1.5475 0.127696 0.063848 brwght 0.000184784917571019 0.000151 1.2222 0.227042 0.113521 TS 0.782621969799936 0.196093 3.9911 0.000203 0.000102 LIFESPAN 0.205789801600120 0.19829 1.0378 0.304065 0.152033 DRAAGTIJD -0.200024940166107 0.177845 -1.1247 0.265778 0.132889 PRED -10.4093369423387 90.933213 -0.1145 0.909296 0.454648 Exposure -93.0029961022486 58.258125 -1.5964 0.116347 0.058173 OverallD 115.585648380122 116.190226 0.9948 0.324355 0.162178 Multiple Linear Regression - Regression Statistics Multiple R 0.599733851324451 R-squared 0.359680692424459 Adjusted R-squared 0.263028721469661 F-TEST (value) 3.72140049366062 F-TEST (DF numerator) 8 F-TEST (DF denominator) 53 p-value 0.00161974327570036 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 364.6541894185 Sum Squared Residuals 7047551.92660455 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -968.52398394278 -30.4760160572204 2 6.3 16.424616588263 -10.1246165882630 3 -999 -185.838634686241 -813.16136531376 4 -999 -294.022783716410 -704.97721628359 5 2.1 -90.2862545777134 92.3862545777134 6 9.1 -149.482488567655 158.582488567655 7 15.8 -181.608587328947 197.408587328947 8 5.2 -323.760481119409 328.960481119409 9 10.9 -278.468040154102 289.368040154101 10 8.3 -152.904615167415 161.204615167415 11 11 -177.821780060988 188.821780060988 12 3.2 -222.372692454096 225.572692454096 13 7.6 -86.013846693013 93.6138466930129 14 -999 -173.750274890582 -825.249725109418 15 6.3 -194.820457740514 201.120457740514 16 8.6 -166.421941094802 175.021941094802 17 6.6 -179.907797441871 186.507797441871 18 9.5 -194.326954006107 203.826954006107 19 4.8 -72.4373554537112 77.2373554537112 20 12 22.4871257047958 -10.4871257047958 21 -999 -998.896748910838 -0.103251089161781 22 3.3 -152.948732295017 156.248732295017 23 11 -90.1117545267733 101.111754526773 24 -999 -479.065977865516 -519.934022134484 25 4.7 -388.403645881167 393.103645881167 26 -999 -179.409742685593 -819.590257314407 27 10.4 3.38923467138311 7.0107653286169 28 7.4 -79.6679440735037 87.0679440735037 29 2.1 -201.038150298478 203.138150298478 30 -999 -195.157894285487 -803.842105714513 31 -999 -1022.89960456270 23.8996045626970 32 7.7 21.5375796331292 -13.8375796331292 33 17.9 -183.423494240606 201.323494240606 34 6.1 8.97216962641719 -2.87216962641719 35 8.2 -407.079401267605 415.279401267605 36 8.4 -188.220269310851 196.620269310851 37 11.9 13.1965944564489 -1.29659445644886 38 10.8 10.4363048065329 0.363695193467061 39 13.8 -189.765084257695 203.565084257695 40 14.3 -212.212082820935 226.512082820935 41 -999 -977.9242788216 -21.0757211783997 42 15.2 -191.127494303643 206.327494303643 43 10 -159.811240136512 169.811240136512 44 11.9 -77.033149739753 88.9331497397531 45 6.5 -179.749689128334 186.249689128334 46 7.5 -139.511127302423 147.011127302423 47 -999 -175.516828929926 -823.483171070074 48 10.6 23.8655237867042 -13.2655237867042 49 7.4 -186.323592986199 193.723592986199 50 8.4 -262.595557887089 270.995557887089 51 5.7 -217.889206339597 223.589206339597 52 4.9 -113.088583419515 117.988583419515 53 -999 -155.021164738382 -843.978835261618 54 3.2 -148.946543846824 152.146543846824 55 -999 -186.558274244974 -812.441725755026 56 8.1 109.622507720936 -101.522507720936 57 11 -88.9454510565469 99.9454510565469 58 4.9 -16.0112164116517 20.9112164116517 59 13.2 -188.071910655574 201.271910655574 60 9.7 -83.6762179345 93.3762179345 61 12.8 -191.439475460568 204.239475460568 62 -999 -999.32115727188 0.321157271880114 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.801420455755839 0.397159088488322 0.198579544244161 13 0.781865730369561 0.436268539260877 0.218134269630439 14 0.959237618447872 0.0815247631042558 0.0407623815521279 15 0.9418610282082 0.116277943583602 0.058138971791801 16 0.905081036642236 0.189837926715528 0.0949189633577642 17 0.857868336867465 0.284263326265071 0.142131663132535 18 0.808668157137202 0.382663685725596 0.191331842862798 19 0.785405008972123 0.429189982055754 0.214594991027877 20 0.746476068906394 0.507047862187212 0.253523931093606 21 0.677312206939257 0.645375586121485 0.322687793060743 22 0.594147402450552 0.811705195098896 0.405852597549448 23 0.540745425010099 0.918509149979803 0.459254574989901 24 0.606598737374378 0.786802525251244 0.393401262625622 25 0.627927618883682 0.744144762232637 0.372072381116319 26 0.851383029076298 0.297233941847404 0.148616970923702 27 0.802852097280269 0.394295805439462 0.197147902719731 28 0.738279209454652 0.523441581090695 0.261720790545348 29 0.677653591845234 0.644692816309532 0.322346408154766 30 0.880427647460493 0.239144705079014 0.119572352539507 31 0.857307372495056 0.285385255009889 0.142692627504944 32 0.80315923980395 0.393681520392101 0.196840760196050 33 0.764005931623344 0.471988136753313 0.235994068376657 34 0.708342714546049 0.583314570907901 0.291657285453951 35 0.72598909257581 0.548021814848381 0.274010907424191 36 0.659879461759995 0.68024107648001 0.340120538240005 37 0.586540777572208 0.826918444855585 0.413459222427792 38 0.528175505564938 0.943648988870125 0.471824494435062 39 0.452592770177771 0.905185540355541 0.54740722982223 40 0.379294593686504 0.758589187373008 0.620705406313496 41 0.29227784570502 0.58455569141004 0.70772215429498 42 0.256177708072970 0.512355416145941 0.74382229192703 43 0.196460649587587 0.392921299175175 0.803539350412413 44 0.138363261329671 0.276726522659342 0.861636738670329 45 0.089698224355194 0.179396448710388 0.910301775644806 46 0.314003389603204 0.628006779206407 0.685996610396796 47 0.506391097171837 0.987217805656327 0.493608902828163 48 0.386105754017224 0.772211508034448 0.613894245982776 49 0.260571762622588 0.521143525245176 0.739428237377412 50 0.165803452502905 0.33160690500581 0.834196547497095 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 1 0.0256410256410256 OK

Charts produced by software:

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Parameters (Session):

par1 = 3 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 3 ; par2 = Do not include Seasonal 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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