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*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: Mon, 30 Nov 2009 12:16:26 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/30/t1259608667z4pw606r6dmkazf.htm/, Retrieved Mon, 30 Nov 2009 20:18:00 +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/2009/Nov/30/t1259608667z4pw606r6dmkazf.htm/}, year = {2009}, } @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 = {2009}, 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:

ws7 link 4 verbetering

Dataseries X:

» Textbox « » Textfile « » CSV «

286602 326011 277915 276687 283042 286602 283042 328282 286602 277915 276687 283042 276687 317480 283042 286602 277915 276687 277915 317539 276687 283042 286602 277915 277128 313737 277915 276687 283042 286602 277103 312276 277128 277915 276687 283042 275037 309391 277103 277128 277915 276687 270150 302950 275037 277103 277128 277915 267140 300316 270150 275037 277103 277128 264993 304035 267140 270150 275037 277103 287259 333476 264993 267140 270150 275037 291186 337698 287259 264993 267140 270150 292300 335932 291186 287259 264993 267140 288186 323931 292300 291186 287259 264993 281477 313927 288186 292300 291186 287259 282656 314485 281477 288186 292300 291186 280190 313218 282656 281477 288186 292300 280408 309664 280190 282656 281477 288186 276836 302963 280408 280190 282656 281477 275216 298989 276836 280408 280190 282656 274352 298423 275216 276836 280408 280190 271311 301631 274352 275216 276836 280408 289802 329765 271311 274352 275216 276836 290726 335083 289802 271311 274352 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -94720.9605158426 + 0.592327661009512X[t] + 0.895766698514853Y1[t] -0.417564650909098Y2[t] + 0.270154944508241Y3[t] -0.157692651463375Y4[t] + 12851.7566275878M1[t] + 8051.82719716753M2[t] + 15042.7024308202M3[t] + 19434.5168649013M4[t] + 18108.0290237541M5[t] + 18650.3443112222M6[t] + 17673.7431743616M7[t] + 20418.5457150754M8[t] + 17570.7707595111M9[t] + 18101.5818362902M10[t] + 20103.1448944525M11[t] + 520.055780191044t + 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) -94720.9605158426 31536.948962 -3.0035 0.004436 0.002218 X 0.592327661009512 0.167347 3.5395 0.000977 0.000489 Y1 0.895766698514853 0.161767 5.5374 2e-06 1e-06 Y2 -0.417564650909098 0.181553 -2.3 0.026368 0.013184 Y3 0.270154944508241 0.152407 1.7726 0.083382 0.041691 Y4 -0.157692651463375 0.108262 -1.4566 0.152496 0.076248 M1 12851.7566275878 4884.982635 2.6309 0.011774 0.005887 M2 8051.82719716753 5756.921631 1.3986 0.169094 0.084547 M3 15042.7024308202 6456.137052 2.33 0.024569 0.012285 M4 19434.5168649013 5730.215284 3.3916 0.001501 0.00075 M5 18108.0290237541 5142.977154 3.5209 0.001032 0.000516 M6 18650.3443112222 5874.301648 3.1749 0.00277 0.001385 M7 17673.7431743616 6624.66122 2.6679 0.01072 0.00536 M8 20418.5457150754 6768.681744 3.0166 0.004281 0.002141 M9 17570.7707595111 7007.172136 2.5075 0.016013 0.008007 M10 18101.5818362902 6211.4447 2.9142 0.005639 0.00282 M11 20103.1448944525 3929.6852 5.1157 7e-06 3e-06 t 520.055780191044 154.667602 3.3624 0.001632 0.000816 Multiple Linear Regression - Regression Statistics Multiple R 0.985124369674081 R-squared 0.970470023725756 Adjusted R-squared 0.958795381942916 F-TEST (value) 83.1263212848346 F-TEST (DF numerator) 17 F-TEST (DF denominator) 43 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3685.96446459631 Sum Squared Residuals 584212363.473471 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 286602 276438.642945773 10163.3570542271 2 283042 279617.252499239 3424.74750076138 3 276687 275247.433621603 1439.56637839672 4 277915 278141.373382996 -226.373382995589 5 277128 276504.908751473 623.09124852682 6 277103 274328.702490210 2774.29750979044 7 275037 273803.408116236 1233.59188376398 8 270150 271006.610572395 -856.610572394643 9 267140 263721.127294147 3418.87270585261 10 264993 265765.043609807 -772.043609807469 11 287259 284064.585417578 3194.41458242155 12 291186 287781.433907464 3404.56609253556 13 292300 294222.009188872 -1922.00918887193 14 288186 288545.555114005 -359.555114005374 15 281477 283530.202877907 -2053.20287790750 16 282656 284162.447686412 -1506.44768641232 17 280190 285175.999604018 -4985.99960401816 18 280408 280268.246807905 139.753192095442 19 276836 278443.978042471 -1607.97804247134 20 275216 275212.096768299 3.90323170146075 21 274352 273037.282874659 1314.71712534145 22 271311 274891.478715301 -3580.47871530065 23 289802 291840.020437621 -2038.02043762125 24 290726 293262.414173577 -2536.41417357664 25 292300 294632.52167068 -2332.52167067987 26 278506 285895.448752782 -7389.44875278206 27 269826 269906.153408989 -80.1534089887796 28 265861 270414.91988997 -4553.91988997006 29 269034 265782.918769614 3251.08123038630 30 264176 267107.7318633 -2931.73186329997 31 255198 256413.363304377 -1215.36330437660 32 253353 252831.601455222 521.39854477773 33 246057 246294.511344679 -237.51134467947 34 235372 238919.264884460 -3547.26488445952 35 258556 255685.95088083 2870.04911917025 36 260993 263674.977140295 -2681.97714029476 37 254663 257977.865645282 -3314.86564528209 38 250643 248699.275559666 1943.72444033395 39 243422 246329.776260896 -2907.77626089623 40 247105 244789.35411637 2315.64588363029 41 248541 250936.815124818 -2395.81512481807 42 245039 246960.304400980 -1921.30440098034 43 237080 240766.393450401 -3686.3934504008 44 237085 236759.207346437 325.792653562820 45 225554 231045.609529229 -5491.6095292287 46 226839 224276.948536537 2562.05146346283 47 247934 251615.493002461 -3681.49300246100 48 248333 250126.367393348 -1793.36739334811 49 246969 248753.536143747 -1784.53614374741 50 245098 242717.468074308 2380.53192569210 51 246263 242661.433830604 3601.56616939579 52 255765 251793.904924252 3971.09507574767 53 264319 260811.357750077 3507.64224992311 54 268347 266408.014437606 1938.98556239443 55 273046 267769.857086515 5276.14291348477 56 273963 273957.483857647 5.51614235262969 57 267430 266434.468957286 995.53104271411 58 271993 266655.264253895 5337.7357461048 59 292710 293054.950261510 -344.950261509565 60 295881 292273.807385316 3607.19261468396 61 293299 294108.424405646 -809.424405645755 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.30299238139651 0.60598476279302 0.69700761860349 22 0.188602494375657 0.377204988751313 0.811397505624343 23 0.127381706422838 0.254763412845677 0.872618293577162 24 0.145455893983202 0.290911787966404 0.854544106016798 25 0.0988623013466604 0.197724602693321 0.90113769865334 26 0.560425227352294 0.879149545295412 0.439574772647706 27 0.684016840304894 0.631966319390212 0.315983159695106 28 0.763017441054194 0.473965117891612 0.236982558945806 29 0.805051604310914 0.389896791378172 0.194948395689086 30 0.717187415728589 0.565625168542822 0.282812584271411 31 0.635143324167674 0.729713351664651 0.364856675832326 32 0.594351743316717 0.811296513366566 0.405648256683283 33 0.670698194771754 0.658603610456493 0.329301805228246 34 0.908981177926782 0.182037644146437 0.0910188220732183 35 0.914695650768441 0.170608698463118 0.085304349231559 36 0.91979165038678 0.16041669922644 0.08020834961322 37 0.87022671042163 0.259546579156741 0.129773289578371 38 0.816599734799673 0.366800530400654 0.183400265200327 39 0.685955294993127 0.628089410013746 0.314044705006873 40 0.675753780303632 0.648492439392737 0.324246219696368 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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