w7

*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, 17 Nov 2009 11:32:13 -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/17/t1258483027pb3na22b5gzz15z.htm/, Retrieved Tue, 17 Nov 2009 19:37:19 +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/17/t1258483027pb3na22b5gzz15z.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:

met dummies en lineaire trend

Dataseries X:

» Textbox « » Textfile « » CSV «

325412 285351 326011 286602 328282 283042 317480 276687 317539 277915 313737 277128 312276 277103 309391 275037 302950 270150 300316 267140 304035 264993 333476 287259 337698 291186 335932 292300 323931 288186 313927 281477 314485 282656 313218 280190 309664 280408 302963 276836 298989 275216 298423 274352 310631 271311 329765 289802 335083 290726 327616 292300 309119 278506 295916 269826 291413 265861 291542 269034 284678 264176 276475 255198 272566 253353 264981 246057 263290 235372 296806 258556 303598 260993 286994 254663 276427 250643 266424 243422 267153 247105 268381 248541 262522 245039 255542 237080 253158 237085 243803 225554 250741 226839 280445 247934 285257 248333 270976 246969 261076 245098 255603 246263 260376 255765 263903 264319 264291 268347 263276 273046 262572 273963 256167 267430 264221 271993 293860 292710 300713 295881 287224 293299

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 Werkl_vrouwen[t] = + 160892.571971533 + 0.64293510412937Werkl_mannen[t] + 1206.41823491207M1[t] -6088.32753259968M2[t] -10892.5884369475M3[t] -16353.9949846445M4[t] -16665.0020024433M5[t] -17115.4251054841M6[t] -19192.3291529422M7[t] -21189.6332953152M8[t] -22855.7574572353M9[t] -23544.7702170680M10[t] -15549.211059945M11[t] -860.874273343648t + 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) 160892.571971533 12480.25029 12.8918 0 0 Werkl_mannen 0.64293510412937 0.042045 15.2917 0 0 M1 1206.41823491207 2890.081795 0.4174 0.678222 0.339111 M2 -6088.32753259968 2887.887095 -2.1082 0.040257 0.020129 M3 -10892.5884369475 3058.029712 -3.562 0.000843 0.000422 M4 -16353.9949846445 3092.075957 -5.289 3e-06 1e-06 M5 -16665.0020024433 3067.28635 -5.4331 2e-06 1e-06 M6 -17115.4251054841 3049.075508 -5.6133 1e-06 0 M7 -19192.3291529422 3049.283698 -6.294 0 0 M8 -21189.6332953152 3069.31263 -6.9037 0 0 M9 -22855.7574572353 3076.478625 -7.4292 0 0 M10 -23544.7702170680 3128.904119 -7.5249 0 0 M11 -15549.211059945 3146.715651 -4.9414 1e-05 5e-06 t -860.874273343648 38.807193 -22.1834 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.986902480169372 R-squared 0.973976505364457 Adjusted R-squared 0.96692847556733 F-TEST (value) 138.19131493479 F-TEST (DF numerator) 13 F-TEST (DF denominator) 48 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4763.60754657105 Sum Squared Residuals 1089213929.17193 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 325412 344700.290831521 -19288.2908315212 2 326011 337348.982605932 -11337.9826059318 3 328282 329394.99845754 -1112.99845753988 4 317480 318986.865049757 -1506.86504975702 5 317539 318604.508066485 -1065.50806648545 6 313737 316787.220763151 -3050.22076315125 7 312276 313833.369064746 -1557.36906474627 8 309391 309646.886723898 -255.886723898323 9 302950 303977.864434754 -1027.86443475432 10 300316 300492.742738149 -176.742738148546 11 304035 306247.045953362 -2212.04595336215 12 333476 335250.975768508 -1774.97576850805 13 337698 338121.325883993 -423.325883992537 14 335932 330681.935549137 5250.06445086273 15 323931 322371.765353058 1559.23464694243 16 313927 311736.032918413 2190.96708158707 17 314485 311322.172115039 3162.82788496098 18 313218 308425.396771872 4792.60322812843 19 309664 305627.77830377 4036.22169622992 20 302963 300473.035696103 2489.96430389671 21 298989 296904.48239215 2084.51760785004 22 298423 294799.099429006 3623.90057099423 23 310631 299978.618661128 10652.3813388722 24 329765 326555.468458185 3209.53154181472 25 335083 327495.084455969 7587.91554403076 26 327616 320351.444269013 7264.55573098653 27 309119 305817.662264962 3301.33773503850 28 295916 293914.704740078 2001.29525992213 29 291413 290193.585761063 1219.41423893752 30 291542 290922.321470081 619.678529919447 31 284678 284861.164413418 -183.164413418378 32 276475 276230.714632828 244.285367171788 33 272566 272517.500930446 48.4990695542256 34 264981 266276.759377541 -1295.75937754149 35 263290 266541.682673699 -3251.68267369856 36 296806 296135.826914435 670.17308556478 37 303598 298048.203724767 5549.79627523308 38 286994 285822.804474773 1171.19552522739 39 276427 277573.070178481 -1146.07017848109 40 266424 266608.154970522 -184.154970522214 41 267153 267804.203667888 -651.203667888241 42 268381 267416.161101034 964.838898966398 43 262522 262226.824045571 295.175954429148 44 255542 254251.525136089 1290.47486391148 45 253158 251727.741376345 1430.25862365459 46 243803 242764.169657453 1038.83034254675 47 250741 250725.026150039 15.9738499611258 48 280445 278976.078958249 1468.92104175072 49 285257 279578.154026365 5678.84597363468 50 270976 270545.570503477 430.429496522534 51 261076 263677.50374596 -2601.50374595996 52 255603 258104.24232123 -2501.24232122998 53 260376 263041.530389525 -2665.53038952481 54 263903 267229.899893863 -3326.89989386303 55 264291 266881.864172494 -2590.86417249443 56 263276 267044.837811082 -3768.83781108166 57 262572 265107.410866305 -2535.41086630453 58 256167 259357.228797851 -3190.22879785095 59 264221 269425.626561773 -5204.62656177266 60 293860 297433.649900622 -3573.64990062217 61 300713 299817.941077385 895.05892261519 62 287224 290002.262597667 -2778.26259766740 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.716160753493636 0.567678493012727 0.283839246506364 18 0.997657295085947 0.00468540982810654 0.00234270491405327 19 0.994368276848613 0.0112634463027739 0.00563172315138693 20 0.98883256530601 0.0223348693879777 0.0111674346939888 21 0.991518133721738 0.016963732556525 0.0084818662782625 22 0.994611144523399 0.0107777109532023 0.00538885547660113 23 0.999944266860385 0.000111466279229489 5.57331396147444e-05 24 0.99984672868118 0.000306542637640555 0.000153271318820278 25 0.999948591761119 0.000102816477762124 5.1408238881062e-05 26 0.999992864120598 1.42717588030777e-05 7.13587940153883e-06 27 0.99999938043548 1.23912903904109e-06 6.19564519520543e-07 28 0.99999981169699 3.76606021410079e-07 1.88303010705040e-07 29 0.999999903965276 1.92069447634967e-07 9.60347238174836e-08 30 0.999999887345435 2.25309130005181e-07 1.12654565002590e-07 31 0.999999608712256 7.8257548837601e-07 3.91287744188004e-07 32 0.999999000893466 1.99821306758102e-06 9.99106533790509e-07 33 0.999996527617844 6.94476431136177e-06 3.47238215568089e-06 34 0.999992110324974 1.57793500510146e-05 7.88967502550731e-06 35 0.999999777266257 4.4546748635223e-07 2.22733743176115e-07 36 0.999999741761624 5.16476751117645e-07 2.58238375558823e-07 37 0.999999793511549 4.12976902057588e-07 2.06488451028794e-07 38 0.999999774808207 4.50383585569391e-07 2.25191792784695e-07 39 0.999998622720279 2.75455944259531e-06 1.37727972129765e-06 40 0.999990882678683 1.82346426333804e-05 9.11732131669019e-06 41 0.999973634250228 5.2731499543341e-05 2.63657497716705e-05 42 0.999902522853399 0.000194954293202126 9.74771466010628e-05 43 0.999620733936464 0.000758532127072915 0.000379266063536458 44 0.99827625770045 0.0034474845991001 0.00172374229955005 45 0.989564697165582 0.0208706056688355 0.0104353028344178 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 23 0.793103448275862 NOK 5% type I error level 28 0.96551724137931 NOK 10% type I error level 28 0.96551724137931 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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