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 11:45:47 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/17/t1258483728oj87c4g6v15cej4.htm/, Retrieved Tue, 17 Nov 2009 19:49:00 +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/17/t1258483728oj87c4g6v15cej4.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:

gebruik van het verleden

Dataseries X:

» Textbox « » Textfile « » CSV «

317539 277915 317480 328282 326011 325412 313737 277128 317539 317480 328282 326011 312276 277103 313737 317539 317480 328282 309391 275037 312276 313737 317539 317480 302950 270150 309391 312276 313737 317539 300316 267140 302950 309391 312276 313737 304035 264993 300316 302950 309391 312276 333476 287259 304035 300316 302950 309391 337698 291186 333476 304035 300316 302950 335932 292300 337698 333476 304035 300316 323931 288186 335932 337698 333476 304035 313927 281477 323931 335932 337698 333476 314485 282656 313927 323931 335932 337698 313218 280190 314485 313927 323931 335932 309664 280408 313218 314485 313927 323931 302963 276836 309664 313218 314485 313927 298989 275216 302963 309664 313218 314485 298423 274352 298989 302963 309664 313218 310631 271311 298423 298989 302963 309664 329765 289802 310631 298423 298989 302963 335083 290726 329765 310631 298423 298989 327616 292300 335083 329765 310631 298423 309119 278506 327616 335083 329765 310631 295916 269826 309119 327616 335083 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkl_vrouwen[t] = + 82576.7903847561 + 0.436927705666708Werkl_mannen[t] + 0.317624637736993`Y_(t)min1`[t] -0.0756883129422179`Y_(t)min2`[t] + 0.058290675108108`Y_(t)min3`[t] + 0.0518235382082249`Y_(t)min4`[t] + 2258.83977242412M1[t] + 2068.42127400081M2[t] + 664.958110818836M3[t] -749.291296780444M4[t] -1634.68943047626M5[t] -2882.0562388897M6[t] + 6329.72868498853M7[t] + 24173.9764088581M8[t] + 21359.3703085145M9[t] + 12184.9433848399M10[t] + 5209.94835691973M11[t] -587.031622280736t + 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) 82576.7903847561 17389.584257 4.7486 2.6e-05 1.3e-05 Werkl_mannen 0.436927705666708 0.059474 7.3465 0 0 `Y_(t)min1` 0.317624637736993 0.136015 2.3352 0.024635 0.012317 `Y_(t)min2` -0.0756883129422179 0.135499 -0.5586 0.579556 0.289778 `Y_(t)min3` 0.058290675108108 0.133921 0.4353 0.665713 0.332857 `Y_(t)min4` 0.0518235382082249 0.092435 0.5606 0.578164 0.289082 M1 2258.83977242412 2484.182074 0.9093 0.368644 0.184322 M2 2068.42127400081 2880.192581 0.7182 0.476836 0.238418 M3 664.958110818836 3016.445979 0.2204 0.826647 0.413323 M4 -749.291296780444 2494.36901 -0.3004 0.765433 0.382717 M5 -1634.68943047626 2466.953743 -0.6626 0.511365 0.255682 M6 -2882.0562388897 2566.122012 -1.1231 0.268084 0.134042 M7 6329.72868498853 2760.03006 2.2934 0.027161 0.01358 M8 24173.9764088581 3487.647038 6.9313 0 0 M9 21359.3703085145 4934.907072 4.3282 9.8e-05 4.9e-05 M10 12184.9433848399 4576.33984 2.6626 0.011115 0.005558 M11 5209.94835691973 3290.293535 1.5834 0.121199 0.0606 t -587.031622280736 92.664886 -6.335 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.996429367559543 R-squared 0.99287148453511 Adjusted R-squared 0.989841865462533 F-TEST (value) 327.721558634855 F-TEST (DF numerator) 17 F-TEST (DF denominator) 40 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2577.79856971278 Sum Squared Residuals 265801818.640531 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 317539 317537.123592791 1.87640720927732 2 313737 317415.556800312 -3678.55680031212 3 312276 313690.099721821 -1414.09972182126 4 309391 310053.484712213 -662.484712212509 5 302950 305421.459245973 -2471.45924597340 6 300316 300162.253143796 153.746856203874 7 304035 307255.925002180 -3220.92500217969 8 333476 335097.421296075 -1621.42129607499 9 337698 341993.967749553 -4295.96774955263 10 335932 331912.19808799 4019.8019120096 11 323931 323581.037193645 349.962806354765 12 313927 312946.401538996 980.598461004077 13 314485 312980.023667893 1504.97633210677 14 313218 311268.463495098 1949.53650490186 15 309664 307723.480259018 1940.51974098216 16 302963 302642.636114952 320.363885047909 17 298989 298558.040291475 430.959708525252 18 298423 295318.257915500 3104.74208450051 19 310631 302160.537206146 8470.4627938537 20 329765 330838.468003424 -1073.46800342374 21 335083 332755.039111946 2327.96088805417 22 327616 324604.492857453 3011.50714254720 23 309119 309989.267349041 -870.267349041006 24 295916 296391.397983473 -475.397983472996 25 291413 293377.537518258 -1964.53751825767 26 291542 292090.339082405 -548.339082405024 27 284678 286630.855784570 -1952.85578457043 28 276475 277570.189422443 -1095.18942244345 29 272566 272979.835830728 -413.835830727965 30 264981 266943.467424127 -1962.46742412741 31 263290 267952.455754559 -4662.45575455911 32 296806 294723.429642659 2082.57035734135 33 303598 302515.368052771 1082.63194722850 34 286994 289117.043103967 -2123.04310396705 35 276427 275876.689234311 550.310765689405 36 266424 266957.871465538 -533.871465537757 37 267153 267245.610609244 -92.6106092441344 38 268381 266607.811636872 1773.18836312798 39 262522 262291.361349818 230.638650182075 40 255542 254382.767759199 1159.23224080057 41 253158 251248.320804262 1909.67919573798 42 243803 243868.910526958 -65.9105269580253 43 250741 249553.675359745 1187.32464025467 44 280445 278438.932050416 2006.06794958412 45 285257 283452.368625774 1804.63137422563 46 270976 272294.716302407 -1318.71630240657 47 261076 261106.006223003 -30.0062230031652 48 255603 255574.329011993 28.6709880066736 49 260376 259825.704611814 550.295388185758 50 263903 263398.828985313 504.171014687295 51 264291 263095.202884773 1195.79711522745 52 263276 262997.921991193 278.078008807477 53 262572 262027.343827562 544.656172438131 54 256167 257397.110989619 -1230.11098961896 55 264221 265995.406677370 -1774.40667736958 56 293860 295253.749007427 -1393.74900742674 57 300713 301632.256459956 -919.256459955673 58 287224 290813.549648183 -3589.54964818318 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.718456741967983 0.563086516064033 0.281543258032017 22 0.991661052423916 0.0166778951521685 0.00833894757608427 23 0.99704147167013 0.00591705665974006 0.00295852832987003 24 0.997853594522693 0.00429281095461376 0.00214640547730688 25 0.994828214321536 0.0103435713569271 0.00517178567846356 26 0.995336207017345 0.0093275859653101 0.00466379298265505 27 0.990182794137493 0.0196344117250146 0.00981720586250732 28 0.982736224733266 0.0345275505334685 0.0172637752667343 29 0.979722069634808 0.0405558607303832 0.0202779303651916 30 0.961814919971406 0.0763701600571884 0.0381850800285942 31 0.999610873794321 0.000778252411358316 0.000389126205679158 32 0.999680180217015 0.000639639565968997 0.000319819782984499 33 0.999609800411543 0.000780399176914278 0.000390199588457139 34 0.998310550053854 0.00337889989229185 0.00168944994614592 35 0.993655078114139 0.0126898437717221 0.00634492188586105 36 0.97707776996115 0.0458444600777015 0.0229222300388507 37 0.93199197819482 0.136016043610359 0.0680080218051796 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.411764705882353 NOK 5% type I error level 14 0.823529411764706 NOK 10% type I error level 15 0.88235294117647 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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