*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, 21 Dec 2010 14:12:32 +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/21/t1292940643gaeuncd8vi9obhj.htm/, Retrieved Tue, 21 Dec 2010 15:10:43 +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/21/t1292940643gaeuncd8vi9obhj.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:

» Textbox « » Textfile « » CSV «

300 2.26 591.000 302 2.57 589.000 400 3.07 584.000 392 2.76 573.000 373 2.51 567.000 379 2.87 569.000 303 3.14 621.000 324 3.11 629.000 353 3.16 628.000 392 2.47 612.000 327 2.57 595.000 376 2.89 597.000 329 2.63 593.000 359 2.38 590.000 413 1.69 580.000 338 1.96 574.000 422 2.19 573.000 390 1.87 573.000 370 1.60 620.000 367 1.63 626.000 406 1.22 620.000 418 1.21 588.000 346 1.49 566.000 350 1.64 557.000 330 1.66 561.000 318 1.77 549.000 382 1.82 532.000 337 1.78 526.000 372 1.28 511.000 422 1.29 499.000 428 1.37 555.000 426 1.12 565.000 396 1.51 542.000 458 2.24 527.000 315 2.94 510.000 337 3.09 514.000 386 3.46 517.000 352 3.64 508.000 383 4.39 493.000 439 4.15 490.000 397 5.21 469.000 453 5.80 478.000 363 5.91 528.000 365 5.39 534.000 474 5.46 518.000 373 4.72 506.000 403 3.14 502.000 384 2.63 516.000 364 2.32 528.000 361 1.93 533.000 419 0.62 536.000 352 0.60 537.000 363 -0.37 524.000 410 -1.10 536.000 361 -1.68 587.000 383 -0.78 597.000 342 -1.19 58 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Bouwvergunningen[t] = + 540.495850285012 + 1.28056921556155Inflatie[t] -0.29853587616463`Werklozen `[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) 540.495850285012 79.369398 6.8099 0 0 Inflatie 1.28056921556155 3.322575 0.3854 0.701208 0.350604 `Werklozen ` -0.29853587616463 0.137402 -2.1727 0.033511 0.016755 Multiple Linear Regression - Regression Statistics Multiple R 0.298051486820141 R-squared 0.088834688795697 Adjusted R-squared 0.0603607728205625 F-TEST (value) 3.11986201242126 F-TEST (DF numerator) 2 F-TEST (DF denominator) 64 p-value 0.0509459515521562 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 40.8557820560027 Sum Squared Residuals 106828.475354086 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 300 366.955233898886 -66.9552338988855 2 302 367.949282108039 -65.9492821080385 3 400 370.082246096642 29.9177539033575 4 392 372.969164277629 19.0308357223707 5 373 374.440237230727 -1.44023723072669 6 379 374.304170396000 4.69582960400042 7 303 359.126058523640 -56.1260585236405 8 324 356.699354437857 -32.6993544378566 9 353 357.061918774799 -4.06191877479926 10 392 360.954900034696 31.0450999653041 11 327 366.158066851051 -39.1580668510507 12 376 365.970777247701 10.0292227522988 13 329 366.831972756314 -37.8319727563137 14 359 367.407438080917 -8.4074380809172 15 413 369.509204083826 43.490795916174 16 338 371.646173029015 -33.6461730290154 17 422 372.239239824759 49.7607601752408 18 390 371.829457675780 18.1705423242205 19 370 357.45251780784 12.5474821921597 20 367 355.699719627319 11.3002803726806 21 406 356.965901505927 49.0340984940731 22 418 366.506243851039 51.4937561489606 23 346 373.432592507019 -27.4325925070185 24 350 376.311500774834 -26.3115007748344 25 330 375.142968654487 -45.1429686544871 26 318 378.866261782174 -60.8662617821745 27 382 384.005400137751 -2.00540013775126 28 337 385.745392626117 -48.7453926261166 29 372 389.583146160805 -17.5831461608053 30 422 393.178382366936 28.8216176330636 31 428 376.562818838962 51.4371811610379 32 426 373.257317773425 52.7426822265746 33 396 380.623064919281 15.3769350807191 34 458 386.03591858911 71.9640814108897 35 315 392.007426934802 -77.007426934802 36 337 391.005368812478 -54.0053688124778 37 386 390.583571793742 -4.58357179374165 38 352 393.500897138024 -41.5008971380244 39 383 398.939362192165 -15.9393621921650 40 439 399.527633208924 39.4723667910759 41 397 407.154289976877 -10.1542899768766 42 453 405.223002928576 47.7769970714238 43 363 390.437071734057 -27.4370717340565 44 365 387.979960484977 -22.9799604849767 45 474 392.8461743487 81.1538256512999 46 373 395.48098364316 -22.4809836431601 47 403 394.651827787231 8.34817221276859 48 384 389.81923522099 -5.8192352209902 49 364 385.839828250191 -21.8398282501906 50 361 383.847726875298 -22.8477268752984 51 419 381.274573574419 37.7254264255811 52 352 380.950426313943 -28.950426313943 53 363 383.589240564989 -20.5892405649885 54 410 379.071994523653 30.928005476347 55 361 363.103934694231 -2.10393469423119 56 383 361.27108822659 21.7289117734097 57 342 365.522628866844 -23.5226288668441 58 369 371.109966447867 -2.10996644786746 59 361 373.759163079282 -12.7591630792815 60 317 369.170669486396 -52.1706694863962 61 386 368.138995023175 17.8610049768248 62 318 369.734119941243 -51.7341199412432 63 407 374.545896902158 32.4541030978421 64 393 378.009071230147 14.9909287698526 65 404 383.088976903931 20.9110230960692 66 498 380.943998045570 117.056001954430 67 438 364.366851594063 73.633148405937 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.164770330154457 0.329540660308914 0.835229669845543 7 0.0753865584062703 0.150773116812541 0.92461344159373 8 0.0764686149286135 0.152937229857227 0.923531385071387 9 0.0894954346756272 0.178990869351254 0.910504565324373 10 0.530381378894851 0.939237242210298 0.469618621105149 11 0.451627764432452 0.903255528864903 0.548372235567548 12 0.370395643070927 0.740791286141854 0.629604356929073 13 0.315424047818472 0.630848095636943 0.684575952181528 14 0.257685365162718 0.515370730325435 0.742314634837282 15 0.386554705359433 0.773109410718866 0.613445294640567 16 0.361818460168446 0.723636920336893 0.638181539831554 17 0.40653534935131 0.81307069870262 0.59346465064869 18 0.332757352808869 0.665514705617739 0.667242647191131 19 0.280679954255701 0.561359908511401 0.7193200457443 20 0.223857318135083 0.447714636270167 0.776142681864917 21 0.202392012294158 0.404784024588315 0.797607987705842 22 0.172943040405584 0.345886080811167 0.827056959594416 23 0.199158075176179 0.398316150352357 0.800841924823821 24 0.191814015091250 0.383628030182499 0.80818598490875 25 0.228026031606926 0.456052063213851 0.771973968393074 26 0.298319247937557 0.596638495875114 0.701680752062443 27 0.241433793288158 0.482867586576316 0.758566206711842 28 0.233879490639144 0.467758981278287 0.766120509360857 29 0.181848372311225 0.36369674462245 0.818151627688775 30 0.194884569019358 0.389769138038716 0.805115430980642 31 0.214003054592809 0.428006109185618 0.785996945407191 32 0.214725453927499 0.429450907854999 0.7852745460725 33 0.170184364329918 0.340368728659837 0.829815635670082 34 0.340699655902341 0.681399311804681 0.65930034409766 35 0.432832945344266 0.865665890688533 0.567167054655734 36 0.438718245255283 0.877436490510566 0.561281754744717 37 0.407076443091343 0.814152886182686 0.592923556908657 38 0.393608085434984 0.787216170869967 0.606391914565017 39 0.373295517296603 0.746591034593206 0.626704482703397 40 0.437979269327501 0.875958538655002 0.562020730672499 41 0.3865147187772 0.7730294375544 0.6134852812228 42 0.441345179230365 0.88269035846073 0.558654820769635 43 0.452770815890492 0.905541631780983 0.547229184109508 44 0.503957300836656 0.992085398326688 0.496042699163344 45 0.615387839922477 0.769224320155046 0.384612160077523 46 0.617892261522718 0.764215476954563 0.382107738477282 47 0.540093348332611 0.919813303334779 0.459906651667389 48 0.476132960814541 0.952265921629082 0.523867039185459 49 0.476372646679757 0.952745293359514 0.523627353320243 50 0.503771712787128 0.992456574425745 0.496228287212872 51 0.463102211162133 0.926204422324265 0.536897788837867 52 0.452701074031978 0.905402148063957 0.547298925968022 53 0.38781304217059 0.77562608434118 0.61218695782941 54 0.41605063797958 0.83210127595916 0.58394936202042 55 0.376250101228069 0.752500202456138 0.623749898771931 56 0.398396428750548 0.796792857501096 0.601603571249452 57 0.343726297751244 0.687452595502489 0.656273702248755 58 0.423796968819523 0.847593937639046 0.576203031180477 59 0.441511229009554 0.883022458019108 0.558488770990446 60 0.325453597342428 0.650907194684856 0.674546402657572 61 0.44392295198481 0.88784590396962 0.55607704801519 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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