Multiple regression (no seiz, no linear)

*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 14:10:34 +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/t1292940704j5z5gs2cf0d98gk.htm/, Retrieved Tue, 21 Dec 2010 15:12:05 +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/t1292940704j5z5gs2cf0d98gk.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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Aantal_vergunningen[t] = + 540.495850285012 + 1.28056921556156Inflatie[t] -0.298535876164629Aantal_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 1.28056921556156 3.322575 0.3854 0.701208 0.350604 Aantal_werklozen -0.298535876164629 0.137402 -2.1727 0.033511 0.016755 Multiple Linear Regression - Regression Statistics Multiple R 0.298051486820140 R-squared 0.0888346887956964 Adjusted R-squared 0.0603607728205618 F-TEST (value) 3.11986201242124 F-TEST (DF numerator) 2 F-TEST (DF denominator) 64 p-value 0.0509459515521572 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 -66.9552338988859 2 302 367.949282108039 -65.9492821080386 3 400 370.082246096642 29.9177539033575 4 392 372.969164277629 19.0308357223707 5 373 374.440237230727 -1.44023723072669 6 379 374.304170396 4.6958296040004 7 303 359.126058523640 -56.1260585236405 8 324 356.699354437857 -32.6993544378566 9 353 357.061918774799 -4.06191877479935 10 392 360.954900034696 31.0450999653041 11 327 366.158066851051 -39.1580668510508 12 376 365.970777247701 10.0292227522988 13 329 366.831972756314 -37.8319727563137 14 359 367.407438080917 -8.40743808091723 15 413 369.509204083826 43.490795916174 16 338 371.646173029015 -33.6461730290154 17 422 372.239239824759 49.7607601752408 18 390 371.829457675780 18.1705423242205 19 370 357.452517807840 12.5474821921597 20 367 355.699719627319 11.3002803726806 21 406 356.965901505927 49.034098494073 22 418 366.506243851039 51.4937561489605 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 -2.00540013775123 28 337 385.745392626117 -48.7453926261165 29 372 389.583146160805 -17.5831461608052 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 71.9640814108898 35 315 392.007426934802 -77.007426934802 36 337 391.005368812478 -54.0053688124777 37 386 390.583571793742 -4.58357179374162 38 352 393.500897138024 -41.5008971380244 39 383 398.939362192165 -15.9393621921650 40 439 399.527633208924 39.4723667910759 41 397 407.154289976877 -10.1542899768765 42 453 405.223002928576 47.7769970714238 43 363 390.437071734057 -27.4370717340565 44 365 387.979960484977 -22.9799604849767 45 474 392.8461743487 81.1538256513 46 373 395.48098364316 -22.4809836431601 47 403 394.651827787231 8.34817221276865 48 384 389.81923522099 -5.81923522099015 49 364 385.839828250191 -21.8398282501905 50 361 383.847726875298 -22.8477268752984 51 419 381.274573574419 37.7254264255812 52 352 380.950426313943 -28.950426313943 53 363 383.589240564988 -20.5892405649884 54 410 379.071994523653 30.9280054763470 55 361 363.103934694231 -2.10393469423118 56 383 361.27108822659 21.7289117734097 57 342 365.522628866844 -23.5226288668441 58 369 371.109966447867 -2.10996644786743 59 361 373.759163079281 -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 0.329540660308915 0.835229669845543 7 0.0753865584062715 0.150773116812543 0.924613441593728 8 0.0764686149286131 0.152937229857226 0.923531385071387 9 0.0894954346756279 0.178990869351256 0.910504565324372 10 0.530381378894852 0.939237242210297 0.469618621105148 11 0.451627764432454 0.903255528864908 0.548372235567546 12 0.370395643070928 0.740791286141856 0.629604356929072 13 0.315424047818473 0.630848095636947 0.684575952181527 14 0.257685365162716 0.515370730325432 0.742314634837284 15 0.386554705359432 0.773109410718865 0.613445294640568 16 0.361818460168447 0.723636920336894 0.638181539831553 17 0.406535349351307 0.813070698702614 0.593464650648693 18 0.332757352808869 0.665514705617739 0.66724264719113 19 0.280679954255701 0.561359908511402 0.719320045744299 20 0.223857318135084 0.447714636270168 0.776142681864916 21 0.202392012294157 0.404784024588314 0.797607987705843 22 0.172943040405587 0.345886080811175 0.827056959594413 23 0.199158075176179 0.398316150352359 0.80084192482382 24 0.191814015091252 0.383628030182504 0.808185984908748 25 0.228026031606925 0.45605206321385 0.771973968393075 26 0.298319247937555 0.596638495875111 0.701680752062445 27 0.241433793288156 0.482867586576312 0.758566206711844 28 0.233879490639145 0.46775898127829 0.766120509360855 29 0.181848372311226 0.363696744622452 0.818151627688774 30 0.194884569019358 0.389769138038716 0.805115430980642 31 0.214003054592807 0.428006109185615 0.785996945407193 32 0.214725453927499 0.429450907854999 0.7852745460725 33 0.170184364329920 0.340368728659839 0.82981563567008 34 0.340699655902341 0.681399311804682 0.659300344097659 35 0.432832945344266 0.865665890688532 0.567167054655734 36 0.438718245255283 0.877436490510566 0.561281754744717 37 0.407076443091343 0.814152886182686 0.592923556908657 38 0.393608085434985 0.78721617086997 0.606391914565015 39 0.373295517296601 0.746591034593203 0.626704482703399 40 0.437979269327501 0.875958538655002 0.562020730672499 41 0.3865147187772 0.7730294375544 0.6134852812228 42 0.441345179230363 0.882690358460727 0.558654820769637 43 0.452770815890492 0.905541631780984 0.547229184109508 44 0.503957300836658 0.992085398326685 0.496042699163342 45 0.615387839922479 0.769224320155043 0.384612160077521 46 0.61789226152272 0.76421547695456 0.38210773847728 47 0.540093348332611 0.919813303334778 0.459906651667389 48 0.476132960814538 0.952265921629076 0.523867039185462 49 0.476372646679756 0.952745293359513 0.523627353320244 50 0.503771712787127 0.992456574425745 0.496228287212873 51 0.463102211162133 0.926204422324266 0.536897788837867 52 0.452701074031977 0.905402148063954 0.547298925968023 53 0.387813042170589 0.775626084341179 0.612186957829411 54 0.416050637979579 0.832101275959158 0.583949362020421 55 0.376250101228071 0.752500202456142 0.623749898771929 56 0.398396428750547 0.796792857501094 0.601603571249453 57 0.343726297751245 0.687452595502489 0.656273702248755 58 0.423796968819522 0.847593937639043 0.576203031180478 59 0.441511229009554 0.883022458019108 0.558488770990446 60 0.325453597342428 0.650907194684857 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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