*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: Fri, 20 Nov 2009 12:32:49 -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/20/t12587458703f9b8cg8ughddh0.htm/, Retrieved Fri, 20 Nov 2009 20:38:02 +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/20/t12587458703f9b8cg8ughddh0.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:

Dataseries X:

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589 130 595 139 584 127 591 135 573 122 589 130 567 117 584 127 569 112 573 122 621 113 567 117 629 149 569 112 628 157 621 113 612 157 629 149 595 147 628 157 597 137 612 157 593 132 595 147 590 125 597 137 580 123 593 132 574 117 590 125 573 114 580 123 573 111 574 117 620 112 573 114 626 144 573 111 620 150 620 112 588 149 626 144 566 134 620 150 557 123 588 149 561 116 566 134 549 117 557 123 532 111 561 116 526 105 549 117 511 102 532 111 499 95 526 105 555 93 511 102 565 124 499 95 542 130 555 93 527 124 565 124 510 115 542 130 514 106 527 124 517 105 510 115 508 105 514 106 493 101 517 105 490 95 508 105 469 93 493 101 478 84 490 95 528 87 469 93 534 116 478 84 518 120 528 87 506 117 534 116 502 109 518 120 516 105 506 117 528 107 502 109 533 109 516 105 536 109 528 107 537 108 533 109 524 107 536 109 536 99 537 108 587 103 524 107 597 131 536 99 581 137 587 103 564 135 597 131

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 74.8461699959766 + 2.19376705976759X[t] + 0.583817180808853Y1[t] -0.784569819676212Y2[t] -10.6853024858533M1[t] -16.6925710430407M2[t] -10.2731451518584M3[t] -12.6971781321019M4[t] + 2.54561934032703M5[t] + 54.8658399069361M6[t] -12.0357994812021M7[t] -66.5419062293564M8[t] -60.0192868381692M9[t] -40.3833766595293M10[t] -10.1516715402114M11[t] + 0.150462479682088t + 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) 74.8461699959766 30.351477 2.466 0.017937 0.008968 X 2.19376705976759 0.332196 6.6038 0 0 Y1 0.583817180808853 0.145715 4.0066 0.000253 0.000127 Y2 -0.784569819676212 0.422976 -1.8549 0.070814 0.035407 M1 -10.6853024858533 6.26046 -1.7068 0.095425 0.047713 M2 -16.6925710430407 7.232645 -2.3079 0.026123 0.013061 M3 -10.2731451518584 7.597654 -1.3521 0.18374 0.09187 M4 -12.6971781321019 7.727253 -1.6432 0.107996 0.053998 M5 2.54561934032703 9.167188 0.2777 0.782647 0.391324 M6 54.8658399069361 8.582989 6.3924 0 0 M7 -12.0357994812021 13.813277 -0.8713 0.388653 0.194326 M8 -66.5419062293564 17.098992 -3.8916 0.000359 0.000179 M9 -60.0192868381692 6.978926 -8.6001 0 0 M10 -40.3833766595293 5.812018 -6.9483 0 0 M11 -10.1516715402114 6.160731 -1.6478 0.107037 0.053518 t 0.150462479682088 0.110129 1.3662 0.179311 0.089656 Multiple Linear Regression - Regression Statistics Multiple R 0.987071748987967 R-squared 0.974310637650165 Adjusted R-squared 0.964912090449005 F-TEST (value) 103.666089747359 F-TEST (DF numerator) 15 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.7464999763229 Sum Squared Residuals 2460.33873720999 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 589 587.817065405867 1.18293459413330 2 584 576.181968704528 7.8180312954722 3 573 574.538236513318 -1.53823651331768 4 567 560.730454268903 6.26954573109736 5 569 562.655739031659 6.34426096834063 6 621 617.740135151246 3.25986484875400 7 629 635.055055854422 -6.05505585442201 8 628 627.823471646475 0.176528353525246 9 612 610.922577455471 1.07742254452880 10 595 601.910903777899 -6.91090377789872 11 597 601.014325886281 -4.01432588628114 12 593 598.268430730348 -5.26843073034825 13 590 581.390553864184 8.60944613581628 14 580 572.733794042289 7.26620595771116 15 574 569.881617249855 4.11838275014532 16 573 556.757713401254 16.2422865987457 17 573 566.774188007267 6.22581199273327 18 620 623.208530391545 -3.20853039154525 19 626 629.01160885468 -3.01160885468073 20 620 614.473404623154 5.52659537684597 21 588 597.34938828947 -9.34938828946997 22 566 576.018933048368 -10.0189330483677 23 557 564.372083023717 -7.37208302371713 24 561 558.242416942586 2.75758305741416 25 549 553.277257385341 -4.27725738534084 26 532 542.085106410199 -10.0851064101989 27 526 527.702016433075 -1.70201643307534 28 511 513.629671597518 -2.62967159751786 29 499 514.87107796446 -15.8710779644599 30 555 556.550678638112 -1.55067863811170 31 565 556.292463150478 8.70753684952182 32 542 549.36232300526 -7.36232300525979 33 527 524.389309915649 2.61069008435057 34 510 506.296564959402 3.7034350405978 35 514 512.884990226418 1.11500977358164 36 517 518.12959348988 -1.12959348987961 37 508 516.99115058403 -8.9911505840297 38 493 504.895297629557 -11.8952976295568 39 490 493.048229014536 -3.04822901453604 40 469 480.768145961011 -11.7681459610114 41 478 479.373469750845 -1.37346975084486 42 528 527.734432818805 0.265567181194724 43 534 536.917983647975 -2.91798364797492 44 518 518.174557199987 -0.174557199987186 45 506 499.016716205797 6.98328379420343 46 502 488.773598214331 13.2264017856686 47 516 505.728600863583 10.2713991364166 48 528 524.359558837186 3.6404411628137 49 533 529.523972760579 3.47602723942096 50 536 529.103833213428 6.89616678657241 51 537 534.829900789216 2.17009921078374 52 524 532.114014771314 -8.11401477131376 53 536 531.325525245769 4.67447475423087 54 587 585.766223000292 1.23377699970823 55 597 593.722888492444 3.27711150755584 56 581 579.166243525124 1.83375647487575 57 564 565.322008133613 -1.32200813361284 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.0283768931458563 0.0567537862917125 0.971623106854144 20 0.0447921881496406 0.0895843762992813 0.95520781185036 21 0.309170099783677 0.618340199567354 0.690829900216323 22 0.225628221591002 0.451256443182004 0.774371778408998 23 0.265094039874138 0.530188079748275 0.734905960125862 24 0.324804866514263 0.649609733028526 0.675195133485737 25 0.369114569877968 0.738229139755936 0.630885430122032 26 0.363631817449975 0.72726363489995 0.636368182550025 27 0.283578874742693 0.567157749485386 0.716421125257307 28 0.40908881612458 0.81817763224916 0.59091118387542 29 0.647702336948023 0.704595326103953 0.352297663051977 30 0.829046626176074 0.341906747647852 0.170953373823926 31 0.919483447029695 0.161033105940611 0.0805165529703053 32 0.87464226715627 0.250715465687459 0.125357732843730 33 0.967230169489098 0.0655396610218032 0.0327698305109016 34 0.96307590606435 0.0738481878712986 0.0369240939356493 35 0.970080048462836 0.0598399030743276 0.0299199515371638 36 0.967809779436742 0.0643804411265154 0.0321902205632577 37 0.995888710644601 0.00822257871079732 0.00411128935539866 38 0.99544503969748 0.00910992060503854 0.00455496030251927 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.1 NOK 5% type I error level 2 0.1 NOK 10% type I error level 8 0.4 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') }

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

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