*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 12:11:22 -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/t1258745130bpezakk0i5yg7pz.htm/, Retrieved Fri, 20 Nov 2009 20:25:42 +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/t1258745130bpezakk0i5yg7pz.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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573 122 589 130 17,9 2849,27 567 117 584 127 17,4 2921,44 569 112 573 122 16,7 2981,85 621 113 567 117 16 3080,58 629 149 569 112 16,6 3106,22 628 157 621 113 19,1 3119,31 612 157 629 149 17,8 3061,26 595 147 628 157 17,2 3097,31 597 137 612 157 18,6 3161,69 593 132 595 147 16,3 3257,16 590 125 597 137 15,1 3277,01 580 123 593 132 19,2 3295,32 574 117 590 125 17,7 3363,99 573 114 580 123 19,1 3494,17 573 111 574 117 18 3667,03 620 112 573 114 17,5 3813,06 626 144 573 111 17,8 3917,96 620 150 620 112 21,1 3895,51 588 149 626 144 17,2 3801,06 566 134 620 150 19,4 3570,12 557 123 588 149 19,8 3701,61 561 116 566 134 17,6 3862,27 549 117 557 123 16,2 3970,1 532 111 561 116 19,5 4138,52 526 105 549 117 19,9 4199,75 511 102 532 111 20 4290,89 499 95 526 105 17,3 4443,91 555 93 511 102 18,9 4502,64 565 124 499 95 18,6 4356,98 542 130 555 93 21,4 4591,27 527 124 565 124 18,6 4696,96 510 115 542 130 19,8 4621,4 514 106 527 124 20,8 4562,84 517 105 510 115 19,6 4202,52 508 105 514 106 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 63.2419011471966 + 1.16232044459361X[t] + 0.780421649089665Y1[t] -0.792732218814561Y2[t] + 2.1038959924636Y3[t] -0.00841697355310678Y4[t] + 2.76698178211044M1[t] + 1.94119087812141M2[t] + 15.8696883851779M3[t] + 71.1133254322051M4[t] + 35.4385310945394M5[t] -25.7506260674336M6[t] -19.305462552463M7[t] -9.41876002842492M8[t] + 12.5861140469189M9[t] + 26.7813873646183M10[t] + 19.3890177289188M11[t] -0.268119756372126t + 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) 63.2419011471966 52.569279 1.203 0.23661 0.118305 X 1.16232044459361 0.35631 3.2621 0.002381 0.00119 Y1 0.780421649089665 0.130898 5.9621 1e-06 0 Y2 -0.792732218814561 0.3909 -2.028 0.04981 0.024905 Y3 2.1038959924636 0.867991 2.4239 0.020362 0.010181 Y4 -0.00841697355310678 0.002094 -4.0189 0.000276 0.000138 M1 2.76698178211044 4.622443 0.5986 0.553089 0.276544 M2 1.94119087812141 4.867364 0.3988 0.69232 0.34616 M3 15.8696883851779 6.404088 2.4781 0.017898 0.008949 M4 71.1133254322051 5.929281 11.9936 0 0 M5 35.4385310945394 12.032187 2.9453 0.005551 0.002776 M6 -25.7506260674336 12.556784 -2.0507 0.047426 0.023713 M7 -19.305462552463 8.113687 -2.3794 0.022612 0.011306 M8 -9.41876002842492 8.46238 -1.113 0.272881 0.13644 M9 12.5861140469189 8.935126 1.4086 0.167299 0.083649 M10 26.7813873646183 6.758611 3.9626 0.000325 0.000163 M11 19.3890177289188 5.787196 3.3503 0.001868 0.000934 t -0.268119756372126 0.15773 -1.6999 0.097549 0.048775 Multiple Linear Regression - Regression Statistics Multiple R 0.991847531674969 R-squared 0.983761526089728 Adjusted R-squared 0.976300605644468 F-TEST (value) 131.855249403537 F-TEST (DF numerator) 17 F-TEST (DF denominator) 37 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.40981784371308 Sum Squared Residuals 1520.17329721456 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 573 577.834528310712 -4.8345283107124 2 567 567.74570286082 -0.745702860820217 3 569 568.992304775555 0.00769522444461956 4 621 622.107538716716 -1.10753871671601 5 629 634.579191413877 -5.5791914138769 6 628 627.359233383478 0.640766616522358 7 612 608.994830982024 3.0051690179756 8 595 598.30216041208 -3.30216041208038 9 597 598.332533531781 -1.33253353178128 10 593 595.46570977598 -2.46570977598044 11 590 586.465390642093 3.53460935790709 12 580 573.797445548672 6.20255445132768 13 574 568.796407928695 5.20359207130536 14 573 559.846516653591 13.1534833464093 15 573 566.324552848744 6.6754471512564 16 620 621.779086947154 -1.77908694715427 17 626 625.156852008574 0.843147991426047 18 620 613.692400877587 6.30759912241258 19 588 590.612011865547 -2.61201186554723 20 566 579.929251812658 -13.9292518126580 21 557 564.434531233533 -7.4345312335326 22 561 558.966306530488 2.03369346951169 23 549 550.311340500483 -1.31134050048295 24 532 537.876362565007 -5.87636256500654 25 526 523.569697021621 2.43030297837865 26 511 509.921316935459 1.07868306454139 27 499 508.550830519589 -9.55083051958893 28 555 554.745483572323 0.254516427676753 29 565 551.61341657332 13.3865834266802 30 542 546.338035154327 -4.33803515432753 31 527 521.990175239284 5.00982476071635 32 510 501.602444476286 8.39755552371353 33 514 508.525177334192 5.47482266580849 34 517 515.665561105431 1.33443889456896 35 508 513.473002888583 -5.47300288858287 36 493 495.550991464417 -2.55099146441657 37 490 491.879508483902 -1.87950848390173 38 469 476.67292188871 -7.67292188871048 39 478 478.687651256193 -0.687651256192748 40 528 529.69800806831 -1.69800806830980 41 534 542.644003104468 -8.64400310446758 42 518 521.357515066629 -3.35751506662908 43 506 509.583190652468 -3.58319065246789 44 502 493.166143298975 8.83385670102484 45 516 512.707757900495 3.29224209950538 46 528 528.9024225881 -0.902422588100215 47 533 529.750265968841 3.24973403115873 48 536 533.775200421905 2.22479957809542 49 537 537.91985825507 -0.919858255069904 50 524 529.81354166142 -5.81354166141999 51 536 532.444660599919 3.55533940008066 52 587 582.669882695497 4.33011730450333 53 597 597.006536899762 -0.00653689976171934 54 581 580.252815517978 0.747184482021662 55 564 565.819791260677 -1.81979126067682 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.198529094071920 0.397058188143841 0.80147090592808 22 0.738814735487518 0.522370529024963 0.261185264512482 23 0.837092289114336 0.325815421771328 0.162907710885664 24 0.801741935672868 0.396516128654264 0.198258064327132 25 0.719802626335485 0.56039474732903 0.280197373664515 26 0.675813552209365 0.64837289558127 0.324186447790635 27 0.840354213785654 0.319291572428693 0.159645786214346 28 0.865954608931249 0.268090782137502 0.134045391068751 29 0.935658563881482 0.128682872237035 0.0643414361185176 30 0.884343621115744 0.231312757768513 0.115656378884256 31 0.987284834403505 0.0254303311929904 0.0127151655964952 32 0.98166039153787 0.0366792169242601 0.0183396084621300 33 0.99973115684092 0.000537686318161881 0.000268843159080941 34 0.998080932662638 0.00383813467472402 0.00191906733736201 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.142857142857143 NOK 5% type I error level 4 0.285714285714286 NOK 10% type I error level 4 0.285714285714286 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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Software written by Ed van Stee & Patrick Wessa

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