Model 4

*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: Wed, 18 Nov 2009 12:08:24 -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/18/t1258571393u50manp7b841e67.htm/, Retrieved Wed, 18 Nov 2009 20:10:05 +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/2009/Nov/18/t1258571393u50manp7b841e67.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:

» Textbox « » Textfile « » CSV «

537 0 544 555 561 562 543 0 537 544 555 561 594 0 543 537 544 555 611 0 594 543 537 544 613 0 611 594 543 537 611 0 613 611 594 543 594 0 611 613 611 594 595 0 594 611 613 611 591 0 595 594 611 613 589 0 591 595 594 611 584 0 589 591 595 594 573 0 584 589 591 595 567 0 573 584 589 591 569 0 567 573 584 589 621 0 569 567 573 584 629 0 621 569 567 573 628 0 629 621 569 567 612 0 628 629 621 569 595 0 612 628 629 621 597 0 595 612 628 629 593 0 597 595 612 628 590 0 593 597 595 612 580 0 590 593 597 595 574 0 580 590 593 597 573 0 574 580 590 593 573 0 573 574 580 590 620 0 573 573 574 580 626 0 620 573 573 574 620 0 626 620 573 573 588 0 620 626 620 573 566 0 588 620 626 620 557 0 566 588 620 626 561 0 557 566 588 620 549 0 561 557 566 588 532 0 549 561 557 566 526 0 532 549 561 557 511 0 526 532 549 561 499 0 511 526 532 549 555 0 499 511 526 532 565 0 555 499 511 526 542 0 565 555 499 511 527 1 542 565 555 499 510 1 527 542 565 555 514 1 510 527 542 565 517 1 514 51 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] = + 29.2336583297075 + 5.23704846344995X[t] + 1.06338606720762Y1[t] -0.0515482671707487Y2[t] -0.0346340509314161Y3[t] -0.0281387763492694Y4[t] -4.86619693288056M1[t] + 6.11414942514553M2[t] + 55.4277308752082M3[t] + 10.1263582422227M4[t] -6.02994002777538M5[t] -10.5865832384230M6[t] -8.0507839315179M7[t] + 10.1382562337091M8[t] + 8.4583139369364M9[t] -0.749293718734123M10[t] -5.88400784734467M11[t] -0.247013195172507t + 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) 29.2336583297075 38.403661 0.7612 0.451104 0.225552 X 5.23704846344995 5.284544 0.991 0.327789 0.163894 Y1 1.06338606720762 0.157471 6.7529 0 0 Y2 -0.0515482671707487 0.228578 -0.2255 0.822755 0.411377 Y3 -0.0346340509314161 0.22941 -0.151 0.880778 0.440389 Y4 -0.0281387763492694 0.188687 -0.1491 0.88222 0.44111 M1 -4.86619693288056 5.010833 -0.9711 0.337466 0.168733 M2 6.11414942514553 5.226909 1.1697 0.249203 0.124601 M3 55.4277308752082 5.462501 10.147 0 0 M4 10.1263582422227 10.905567 0.9285 0.358834 0.179417 M5 -6.02994002777538 11.118038 -0.5424 0.590659 0.295329 M6 -10.5865832384230 10.891052 -0.972 0.337019 0.16851 M7 -8.0507839315179 5.32993 -1.5105 0.13898 0.06949 M8 10.1382562337091 5.701147 1.7783 0.083154 0.041577 M9 8.4583139369364 6.428909 1.3157 0.195967 0.097984 M10 -0.749293718734123 6.377451 -0.1175 0.907074 0.453537 M11 -5.88400784734467 5.152017 -1.1421 0.260385 0.130192 t -0.247013195172507 0.11873 -2.0805 0.0441 0.02205 Multiple Linear Regression - Regression Statistics Multiple R 0.99068212547478 R-squared 0.981451073735228 Adjusted R-squared 0.973365644337764 F-TEST (value) 121.385151670855 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.05513794444369 Sum Squared Residuals 1941.22388519004 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 537 538.749485602019 -1.74948560201902 2 543 542.842090315235 0.157909684764762 3 594 599.199620061908 -5.19962006190758 4 611 608.126598954675 2.87340104532457 5 613 607.161056135183 5.8389438648174 6 611 601.672682066277 9.32731793372288 7 594 599.707743049606 -5.70774304960619 8 595 599.127676111672 -4.12767611167222 9 591 599.153417778002 -8.15341777800165 10 589 586.03876080969 2.96123919030995 11 584 579.180179567181 4.81982043281908 12 573 579.713737845033 -6.71373784503289 13 567 563.34284552081 3.65715447919031 14 569 568.492341026651 0.507658973348595 15 621 620.516639460973 0.483360539026781 16 629 630.6785634387 -1.67856343870026 17 628 620.201395174544 7.7986048254555 18 612 612.064718363019 -0.0647183630185552 19 595 595.650586888987 -0.650586888986726 20 597 596.149346831381 0.850653168619085 21 593 597.807767607006 -4.80776760700562 22 590 585.035505240413 4.96449475958699 23 580 577.078903879765 2.92109612023514 24 574 572.3189413124 1.68105868759979 25 573 561.557354711 11.4426452889997 26 573 571.967348248033 1.03265175196732 27 620 621.574656839175 -1.57465683917477 28 626 626.208882878802 -0.208882878801795 29 620 613.791258036201 6.20874196379898 30 588 600.670195230334 -12.6701952303341 31 566 567.709590000443 -1.70959000044332 32 557 563.945639688887 -6.94563968888702 33 561 554.859393757731 6.14060624226932 34 549 551.784641543923 -2.78464154392263 35 532 534.366847883032 -2.36684788303185 36 526 522.659571382141 3.34042861785876 37 511 512.345418898525 -1.34541889852512 38 499 508.363694838314 -9.36369483831425 39 555 546.1290177978 8.87098220219973 40 565 561.437174361385 3.56282563861531 41 542 553.618710863144 -11.6187108631444 42 527 527.476899167323 -0.476899167323512 43 510 513.078392430996 -3.07839243099585 44 514 514.231275674012 -0.231275674011911 45 517 518.600887612804 -1.60088761280436 46 508 513.141092405974 -5.1410924059743 47 493 498.374068670022 -5.37406867002236 48 490 488.307749460426 1.69225053957433 49 469 481.004895267646 -12.0048952676459 50 478 470.334525571766 7.66547442823356 51 528 530.580065840144 -2.58006584014417 52 534 538.548780366438 -4.54878036643783 53 518 526.227579790928 -8.22757979092746 54 506 502.115505173047 3.8844948269533 55 502 490.853687629968 11.1463123700321 56 516 505.546061694048 10.4539383059521 57 528 519.578533244458 8.42146675554231 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.211585319202983 0.423170638405967 0.788414680797017 22 0.116372353265211 0.232744706530423 0.883627646734789 23 0.0583010899222116 0.116602179844423 0.941698910077788 24 0.0385348745640576 0.0770697491281152 0.961465125435942 25 0.0676215770206359 0.135243154041272 0.932378422979364 26 0.0565000047343184 0.113000009468637 0.943499995265682 27 0.0282525263782780 0.0565050527565561 0.971747473621722 28 0.0142758007557484 0.0285516015114969 0.985724199244252 29 0.177449948841074 0.354899897682148 0.822550051158926 30 0.543770476663035 0.912459046673931 0.456229523336965 31 0.437212682272969 0.874425364545937 0.562787317727031 32 0.496222777127519 0.992445554255037 0.503777222872481 33 0.392047397306964 0.784094794613928 0.607952602693036 34 0.284735508114594 0.569471016229188 0.715264491885406 35 0.240609785658578 0.481219571317155 0.759390214341422 36 0.189880964364185 0.379761928728370 0.810119035635815 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 1 0.0625 NOK 10% type I error level 3 0.1875 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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