*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: Thu, 19 Nov 2009 02:24:32 -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/19/t12586227396mxq03m67eiyb02.htm/, Retrieved Thu, 19 Nov 2009 10:25:52 +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/19/t12586227396mxq03m67eiyb02.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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519 97.4 517 97 510 105.4 509 102.7 501 98.1 507 104.5 569 87.4 580 89.9 578 109.8 565 111.7 547 98.6 555 96.9 562 95.1 561 97 555 112.7 544 102.9 537 97.4 543 111.4 594 87.4 611 96.8 613 114.1 611 110.3 594 103.9 595 101.6 591 94.6 589 95.9 584 104.7 573 102.8 567 98.1 569 113.9 621 80.9 629 95.7 628 113.2 612 105.9 595 108.8 597 102.3 593 99 590 100.7 580 115.5 574 100.7 573 109.9 573 114.6 620 85.4 626 100.5 620 114.8 588 116.5 566 112.9 557 102 561 106 549 105.3 532 118.8 526 106.1 511 109.3 499 117.2 555 92.5 565 104.2 542 112.5 527 122.4 510 113.3 514 100 517 110.7 508 112.8 493 109.8 490 117.3 469 109.1 478 115.9 528 96 534 99.8 518 116.8 506 115.7 502 99.4 516 94.3

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 760.910465164322 -2.06240628200625X[t] + 3.45928596790644M1[t] + 0.653985478545425M2[t] + 10.6593264140061M3[t] -7.49846960282977M4[t] -20.8087207010408M5[t] + 0.136244178883754M6[t] + 2.29792932742970M7[t] + 31.6605759872561M8[t] + 56.4080613861209M9[t] + 41.8549160805557M10[t] + 10.3472950039748M11[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) 760.910465164322 88.594009 8.5887 0 0 X -2.06240628200625 0.877141 -2.3513 0.022069 0.011034 M1 3.45928596790644 21.432277 0.1614 0.872326 0.436163 M2 0.653985478545425 21.483107 0.0304 0.975817 0.487909 M3 10.6593264140061 23.722802 0.4493 0.654841 0.327421 M4 -7.49846960282977 22.032479 -0.3403 0.734812 0.367406 M5 -20.8087207010408 21.720785 -0.958 0.341967 0.170984 M6 0.136244178883754 24.429438 0.0056 0.995569 0.497784 M7 2.29792932742970 23.580127 0.0975 0.922698 0.461349 M8 31.6605759872561 21.467921 1.4748 0.145587 0.072793 M9 56.4080613861209 24.694235 2.2843 0.02597 0.012985 M10 41.8549160805557 24.789402 1.6884 0.09661 0.048305 M11 10.3472950039748 22.192377 0.4663 0.64275 0.321375 Multiple Linear Regression - Regression Statistics Multiple R 0.562739380611654 R-squared 0.316675610491188 Adjusted R-squared 0.177694378726684 F-TEST (value) 2.27854945930957 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0.0186566079569896 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 37.0937250185948 Sum Squared Residuals 81180.7217095526 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 519 563.491379264817 -44.4913792648167 2 517 561.511041288261 -44.5110412882611 3 510 554.192169454869 -44.1921694548693 4 509 541.60287039945 -32.6028703994503 5 501 537.779688198468 -36.779688198468 6 507 545.525252873553 -38.5252528735526 7 569 582.954085444405 -13.9540854444054 8 580 607.160716399216 -27.1607163992161 9 578 590.866316786157 -12.8663167861567 10 565 572.39459954478 -7.39459954477948 11 547 567.90450076248 -20.9045007624805 12 555 561.063296437916 -6.06329643791635 13 562 568.234913713434 -6.23491371343404 14 561 561.511041288261 -0.511041288261143 15 555 539.136603596224 15.8633964037764 16 544 541.190389143049 2.80961085695095 17 537 539.223372595872 -2.22337259587238 18 543 531.294649527709 11.7053504722905 19 594 582.954085444405 11.0459145555946 20 611 592.930113053373 18.0698869466270 21 613 581.99796977353 31.0020302264702 22 611 575.281968339588 35.7180316604118 23 594 556.973747467847 37.0262525321526 24 595 551.369986912487 43.630013087513 25 591 569.266116854437 21.7338831455628 26 589 563.779688198468 25.220311801532 27 584 555.635853852274 28.3641461477264 28 573 541.39662977125 31.6033702287503 29 567 537.779688198468 29.2203118015320 30 569 526.138633822694 42.8613661773062 31 621 596.359726277446 24.6402737225540 32 629 595.19875996358 33.8012400364201 33 628 583.854135427335 44.1458645726646 34 612 584.356555980416 27.6434440195843 35 595 546.867956686017 48.1320433139832 36 597 549.926302515083 47.0736974849174 37 593 560.19152921361 32.8084707863903 38 590 553.880138044838 36.119861955162 39 580 533.361866006606 46.6381339933939 40 574 545.727682963463 28.2723170365372 41 573 513.443294070794 59.5567059292057 42 573 524.694949425289 48.3050505747105 43 620 587.078898008418 32.9211019915821 44 626 585.29920980995 40.7007901900501 45 620 580.554285376125 39.4457146238746 46 588 562.495049391149 25.5049506088505 47 566 538.412090929791 27.5879090702089 48 557 550.545024399685 6.45497560031553 49 561 545.754685239566 15.2453147604341 50 549 544.393069147609 4.60693085239073 51 532 526.555925275985 5.44407472401448 52 526 534.590689040629 -8.59068904062907 53 511 514.680737839998 -3.68073783999802 54 499 519.332693092073 -20.3326930920732 55 555 572.435813406174 -17.4358134061736 56 565 577.668306566527 -12.6683065665268 57 542 585.29781982474 -43.2978198247398 58 527 550.326852327313 -23.3268523273126 59 510 537.587128416989 -27.5871284169886 60 514 554.669836963697 -40.669836963697 61 517 536.061375714136 -19.0613757141365 62 508 528.925022032562 -20.9250220325624 63 493 545.117581814042 -52.1175818140418 64 490 511.491738682159 -21.4917386821591 65 469 515.093219096399 -46.0932190963993 66 478 522.013821258681 -44.0138212586814 67 528 565.217391419152 -37.2173914191517 68 534 586.742894207354 -52.7428942073543 69 518 576.429472812113 -58.4294728121129 70 506 564.144974416755 -58.1449744167545 71 502 566.254575736875 -64.2545757368755 72 516 566.425552771133 -50.4255527711326 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.4358344776658 0.8716689553316 0.5641655223342 17 0.359282441641826 0.718564883283652 0.640717558358174 18 0.225727758686337 0.451455517372674 0.774272241313663 19 0.152559919667847 0.305119839335694 0.847440080332153 20 0.0849096755653747 0.169819351130749 0.915090324434625 21 0.0500888331591953 0.100177666318391 0.949911166840805 22 0.0634562278450795 0.126912455690159 0.93654377215492 23 0.0416580930508185 0.083316186101637 0.958341906949182 24 0.0278714651645578 0.0557429303291156 0.972128534835442 25 0.0512867216595767 0.102573443319153 0.948713278340423 26 0.0674102885773216 0.134820577154643 0.932589711422678 27 0.105773450152467 0.211546900304935 0.894226549847533 28 0.102476585020777 0.204953170041555 0.897523414979223 29 0.0961712832827984 0.192342566565597 0.903828716717202 30 0.0772689871225576 0.154537974245115 0.922731012877442 31 0.0850934043140457 0.170186808628091 0.914906595685954 32 0.067530510102559 0.135061020205118 0.932469489897441 33 0.0640860281079343 0.128172056215869 0.935913971892066 34 0.0549454815233865 0.109890963046773 0.945054518476613 35 0.0509515990661706 0.101903198132341 0.94904840093383 36 0.0548063760185757 0.109612752037151 0.945193623981424 37 0.0430882367998698 0.0861764735997396 0.95691176320013 38 0.0350674529536257 0.0701349059072514 0.964932547046374 39 0.0344639342971967 0.0689278685943935 0.965536065702803 40 0.0344733827207722 0.0689467654415444 0.965526617279228 41 0.0455476029400157 0.0910952058800313 0.954452397059984 42 0.0677352345833527 0.135470469166705 0.932264765416647 43 0.0964526179047947 0.192905235809589 0.903547382095205 44 0.143901289045322 0.287802578090644 0.856098710954678 45 0.316416734937357 0.632833469874714 0.683583265062643 46 0.521151208577732 0.957697582844536 0.478848791422268 47 0.681050074189525 0.63789985162095 0.318949925810475 48 0.745448656239074 0.509102687521852 0.254551343760926 49 0.771206852710771 0.457586294578457 0.228793147289229 50 0.801778681965382 0.396442636069236 0.198221318034618 51 0.836131165234399 0.327737669531202 0.163868834765601 52 0.855366084257952 0.289267831484095 0.144633915742048 53 0.913251425566058 0.173497148867884 0.0867485744339422 54 0.888842569875084 0.222314860249832 0.111157430124916 55 0.893423340267359 0.213153319465283 0.106576659732641 56 0.895051610999712 0.209896778000575 0.104948389000288 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 7 0.170731707317073 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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