paper

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 18 Dec 2009 10:04:51 -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/Dec/18/t1261155994j62trw1qdi16rqh.htm/, Retrieved Fri, 18 Dec 2009 18:06:46 +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/Dec/18/t1261155994j62trw1qdi16rqh.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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593530 3922 18004 707169 610763 3759 17537 703434 612613 4138 20366 701017 611324 4634 22782 696968 594167 3996 19169 688558 595454 4308 13807 679237 590865 4143 29743 677362 589379 4429 25591 676693 584428 5219 29096 670009 573100 4929 26482 667209 567456 5761 22405 662976 569028 5592 27044 660194 620735 4163 17970 652270 628884 4962 18730 648024 628232 5208 19684 629295 612117 4755 19785 624961 595404 4491 18479 617306 597141 5732 10698 607691 593408 5731 31956 596219 590072 5040 29506 591130 579799 6102 34506 584528 574205 4904 27165 576798 572775 5369 26736 575683 572942 5578 23691 574369 619567 4619 18157 566815 625809 4731 17328 573074 619916 5011 18205 567739 587625 5299 20995 571942 565742 4146 17382 570274 557274 4625 9367 568800 560576 4736 31124 558115 548854 4219 26551 550591 531673 5116 30651 548872 525919 4205 25859 547009 511038 4121 25100 545946 498662 5103 25778 539702 555362 4300 20418 542427 564591 4578 18688 542968 541657 3809 20424 536640 527070 5526 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Werk[t] = + 386446.478226036 + 26.6794038315384Bouwvergun[t] -5.16843871470594Auto[t] + 0.279876360124689Hyp[t] + 36329.1227013538M1[t] + 33986.2757199777M2[t] + 33433.7741251689M3[t] + 22139.4363417723M4[t] + 3594.12117399042M5[t] -38101.8143140329M6[t] + 65990.9868913048M7[t] + 48232.3230425884M8[t] + 43147.6305551091M9[t] + 34906.1567168134M10[t] + 3146.90939054105M11[t] -700.464388065671t + 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) 386446.478226036 75939.864683 5.0888 7e-06 3e-06 Bouwvergun 26.6794038315384 5.304573 5.0295 8e-06 4e-06 Auto -5.16843871470594 1.491931 -3.4643 0.001179 0.000589 Hyp 0.279876360124689 0.065804 4.2532 0.000105 5.3e-05 M1 36329.1227013538 14514.449541 2.503 0.016014 0.008007 M2 33986.2757199777 16171.327203 2.1016 0.041215 0.020608 M3 33433.7741251689 14536.218422 2.3 0.026138 0.013069 M4 22139.4363417723 12671.763158 1.7471 0.087434 0.043717 M5 3594.12117399042 16145.89278 0.2226 0.824852 0.412426 M6 -38101.8143140329 23334.742015 -1.6328 0.109482 0.054741 M7 65990.9868913048 14355.75533 4.5968 3.5e-05 1.7e-05 M8 48232.3230425884 12672.224013 3.8061 0.000424 0.000212 M9 43147.6305551091 13873.233955 3.1101 0.003241 0.001621 M10 34906.1567168134 12534.753672 2.7848 0.007809 0.003905 M11 3146.90939054105 11795.719881 0.2668 0.790854 0.395427 t -700.464388065671 237.518768 -2.9491 0.005041 0.00252 Multiple Linear Regression - Regression Statistics Multiple R 0.928817949369446 R-squared 0.862702783070862 Adjusted R-squared 0.816937044094483 F-TEST (value) 18.8504064911117 F-TEST (DF numerator) 15 F-TEST (DF denominator) 45 p-value 1.39888101102770e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 18170.9469313304 Sum Squared Residuals 14858249057.1551 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 593530 631579.073460067 -38049.0734600667 2 610763 625555.341940788 -14792.3419407877 3 612613 619115.895723742 -6502.89572374163 4 611324 606733.910535848 4590.08946415201 5 594167 586786.480223063 7380.51977693703 6 595454 577818.495177945 17635.5048220551 7 590865 593919.722830226 -3054.72283022557 8 589379 604363.024347799 -14984.0243477991 9 584428 599668.525213052 -15240.5252130517 10 573100 595716.204867436 -22616.2048674363 11 567456 605340.765148386 -37884.7651483865 12 569028 572229.568890862 -3201.56889086211 13 620735 614414.031748496 6320.96825150442 14 628884 627571.195592187 1312.80440781297 15 628232 622708.868069266 5523.1319307338 16 612117 596893.299507151 15223.7004928486 17 595404 575211.684764429 20192.3152355708 18 597141 603449.035479807 -6308.03547980718 19 593408 593733.281092679 -325.281092678557 20 590072 568077.068862658 21994.9311373415 21 579799 562935.501553134 16863.4984468656 22 574205 557809.701877482 16395.2981225175 23 572775 539661.111011880 33113.8889881204 24 572942 556759.87098314 16182.1290168599 25 619567 593290.934844784 26276.0651552163 26 625809 599272.098536986 26536.9014630141 27 619916 599463.50449288 20452.4955071202 28 587625 581908.746952475 5716.25304752492 29 565742 550108.350086408 15633.6499135916 30 557274 561503.883189171 -4229.88318917053 31 560576 552417.433807954 8158.5661920459 32 548854 541694.534299039 7159.46570096127 33 531673 538169.096467035 -6496.09646703502 34 525919 529167.970012101 -3248.97001210071 35 511038 498092.524789563 12945.4752104372 36 498662 515192.576132338 -16530.5761323375 37 555362 557863.167761064 -2501.16776106392 38 564591 571329.542744059 -6738.54274405854 39 541657 538816.647999133 2840.35200086744 40 527070 549301.346232329 -22231.3462323289 41 509846 523660.213594542 -13814.2135945418 42 514258 505933.626616995 8324.37338300519 43 516922 526381.983843136 -9459.9838431365 44 507561 526482.999903789 -18921.9999037889 45 492622 508446.132566516 -15824.1325665156 46 490243 494394.13843659 -4151.13843658989 47 469357 480616.304869075 -11259.3048690747 48 477580 487422.691948718 -9842.69194871811 49 528379 534180.703384399 -5801.70338439863 50 533590 539908.821185981 -6318.82118598081 51 517945 540258.08371498 -22313.0837149798 52 506174 509472.696772197 -3298.69677219666 53 501866 531258.271331558 -29392.2713315576 54 516141 531562.959536083 -15421.9595360826 55 528222 523540.578426005 4681.42157399472 56 532638 527886.372586715 4751.6274132851 57 536322 515624.744200263 20697.2557997366 58 536535 522913.984806391 13621.0151936093 59 523597 520512.294181096 3084.70581890354 60 536214 522821.292044942 13392.7079550578 61 586570 572815.088801191 13754.9111988086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.204323024179295 0.408646048358589 0.795676975820705 20 0.0921147140074487 0.184229428014897 0.907885285992551 21 0.0523162134872807 0.104632426974561 0.94768378651272 22 0.0406520902702437 0.0813041805404875 0.959347909729756 23 0.0318346800637909 0.0636693601275817 0.96816531993621 24 0.0227518821785922 0.0455037643571845 0.977248117821408 25 0.014736710625919 0.029473421251838 0.985263289374081 26 0.0362644377718795 0.0725288755437589 0.96373556222812 27 0.279497019060363 0.558994038120725 0.720502980939637 28 0.898477641158335 0.203044717683331 0.101522358841665 29 0.970141483718074 0.0597170325638529 0.0298585162819264 30 0.970887120152538 0.0582257596949244 0.0291128798474622 31 0.970797553316126 0.0584048933677472 0.0292024466838736 32 0.968141170725034 0.0637176585499323 0.0318588292749662 33 0.960187706438813 0.0796245871223746 0.0398122935611873 34 0.951650760652283 0.0966984786954341 0.0483492393477171 35 0.979516459219216 0.040967081561568 0.020483540780784 36 0.98526088620944 0.0294782275811178 0.0147391137905589 37 0.9676337370605 0.0647325258789984 0.0323662629394992 38 0.938880955726283 0.122238088547435 0.0611190442737174 39 0.890357441834379 0.219285116331243 0.109642558165621 40 0.8795428355651 0.240914328869802 0.120457164434901 41 0.811686814400414 0.376626371199172 0.188313185599586 42 0.888018630750782 0.223962738498436 0.111981369249218 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 4 0.166666666666667 NOK 10% type I error level 14 0.583333333333333 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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