Model 3

*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: Sat, 19 Dec 2009 04:34:37 -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/19/t1261222631df92rpb2qhoakvw.htm/, Retrieved Sat, 19 Dec 2009 12:37:23 +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/19/t1261222631df92rpb2qhoakvw.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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3397 562 3971 561 4625 555 4486 544 4132 537 4685 543 3172 594 4280 611 4207 613 4158 611 3933 594 3151 595 3616 591 4221 589 4436 584 4807 573 4849 567 5024 569 3521 621 4650 629 5393 628 5147 612 4845 595 3995 597 4493 593 4680 590 5463 580 4761 574 5307 573 5069 573 3501 620 4952 626 5152 620 5317 588 5189 566 4030 557 4420 561 4571 549 4551 532 4819 526 5133 511 4532 499 3339 555 4380 565 4632 542 4719 527 4212 510 3615 514 3420 517 4571 508 4407 493 4386 490 4386 469 4744 478 3185 528 3890 534 4520 518 3990 506 3809 502 3236 516 3551 528 3264 533 3579 536 3537 537 3038 524 2888 536 2198 587

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 wng[t] = + 2727.25935723583 + 2.09494716519532totWL[t] + 165.006847063743M1[t] + 577.472514215335M2[t] + 900.047934804501M3[t] + 876.401812008212M4[t] + 914.516284788634M5[t] + 932.698128699786M6[t] -504.209140373502M7[t] + 715.264521937913M8[t] + 1092.05091787084M9[t] + 1017.66396509405M10[t] + 789.277012317263M11[t] -7.95086087920528t + 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) 2727.25935723583 1627.251803 1.676 0.09963 0.049815 totWL 2.09494716519532 2.662294 0.7869 0.434848 0.217424 M1 165.006847063743 329.987144 0.5 0.619117 0.309558 M2 577.472514215335 330.069349 1.7495 0.085985 0.042992 M3 900.047934804501 331.377286 2.7161 0.0089 0.00445 M4 876.401812008212 332.830795 2.6332 0.011061 0.00553 M5 914.516284788634 337.125188 2.7127 0.008981 0.00449 M6 932.698128699786 334.94034 2.7847 0.007414 0.003707 M7 -504.209140373502 338.747498 -1.4885 0.142558 0.071279 M8 715.264521937913 354.704575 2.0165 0.048827 0.024413 M9 1092.05091787084 350.324661 3.1173 0.002947 0.001474 M10 1017.66396509405 345.222946 2.9478 0.00475 0.002375 M11 789.277012317263 344.199151 2.2931 0.025839 0.01292 t -7.95086087920528 4.885117 -1.6276 0.109548 0.054774 Multiple Linear Regression - Regression Statistics Multiple R 0.724496010016475 R-squared 0.524894468529793 Adjusted R-squared 0.408359149489931 F-TEST (value) 4.50416640083378 F-TEST (DF numerator) 13 F-TEST (DF denominator) 53 p-value 4.16622543002454e-05 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 543.976531464733 Sum Squared Residuals 15683254.7395733 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3397 4061.67565026016 -664.67565026016 2 3971 4464.09550936733 -493.09550936733 3 4625 4766.15038608612 -141.150386086119 4 4486 4711.50898359348 -225.508983593476 5 4132 4727.00796533833 -595.007965338326 6 4685 4749.80863136144 -64.8086313614446 7 3172 3411.79280683391 -239.792806833911 8 4280 4658.92971007444 -378.929710074443 9 4207 5031.95513945855 -824.955139458552 10 4158 4945.42743147217 -787.42743147217 11 3933 4673.47551600786 -740.475516007857 12 3151 3878.34258997658 -727.342589976584 13 3616 4027.01878750034 -411.01878750034 14 4221 4427.34369944234 -206.343699442336 15 4436 4731.49352332632 -295.493523326320 16 4807 4676.85212083368 130.147879166323 17 4849 4694.44604974372 154.553950256277 18 5024 4708.86692710606 315.13307289394 19 3521 3372.94604974372 148.053950256277 20 4650 4601.2284284975 48.7715715025052 21 5393 4967.96901638602 425.030983613982 22 5147 4852.1120480869 294.887951913099 23 4845 4580.16013262259 264.839867377411 24 3995 3787.12215375651 207.877846243489 25 4493 3935.79835128027 557.201648719732 26 4680 4334.02831605707 345.971683942932 27 5463 4627.70340411508 835.296595884924 28 4761 4583.53673744841 177.463262551591 29 5307 4611.60540218443 695.394597815569 30 5069 4621.83638521638 447.163614783622 31 3501 3275.44077202806 225.559227971936 32 4952 4499.53325645145 452.466743548554 33 5152 4855.79910851399 296.200891486008 34 5317 4706.42298557175 610.57701442825 35 5189 4423.99633428146 765.003665718539 36 4030 3607.91393659823 422.086063401765 37 4420 3773.34971144355 646.650288556446 38 4571 4152.7251517336 418.274848266404 39 4551 4431.73560963524 119.264390364763 40 4819 4387.56894296857 431.43105703143 41 5133 4386.30834739186 746.691652608142 42 4532 4371.39996444146 160.600035558539 43 3339 3043.85887573990 295.141124260095 44 4380 4276.33114882407 103.668851175932 45 4632 4596.98289907829 35.0171009217064 46 4719 4483.22087794437 235.779122055628 47 4212 4211.26896248006 0.731037519940486 48 3615 3422.42087794437 192.579122055628 49 3420 3585.7617056245 -165.761705624496 50 4571 3971.42198741012 599.578012589875 51 4407 4254.62233964216 152.377660357844 52 4386 4216.74051447108 169.259485528925 53 4386 4202.91023590319 183.089764096809 54 4744 4231.99574342190 512.004256578104 55 3185 2891.88497172917 293.115028270832 56 3890 4115.97745615255 -225.977456152549 57 4520 4451.29383656314 68.7061634368574 58 3990 4343.81665692481 -353.816656924807 59 3809 4099.09905460803 -290.099054608034 60 3236 3331.2004417243 -95.2004417242997 61 3551 3513.39579389118 37.6042061088185 62 3264 3928.38533598954 -664.385335989545 63 3579 4249.29473719509 -670.294737195092 64 3537 4219.79270068479 -682.792700684792 65 3038 4222.72199943847 -1184.72199943847 66 2888 4258.09234845276 -1370.09234845276 67 2198 2920.07652392523 -722.076523925229 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.315275030665967 0.630550061331934 0.684724969334033 18 0.26982648616927 0.53965297233854 0.73017351383073 19 0.191890075747580 0.383780151495159 0.80810992425242 20 0.132416904628123 0.264833809256246 0.867583095371877 21 0.216910167037262 0.433820334074524 0.783089832962738 22 0.174389282820177 0.348778565640354 0.825610717179823 23 0.129968386825101 0.259936773650201 0.8700316131749 24 0.103784268233149 0.207568536466297 0.896215731766851 25 0.069726873713594 0.139453747427188 0.930273126286406 26 0.130469437804799 0.260938875609598 0.869530562195201 27 0.0977831188410926 0.195566237682185 0.902216881158907 28 0.3713866019329 0.7427732038658 0.6286133980671 29 0.295363906532786 0.590727813065572 0.704636093467214 30 0.359804770523393 0.719609541046785 0.640195229476607 31 0.480607824970804 0.961215649941607 0.519392175029196 32 0.433079219447322 0.866158438894644 0.566920780552678 33 0.402609452743814 0.805218905487628 0.597390547256186 34 0.371476075654907 0.742952151309815 0.628523924345093 35 0.446536209286312 0.893072418572623 0.553463790713688 36 0.387966824956994 0.775933649913988 0.612033175043006 37 0.379928487846319 0.759856975692638 0.620071512153681 38 0.368735092770901 0.737470185541802 0.631264907229099 39 0.500166656484976 0.999666687030049 0.499833343515024 40 0.428455446219614 0.856910892439227 0.571544553780386 41 0.59452135741808 0.810957285163839 0.405478642581920 42 0.581292051097987 0.837415897804027 0.418707948902013 43 0.505051673638047 0.989896652723905 0.494948326361953 44 0.46753842915207 0.93507685830414 0.53246157084793 45 0.365742292696618 0.731484585393236 0.634257707303382 46 0.415501079502744 0.831002159005487 0.584498920497256 47 0.354650774094216 0.709301548188431 0.645349225905784 48 0.263119682312816 0.526239364625632 0.736880317687184 49 0.426212057382418 0.852424114764836 0.573787942617582 50 0.511249502487573 0.977500995024854 0.488750497512427 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 0 0 OK

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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