*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: Sun, 20 Dec 2009 11:40:45 -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/20/t126133462228l8dx0jsbo7thd.htm/, Retrieved Sun, 20 Dec 2009 19:43:54 +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/20/t126133462228l8dx0jsbo7thd.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:

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Dataseries X:

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4138 613 5560 4634 611 3922 3996 594 3759 4308 595 4138 4143 591 4634 4429 589 3996 5219 584 4308 4929 573 4143 5755 567 4429 5592 569 5219 4163 621 4929 4962 629 5755 5208 628 5592 4755 612 4163 4491 595 4962 5732 597 5208 5731 593 4755 5040 590 4491 6102 580 5732 4904 574 5731 5369 573 5040 5578 573 6102 4619 620 4904 4731 626 5369 5011 620 5578 5299 588 4619 4146 566 4731 4625 557 5011 4736 561 5299 4219 549 4146 5116 532 4625 4205 526 4736 4121 511 4219 5103 499 5116 4300 555 4205 4578 565 4121 3809 542 5103 5526 527 4300 4247 510 4578 3830 514 3809 4394 517 5526 4826 508 4247 4409 493 3830 4569 490 4394 4106 469 4826 4794 478 4409 3914 528 4569 3793 534 4106 4405 518 4794 4022 506 3914 4100 502 3793 4788 516 4405 3163 528 4022 3585 533 4100 3903 536 4788 4178 537 3163 3863 524 3585 4187 536 3903

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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1793.72489341894 + 1.6063977661368X[t] + 0.427962828713485`yt-3`[t] -252.499755260931M1[t] + 603.668966609273M2[t] -90.4715413427234M3[t] + 312.032103289648M4[t] -47.4313553108066M5[t] + 234.187147811827M6[t] + 590.986007695037M7[t] + 311.521538341208M8[t] + 430.915726239081M9[t] + 618.343590382069M10[t] -185.133169059902M11[t] -9.78223844663726t + 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) 1793.72489341894 2025.673184 0.8855 0.380815 0.190407 X 1.6063977661368 3.060266 0.5249 0.602334 0.301167 `yt-3` 0.427962828713485 0.129677 3.3002 0.001948 0.000974 M1 -252.499755260931 333.21998 -0.7578 0.452729 0.226365 M2 603.668966609273 345.116188 1.7492 0.087396 0.043698 M3 -90.4715413427234 351.353336 -0.2575 0.798025 0.399013 M4 312.032103289648 344.517975 0.9057 0.370138 0.185069 M5 -47.4313553108066 339.38632 -0.1398 0.889505 0.444753 M6 234.187147811827 348.352758 0.6723 0.505008 0.252504 M7 590.986007695037 348.354776 1.6965 0.097019 0.048509 M8 311.521538341208 353.327156 0.8817 0.382852 0.191426 M9 430.915726239081 364.910192 1.1809 0.24414 0.12207 M10 618.343590382069 360.807295 1.7138 0.093771 0.046885 M11 -185.133169059902 344.065913 -0.5381 0.5933 0.29665 t -9.78223844663726 7.018747 -1.3937 0.170561 0.08528 Multiple Linear Regression - Regression Statistics Multiple R 0.736405222894403 R-squared 0.542292652306156 Adjusted R-squared 0.393271655382578 F-TEST (value) 3.63903519303565 F-TEST (DF numerator) 14 F-TEST (DF denominator) 43 p-value 0.000545270742913884 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 483.846579610374 Sum Squared Residuals 10066623.0418283 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4138 4895.63805800023 -757.638058000227 2 4634 5037.80863245882 -403.808632458819 3 3996 4236.81918295556 -240.819182955560 4 4308 4793.34489898984 -485.344898989843 5 4143 4629.94317392009 -486.943173920093 6 4429 4625.52635834461 -196.526358344613 7 5219 5098.03539350911 120.964606490892 8 4929 4720.50444354341 208.495556456587 9 5755 4942.87537540988 812.124624590116 10 5592 5461.82443132216 130.175568677837 11 4163 4607.98889694576 -444.988896945757 12 4962 5149.68830620546 -187.688306205456 13 5208 4816.04197365145 391.958026348548 14 4755 5025.16721058526 -270.167210585259 15 4491 4635.87800230437 -144.878002304375 16 5732 5137.0910598859 594.9089401141 17 5731 4567.55261036705 1163.44738963295 18 5040 4721.58749496428 318.412505035723 19 6102 5583.64200917292 518.357990827083 20 4904 5284.32895194692 -380.328951946917 21 5369 5096.612188991 272.387811009003 22 5578 5728.75433878107 -150.754338781071 23 4619 4478.29656710214 140.703432897865 24 4731 4862.28859966399 -131.288599663992 25 5011 4679.81245056072 331.187549439278 26 5299 5064.37785273168 234.622147268322 27 4146 4373.04619229394 -227.046192293945 28 4625 4871.13961062422 -246.139610624224 29 4736 4631.57279931116 104.427200688837 30 4219 4390.69114928687 -171.691149286869 31 5116 4915.39320365288 200.606796347124 32 4205 4664.01198324279 -459.011983242786 33 4121 4528.27118375710 -407.271183757097 34 5103 5070.5226936158 32.4773063841965 35 4300 3957.34783367287 342.65216632713 36 4578 4112.81386433557 465.18613566443 37 3809 4233.8442198035 -424.844219803498 38 5526 4712.48058527808 813.519414721915 39 4247 4100.22274323747 146.777256762526 40 3830 4170.26632520708 -340.266325207084 41 4394 4540.65199835946 -146.651998359458 42 4826 4250.66622521567 575.333774784325 43 4409 4395.12638058667 13.8736194133276 44 4569 4342.4315148822 226.568485117798 45 4106 4603.18905324879 -497.18905324879 46 4794 4616.83175926685 177.168240733150 47 3914 3952.36670227924 -38.3667022792384 48 3793 3939.20922979498 -146.209229794980 49 4405 3945.6632979841 459.336702015899 50 4022 4396.16571894616 -374.165718946159 51 4100 3634.03387920865 465.966120791354 52 4788 4311.15810529295 476.841894707051 53 3163 3797.27941804223 -634.279418042234 54 3585 4110.52877218857 -525.528772188566 55 3903 4756.80301307843 -853.803013078426 56 4178 3773.72310638468 404.276893615317 57 3863 4043.05219859323 -180.052198593231 58 4187 4376.06677701411 -189.066777014113 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.721111975477936 0.557776049044128 0.278888024522064 19 0.615504931917505 0.768990136164989 0.384495068082495 20 0.631114043046127 0.737771913907746 0.368885956953873 21 0.795610775691923 0.408778448616153 0.204389224308077 22 0.742527484981339 0.514945030037322 0.257472515018661 23 0.661697189862316 0.676605620275369 0.338302810137684 24 0.649070963740619 0.701858072518763 0.350929036259381 25 0.578228274944256 0.843543450111488 0.421771725055744 26 0.488047947862906 0.976095895725813 0.511952052137094 27 0.422152938647464 0.844305877294928 0.577847061352536 28 0.336661977425142 0.673323954850283 0.663338022574858 29 0.276117373877017 0.552234747754034 0.723882626122983 30 0.205500630061331 0.411001260122662 0.794499369938669 31 0.164039340110848 0.328078680221697 0.835960659889152 32 0.156960219616469 0.313920439232937 0.843039780383531 33 0.129068192107019 0.258136384214037 0.870931807892981 34 0.123167738160073 0.246335476320146 0.876832261839927 35 0.114625433918326 0.229250867836653 0.885374566081674 36 0.0912000691086244 0.182400138217249 0.908799930891376 37 0.112630687092782 0.225261374185564 0.887369312907218 38 0.295129842365564 0.590259684731128 0.704870157634436 39 0.198629537795486 0.397259075590972 0.801370462204514 40 0.923932016699468 0.152135966601064 0.0760679833005322 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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