Multiple Regression 4 LAGS WS7

*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: Mon, 23 Nov 2009 09:53:34 -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/23/t1258995388moli460nc2gglrx.htm/, Retrieved Mon, 23 Nov 2009 17:56:40 +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/23/t1258995388moli460nc2gglrx.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:

KVN WS7

Dataseries X:

» Textbox « » Textfile « » CSV «

9283 4359 8947 9627 8700 9487 8829 5382 9283 8947 9627 8700 9947 4459 8829 9283 8947 9627 9628 6398 9947 8829 9283 8947 9318 4596 9628 9947 8829 9283 9605 3024 9318 9628 9947 8829 8640 1887 9605 9318 9628 9947 9214 2070 8640 9605 9318 9628 9567 1351 9214 8640 9605 9318 8547 2218 9567 9214 8640 9605 9185 2461 8547 9567 9214 8640 9470 3028 9185 8547 9567 9214 9123 4784 9470 9185 8547 9567 9278 4975 9123 9470 9185 8547 10170 4607 9278 9123 9470 9185 9434 6249 10170 9278 9123 9470 9655 4809 9434 10170 9278 9123 9429 3157 9655 9434 10170 9278 8739 1910 9429 9655 9434 10170 9552 2228 8739 9429 9655 9434 9687 1594 9552 8739 9429 9655 9019 2467 9687 9552 8739 9429 9672 2222 9019 9687 9552 8739 9206 3607 9672 9019 9687 9552 9069 4685 9206 9672 9019 9687 9788 4962 9069 9206 9672 9019 10312 5770 9788 9069 9206 9672 10105 5480 10312 9788 9069 9206 9863 5000 10105 10312 9788 9069 9656 3228 9863 10105 10312 9788 9295 1993 9656 9863 10105 10312 9946 2288 9295 9656 9863 10105 9701 1580 9946 92 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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 15001.1563321387 -0.243095727578729X[t] -0.144308864506109Y1[t] -0.297268824851053Y2[t] -0.0695082353211447Y3[t] -0.0916911246535985Y4[t] + 612.266107919829M1[t] + 651.014606916987M2[t] + 1313.99791057461M3[t] + 1387.23905775529M4[t] + 1213.66646546364M5[t] + 657.42153840102M6[t] -414.104936507337M7[t] -13.3237391022010M8[t] -134.219423617270M9[t] -670.981487522302M10[t] + 161.176030302722M11[t] + 32.9594911392901t + 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) 15001.1563321387 3340.865172 4.4902 6.4e-05 3.2e-05 X -0.243095727578729 0.135592 -1.7928 0.080961 0.04048 Y1 -0.144308864506109 0.180172 -0.801 0.42814 0.21407 Y2 -0.297268824851053 0.171246 -1.7359 0.090682 0.045341 Y3 -0.0695082353211447 0.163475 -0.4252 0.673096 0.336548 Y4 -0.0916911246535985 0.169492 -0.541 0.591681 0.29584 M1 612.266107919829 348.62584 1.7562 0.087107 0.043554 M2 651.014606916987 381.81188 1.7051 0.096346 0.048173 M3 1313.99791057461 351.430606 3.739 0.000607 0.000304 M4 1387.23905775529 417.902565 3.3195 0.001997 0.000999 M5 1213.66646546364 396.781822 3.0588 0.00406 0.00203 M6 657.42153840102 254.316982 2.585 0.0137 0.00685 M7 -414.104936507337 304.502418 -1.3599 0.181863 0.090932 M8 -13.3237391022010 254.745921 -0.0523 0.958562 0.479281 M9 -134.219423617270 298.130636 -0.4502 0.655122 0.327561 M10 -670.981487522302 250.204898 -2.6817 0.010778 0.005389 M11 161.176030302722 259.608975 0.6208 0.53841 0.269205 t 32.9594911392901 7.406788 4.4499 7.3e-05 3.6e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.927357690488603 R-squared 0.859992286108355 Adjusted R-squared 0.797357256209461 F-TEST (value) 13.7302127499031 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 2.50983678284911e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 230.548256194616 Sum Squared Residuals 2019794.94050637 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9283 8959.19392022221 323.806079777788 2 8829 8943.59678443 -114.596784429997 3 9947 9791.8187625824 155.181237417610 4 9628 9439.2747187883 188.725281211707 5 9318 9451.15662127897 -133.156621278974 6 9605 9413.49973573748 191.500264262525 7 8640 8621.73173552072 18.2682644792815 8 9214 9115.72482914843 98.2751708515681 9 9567 9415.08097676197 151.919023238034 10 8547 8519.70116785963 27.2988321403733 11 9185 9416.5892698625 -231.589269862504 12 9470 9284.51548633558 185.484513664421 13 9123 9310.61088415209 -187.610884152085 14 9278 9350.41984423385 -72.4198442338461 15 10170 10138.2974904091 31.7025095909239 16 9434 9668.52215618357 -234.522156183571 17 9655 9740.05747903397 -85.0574790339656 18 9429 9729.05031087745 -300.050310877448 19 8739 8929.9106704907 -190.910670490708 20 9552 9505.22613632973 46.7738636702739 21 9687 9654.65013917676 32.3498608232441 22 9019 8746.14662146586 272.853378534144 23 9672 9733.84579451704 -61.8457945170388 24 9206 9289.35506302335 -83.3550630233505 25 9069 9579.708055351 -510.708055350998 26 9788 9758.23690936996 29.7630906300377 27 10312 10167.2426449688 144.757355031184 28 10105 10106.8376065451 -1.83760654508185 29 9863 9919.59878824297 -56.5987882429714 30 9656 9821.18813960958 -165.188139609575 31 9295 9150.99742535995 144.002574640050 32 9946 9662.45607685053 283.543923149465 33 9701 9796.5780904559 -95.578090455899 34 9049 9049.59788892604 -0.597888926040874 35 10190 10049.7950205089 140.204979491148 36 9706 9565.5580560926 140.441943907405 37 9765 9750.57525724337 14.4247427566306 38 9893 9886.82765385547 6.17234614452517 39 9994 10248.0017692538 -254.001769253801 40 10433 10396.3077641037 36.6922358962526 41 10073 10210.7307873629 -137.730787362899 42 10112 10138.5626942467 -26.5626942466699 43 9266 9422.45123850422 -156.451238504224 44 9820 9877.55320206038 -57.5532020603755 45 10097 10185.6907936054 -88.690793605379 46 9115 9414.55432174848 -299.554321748477 47 10411 10257.7699151116 153.230084888394 48 9678 9920.57139454847 -242.571394548475 49 10408 10047.9118830313 360.088116968665 50 10153 10001.9188081107 151.081191889280 51 10368 10445.6393327859 -77.6393327859171 52 10581 10570.0577543793 10.9422456206928 53 10597 10184.4563240812 412.54367591881 54 10680 10379.6991195288 300.300880471169 55 9738 9552.9089301244 185.091069875601 56 9556 9927.03975561093 -371.039755610931 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.125199070002969 0.250398140005938 0.874800929997031 22 0.0610685090683073 0.122137018136615 0.938931490931693 23 0.117884781322921 0.235769562645841 0.88211521867708 24 0.0777549599646525 0.155509919929305 0.922245040035348 25 0.202729983748780 0.405459967497559 0.79727001625122 26 0.382026376352 0.764052752704 0.617973623648 27 0.504732362245513 0.990535275508974 0.495267637754487 28 0.425980304986233 0.851960609972465 0.574019695013767 29 0.341790231248307 0.683580462496613 0.658209768751693 30 0.269543235594573 0.539086471189146 0.730456764405427 31 0.222203269193461 0.444406538386923 0.777796730806539 32 0.494261085952583 0.988522171905167 0.505738914047417 33 0.365228716505273 0.730457433010546 0.634771283494727 34 0.80196531485783 0.396069370284341 0.198034685142170 35 0.708751671910786 0.582496656178428 0.291248328089214 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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