Multiple Regression 2 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 10:09:30 -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/t1258996269s7y220nn9u07udg.htm/, Retrieved Mon, 23 Nov 2009 18:11:22 +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/t1258996269s7y220nn9u07udg.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 «

9627 2249 8700 9487 8947 2687 9627 8700 9283 4359 8947 9627 8829 5382 9283 8947 9947 4459 8829 9283 9628 6398 9947 8829 9318 4596 9628 9947 9605 3024 9318 9628 8640 1887 9605 9318 9214 2070 8640 9605 9567 1351 9214 8640 8547 2218 9567 9214 9185 2461 8547 9567 9470 3028 9185 8547 9123 4784 9470 9185 9278 4975 9123 9470 10170 4607 9278 9123 9434 6249 10170 9278 9655 4809 9434 10170 9429 3157 9655 9434 8739 1910 9429 9655 9552 2228 8739 9429 9687 1594 9552 8739 9019 2467 9687 9552 9672 2222 9019 9687 9206 3607 9672 9019 9069 4685 9206 9672 9788 4962 9069 9206 10312 5770 9788 9069 10105 5480 10312 9788 9863 5000 10105 10312 9656 3228 9863 10105 9295 1993 9656 9863 9946 2288 9295 9656 9701 1580 9946 9295 9049 2111 9701 9946 10190 2192 9049 9701 9706 3601 10190 9049 9765 4665 9706 10190 9893 4876 9765 9706 9994 5813 9893 9765 10433 5589 9994 9893 10073 5331 10433 9994 10112 3075 10073 10433 9266 2002 10112 10073 9820 2306 9266 10112 10097 1507 9820 9266 9115 1992 10097 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 11530.2416951373 -0.259549357501086X[t] -0.0622607723033541Y1[t] -0.229673673228820Y2[t] + 1011.70358259052M1[t] + 688.167517972763M2[t] + 1327.0896144447M3[t] + 1409.30209454738M4[t] + 2010.41806827211M5[t] + 2079.33498696616M6[t] + 1856.22016254202M7[t] + 1246.47376015360M8[t] + 128.215142601614M9[t] + 624.499650722314M10[t] + 521.174273946823M11[t] + 26.4262219167830t + 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) 11530.2416951373 2073.680595 5.5603 2e-06 1e-06 X -0.259549357501086 0.123969 -2.0937 0.042366 0.021183 Y1 -0.0622607723033541 0.164574 -0.3783 0.707102 0.353551 Y2 -0.229673673228820 0.163221 -1.4071 0.166744 0.083372 M1 1011.70358259052 210.542169 4.8052 2e-05 1e-05 M2 688.167517972763 204.737438 3.3612 0.001662 0.000831 M3 1327.0896144447 375.759811 3.5317 0.001018 0.000509 M4 1409.30209454738 402.297124 3.5031 0.001106 0.000553 M5 2010.41806827211 414.898201 4.8456 1.8e-05 9e-06 M6 2079.33498696616 462.444882 4.4964 5.4e-05 2.7e-05 M7 1856.22016254202 424.982123 4.3678 8e-05 4e-05 M8 1246.47376015360 208.361248 5.9823 0 0 M9 128.215142601614 160.600643 0.7983 0.42916 0.21458 M10 624.499650722314 199.226135 3.1346 0.003136 0.001568 M11 521.174273946823 223.258211 2.3344 0.024431 0.012215 t 26.4262219167830 4.764474 5.5465 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.922374588345396 R-squared 0.850774881225338 Adjusted R-squared 0.797480195948673 F-TEST (value) 15.9635970605468 F-TEST (DF numerator) 15 F-TEST (DF denominator) 42 p-value 9.89652804150865e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 230.419594494323 Sum Squared Residuals 2229913.96013099 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9627 9264.06213766365 362.937862336351 2 8947 8976.30712128305 -29.307121283052 3 9283 9037.11874401312 245.881255986878 4 8829 9015.49693161065 -186.496931610649 5 9947 9833.6992206465 113.300779353496 6 9628 9460.44046127346 167.559538726542 7 9318 9494.5458206780 -176.545820678007 8 9605 9411.8039713721 193.196028627890 9 8640 8668.40919226552 -28.4091922655165 10 9214 9137.78769093637 76.212309063633 11 9567 9433.40193548463 133.598064515374 12 8547 8559.81384944472 -12.8138494447178 13 9185 9517.3043411789 -332.304341178906 14 9470 9267.57478673867 202.425213261329 15 9123 9312.87830972904 -189.878309729039 16 9278 9328.09057558485 -50.0905755848496 17 10170 10121.1932796901 48.8067203098561 18 9434 9699.22034703913 -265.220347039127 19 9655 9717.2378312285 -62.2378312284959 20 9429 9717.97338216602 -288.973382166024 21 8739 8913.11208809167 -174.112088091666 22 9552 9448.15230548283 103.847694517169 23 9687 9643.66426992507 43.3357300749297 24 9019 8727.1997282006 291.800271799402 25 9672 9839.50337530842 -167.503375308419 26 9206 9295.6834018712 -89.6834018712014 27 9069 9560.2741241487 -491.274124148692 28 9788 9712.57531167055 75.4246883294507 29 10312 10117.1014243974 194.898575602578 30 10105 10089.9538629451 15.0461370549167 31 9863 9910.38792713314 -47.387927133141 32 9656 9849.5987654092 -193.598765409206 33 9295 9146.77883507601 148.221164923985 34 9946 9662.94109381055 283.058906189446 35 9701 9812.18331732874 -111.183317328735 36 9049 9045.35088440798 3.64911559202179 37 10190 10159.3212644405 30.6787355594572 38 9706 9575.2140707676 130.785929232399 39 9765 9732.4784254159 32.5215745840966 40 9893 9893.8408852795 -0.840885279493136 41 9994 10256.6652073672 -262.665207367159 42 10433 10374.4608358823 58.5391641176993 43 10073 10194.2064475729 -121.206447572942 44 10112 10118.0167531055 -6.01675310550995 45 9266 9384.93517031152 -118.935170311519 46 9820 9872.45823578139 -52.4582357813851 47 10097 10162.7504772616 -65.7504772615684 48 9115 9397.6355379467 -282.635537946706 49 10411 10304.8088814085 106.191118591516 50 9678 9892.22061933947 -214.220619339474 51 10408 10005.2503966932 402.749603306757 52 10153 9990.99629585446 162.003704145541 53 10368 10462.3408678988 -94.3408678987702 54 10581 10556.9244928600 24.0755071399683 55 10597 10189.6219733874 407.378026612586 56 10680 10384.6071279471 295.392872052850 57 9738 9564.76471425528 173.235285744716 58 9556 9966.66067398886 -410.660673988863 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.72260573591837 0.554788528163259 0.277394264081629 20 0.665837952482096 0.668324095035808 0.334162047517904 21 0.530135518098317 0.939728963803365 0.469864481901683 22 0.413234811258289 0.826469622516578 0.586765188741711 23 0.386375970932413 0.772751941864825 0.613624029067587 24 0.465258930207992 0.930517860415984 0.534741069792008 25 0.370913747932148 0.741827495864295 0.629086252067852 26 0.266983125272849 0.533966250545699 0.73301687472715 27 0.517696185931193 0.964607628137614 0.482303814068807 28 0.488514997870635 0.977029995741269 0.511485002129365 29 0.510208767612442 0.979582464775116 0.489791232387558 30 0.442684984136163 0.885369968272327 0.557315015863837 31 0.357684996152788 0.715369992305576 0.642315003847212 32 0.367181967200262 0.734363934400524 0.632818032799738 33 0.311507037381165 0.62301407476233 0.688492962618835 34 0.552304981592832 0.895390036814336 0.447695018407168 35 0.435895396989086 0.871790793978173 0.564104603010914 36 0.349676554919542 0.699353109839084 0.650323445080458 37 0.257131316864536 0.514262633729071 0.742868683135465 38 0.411779316307412 0.823558632614825 0.588220683692588 39 0.288291859469662 0.576583718939323 0.711708140530338 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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