Multiple regression analysis: include monthly dummies

*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, 14 Nov 2009 05:18:51 -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/Nov/14/t12582012025je4ccwu67hnjg9.htm/, Retrieved Sat, 14 Nov 2009 13:20:15 +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/14/t12582012025je4ccwu67hnjg9.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:

» Textbox « » Textfile « » CSV «

8,4 99 8,4 98.6 8,4 98.6 8,6 98.5 8,9 98.9 8,8 99.4 8,3 99.8 7,5 99.9 7,2 100 7,4 100.1 8,8 100.1 9,3 100.2 9,3 100.3 8,7 100 8,2 99.9 8,3 99.4 8,5 99.8 8,6 99.6 8,5 100 8,2 99.9 8,1 100.3 7,9 100.6 8,6 100.7 8,7 100.8 8,7 100.8 8,5 100.6 8,4 101.1 8,5 101.1 8,7 100.9 8,7 101.1 8,6 101.2 8,5 101.4 8,3 101.9 8 102.1 8,2 102.1 8,1 103 8,1 103.4 8 103.2 7,9 103.1 7,9 103 8 103.7 8 103.4 7,9 103.5 8 103.8 7,7 104 7,2 104.2 7,5 104.4 7,3 104.4 7 104.9 7 105.3 7 105.2 7,2 105.4 7,3 105.4 7,1 105.5 6,8 105.7 6,4 105.6 6,1 105.8 6,5 105.4 7,7 105.5 7,9 105.8 7,5 106.1 6,9 106 6,6 105.5 6,9 105.4 7,7 106 8 106.1 8 106.4 7,7 106 7,3 106 7,4 106 8,1 106 8,3 106.1 8,2 106.1

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 werkl[t] = + 27.862457704015 -0.189544972149105afzetp[t] -0.178728142494257M1[t] -0.558499469364017M2[t] -0.734643384638138M3[t] -0.603597881853048M4[t] -0.260241974005832M5[t] -0.230938975862558M6[t] -0.366886066158616M7[t] -0.666886066158615M8[t] -0.889325572657158M9[t] -0.926689241180551M10[t] -0.164052909703943M11[t] + 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) 27.862457704015 2.113952 13.1803 0 0 afzetp -0.189544972149105 0.020372 -9.3041 0 0 M1 -0.178728142494257 0.247576 -0.7219 0.473153 0.236576 M2 -0.558499469364017 0.257729 -2.167 0.034215 0.017108 M3 -0.734643384638138 0.25782 -2.8494 0.005993 0.002996 M4 -0.603597881853048 0.258013 -2.3394 0.022661 0.01133 M5 -0.260241974005832 0.257456 -1.0108 0.316161 0.158081 M6 -0.230938975862558 0.257359 -0.8973 0.373124 0.186562 M7 -0.366886066158616 0.25706 -1.4272 0.158695 0.079348 M8 -0.666886066158615 0.25706 -2.5943 0.011895 0.005948 M9 -0.889325572657158 0.256872 -3.4621 0.000994 0.000497 M10 -0.926689241180551 0.256834 -3.6081 0.00063 0.000315 M11 -0.164052909703943 0.256804 -0.6388 0.525367 0.262684 Multiple Linear Regression - Regression Statistics Multiple R 0.811643807977646 R-squared 0.658765671028454 Adjusted R-squared 0.590518805234145 F-TEST (value) 9.65268753899884 F-TEST (DF numerator) 12 F-TEST (DF denominator) 60 p-value 4.30271707152485e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.444709263038103 Sum Squared Residuals 11.8659797179136 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.4 8.91877731875937 -0.518777318759372 2 8.4 8.6148239807492 -0.214823980749204 3 8.4 8.43868006547508 -0.0386800654750822 4 8.6 8.58868006547508 0.0113199345249173 5 8.9 8.85621798446266 0.0437820155373440 6 8.8 8.79074849653137 0.00925150346862508 7 8.3 8.57898341737568 -0.278983417375678 8 7.5 8.26002892016077 -0.760028920160768 9 7.2 8.01863491644731 -0.818634916447314 10 7.4 7.96231675070901 -0.562316750709013 11 8.8 8.72495308218562 0.0750469178143812 12 9.3 8.87005149467465 0.429948505325351 13 9.3 8.67236885496549 0.627631145034516 14 8.7 8.34946101974046 0.350538980259543 15 8.2 8.19227160168124 0.00772839831875522 16 8.3 8.41808959054089 -0.118089590540886 17 8.5 8.68562750952846 -0.185627509528463 18 8.6 8.75283950210156 -0.152839502101558 19 8.5 8.54107442294586 -0.0410744229458577 20 8.2 8.26002892016077 -0.0600289201607676 21 8.1 7.96177142480258 0.138228575197415 22 7.9 7.86754426463446 0.0324557353655402 23 8.6 8.61122609889616 -0.0112260988961556 24 8.7 8.75632451138519 -0.0563245113851899 25 8.7 8.57759636889093 0.122403631109067 26 8.5 8.235734036451 0.264265963549006 27 8.4 7.96481763510232 0.435182364897681 28 8.5 8.0958631378874 0.40413686211259 29 8.7 8.47712804016444 0.222871959835554 30 8.7 8.4685220438779 0.231477956122100 31 8.6 8.31362045636693 0.286379543633068 32 8.5 7.97571146193711 0.524288538062891 33 8.3 7.65849946936401 0.641500530635986 34 8 7.5832268064108 0.416773193589198 35 8.2 8.3458631378874 -0.145863137887410 36 8.1 8.33932557265716 -0.239325572657158 37 8.1 8.08477944130326 0.015220558696742 38 8 7.74291710886332 0.257082891136680 39 7.9 7.58572769080411 0.314272309195890 40 7.9 7.73572769080411 0.164272309195891 41 8 7.94640211814695 0.0535978818530483 42 8 8.03256860793496 -0.0325686079349559 43 7.9 7.87766702042399 0.0223329795760104 44 8 7.52080352877926 0.479196471220741 45 7.7 7.2604550278509 0.439544972149105 46 7.2 7.18518236489768 0.0148176351023201 47 7.5 7.90990970194447 -0.409909701944466 48 7.3 8.0739626116484 -0.773962611648409 49 7 7.8004619830796 -0.8004619830796 50 7 7.3448726673502 -0.3448726673502 51 7 7.18768324929099 -0.187683249290987 52 7.2 7.28081975764626 -0.0808197576462561 53 7.3 7.62417566549347 -0.324175665493473 54 7.1 7.63452416642184 -0.534524166421837 55 6.8 7.46066808169596 -0.660668081695958 56 6.4 7.17962257891087 -0.77962257891087 57 6.1 6.9192740779825 -0.819274077982507 58 6.5 6.95772839831875 -0.457728398318754 59 7.7 7.70141023258045 -0.00141023258045101 60 7.9 7.80859965063966 0.0914003493603366 61 7.5 7.57300801650068 -0.073008016500676 62 6.9 7.21219118684583 -0.312191186845826 63 6.6 7.13081975764626 -0.530819757646257 64 6.9 7.28081975764626 -0.380819757646256 65 7.7 7.51044868220401 0.189551317795990 66 8 7.52079718313237 0.479202816867626 67 8 7.32798660119158 0.672013398808416 68 7.7 7.10380459005123 0.596195409948773 69 7.3 6.88136508355268 0.418634916447315 70 7.4 6.84400141502929 0.555998584970708 71 8.1 7.6066377465059 0.493362253494101 72 8.3 7.75173615899493 0.548263841005068 73 8.2 7.57300801650068 0.626991983499324 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.455070840551577 0.910141681103154 0.544929159448423 17 0.407600087532378 0.815200175064756 0.592399912467622 18 0.285990130023005 0.57198026004601 0.714009869976995 19 0.187834774270815 0.375669548541630 0.812165225729185 20 0.238518006125678 0.477036012251356 0.761481993874322 21 0.333649669404469 0.667299338808938 0.666350330595531 22 0.280598059746178 0.561196119492357 0.719401940253822 23 0.21367804341037 0.42735608682074 0.78632195658963 24 0.219912812593181 0.439825625186362 0.780087187406819 25 0.162045409423105 0.32409081884621 0.837954590576895 26 0.110119988153509 0.220239976307018 0.889880011846491 27 0.073895203418545 0.14779040683709 0.926104796581455 28 0.047569423942351 0.095138847884702 0.952430576057649 29 0.0284577423503733 0.0569154847007466 0.971542257649627 30 0.0163731757960353 0.0327463515920705 0.983626824203965 31 0.00954880911841636 0.0190976182368327 0.990451190881584 32 0.0107471582575501 0.0214943165151002 0.98925284174245 33 0.0114717928680272 0.0229435857360545 0.988528207131973 34 0.00727577892695357 0.0145515578539071 0.992724221073046 35 0.00900158258446219 0.0180031651689244 0.990998417415538 36 0.0229023211939820 0.0458046423879640 0.977097678806018 37 0.0238662328888059 0.0477324657776117 0.976133767111194 38 0.0205485971019279 0.0410971942038559 0.979451402898072 39 0.0184585063846128 0.0369170127692255 0.981541493615387 40 0.0154600038102840 0.0309200076205679 0.984539996189716 41 0.0114097046905800 0.0228194093811601 0.98859029530942 42 0.00826681199603015 0.0165336239920603 0.99173318800397 43 0.0059650225422706 0.0119300450845412 0.99403497745773 44 0.0117502531708912 0.0235005063417825 0.988249746829109 45 0.0746545595400973 0.149309119080195 0.925345440459903 46 0.160198427677807 0.320396855355615 0.839801572322193 47 0.198597880299571 0.397195760599142 0.801402119700429 48 0.296482073356868 0.592964146713737 0.703517926643132 49 0.363679356816687 0.727358713633374 0.636320643183313 50 0.522944172065068 0.954111655869865 0.477055827934932 51 0.629651513457192 0.740696973085616 0.370348486542808 52 0.550661878165937 0.898676243668126 0.449338121834063 53 0.550801336602287 0.898397326795426 0.449198663397713 54 0.451564363430038 0.903128726860076 0.548435636569962 55 0.346067125246831 0.692134250493663 0.653932874753169 56 0.374453597684712 0.748907195369425 0.625546402315288 57 0.649561992855417 0.700876014289166 0.350438007144583 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 15 0.357142857142857 NOK 10% type I error level 17 0.404761904761905 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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