JJ Workshop 7, Multiple Regression (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: Fri, 20 Nov 2009 12:09:34 -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/20/t1258744295w60tct8u3te8z41.htm/, Retrieved Fri, 20 Nov 2009 20:11:47 +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/20/t1258744295w60tct8u3te8z41.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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95.1 93.8 97 93.8 112.7 107.6 102.9 101 97.4 95.4 111.4 96.5 87.4 89.2 96.8 87.1 114.1 110.5 110.3 110.8 103.9 104.2 101.6 88.9 94.6 89.8 95.9 90 104.7 93.9 102.8 91.3 98.1 87.8 113.9 99.7 80.9 73.5 95.7 79.2 113.2 96.9 105.9 95.2 108.8 95.6 102.3 89.7 99 92.8 100.7 88 115.5 101.1 100.7 92.7 109.9 95.8 114.6 103.8 85.4 81.8 100.5 87.1 114.8 105.9 116.5 108.1 112.9 102.6 102 93.7 106 103.5 105.3 100.6 118.8 113.3 106.1 102.4 109.3 102.1 117.2 106.9 92.5 87.3 104.2 93.1 112.5 109.1 122.4 120.3 113.3 104.9 100 92.6 110.7 109.8 112.8 111.4 109.8 117.9 117.3 121.6 109.1 117.8 115.9 124.2 96 106.8 99.8 102.7 116.8 116.8 115.7 113.6 99.4 96.1 94.3 85

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 TIA[t] = + 61.8575669338312 + 0.424343554858512IAidM[t] -2.33777469667370M1[t] -0.577049301940704M2[t] + 5.13951514947417M3[t] + 0.904259181572388M4[t] + 0.561433162386583M5[t] + 7.66866066909776M6[t] -10.6409835660198M7[t] -0.580591902319806M8[t] + 6.66122411022697M9[t] + 5.794379453676M10[t] + 3.07952396301393M11[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) 61.8575669338312 5.490523 11.2662 0 0 IAidM 0.424343554858512 0.058109 7.3026 0 0 M1 -2.33777469667370 2.414311 -0.9683 0.337852 0.168926 M2 -0.577049301940704 2.402117 -0.2402 0.8112 0.4056 M3 5.13951514947417 2.562361 2.0058 0.050656 0.025328 M4 0.904259181572388 2.467124 0.3665 0.715619 0.35781 M5 0.561433162386583 2.437055 0.2304 0.818801 0.409401 M6 7.66866066909776 2.550586 3.0066 0.004231 0.002116 M7 -10.6409835660198 2.373224 -4.4838 4.7e-05 2.4e-05 M8 -0.580591902319806 2.369602 -0.245 0.80751 0.403755 M9 6.66122411022697 2.586893 2.575 0.013232 0.006616 M10 5.794379453676 2.629592 2.2035 0.032493 0.016247 M11 3.07952396301393 2.449803 1.257 0.214947 0.107473 Multiple Linear Regression - Regression Statistics Multiple R 0.928405747616052 R-squared 0.86193723220652 Adjusted R-squared 0.826687163833717 F-TEST (value) 24.4520726340359 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 3.33066907387547e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.74664781678294 Sum Squared Residuals 659.756383561207 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 99.3232176828856 -4.22321768288557 2 97 101.083943077619 -4.08394307761878 3 112.7 112.656448586081 0.0435514139188484 4 102.9 105.620525156113 -2.72052515611318 5 97.4 102.901375229720 -5.50137522971972 6 111.4 110.475380646775 0.924619353224741 7 87.4 89.0680284611906 -1.6680284611906 8 96.8 98.2372986596877 -1.43729865968767 9 114.1 115.408753855924 -1.30875385592365 10 110.3 114.669212265830 -4.36921226583022 11 103.9 109.153689313102 -5.25368931310196 12 101.6 99.5817089607528 2.01829103924719 13 94.6 97.6258434634518 -3.02584346345177 14 95.9 99.4714375691565 -3.57143756915646 15 104.7 106.842941884520 -2.14294188451953 16 102.8 101.504392673986 1.29560732601438 17 98.1 99.676364212795 -1.57636421279503 18 113.9 111.833280022322 2.06671997767750 19 80.9 82.405834649912 -1.50583464991196 20 95.7 94.8849845763054 0.815015423694568 21 113.2 109.637681509848 3.56231849015212 22 105.9 108.049452810037 -2.14945281003743 23 108.8 105.504334741319 3.29566525868124 24 102.3 99.9211838046396 2.37881619536038 25 99 98.8988741280273 0.101125871972705 26 100.7 98.6227504594394 2.07724954056056 27 115.5 109.898215479501 5.60178452049918 28 100.7 102.098473650788 -1.39847365078754 29 109.9 103.071112651663 6.82888734833688 30 114.6 113.573088597242 1.02691140275759 31 85.4 85.9278861552376 -0.527886155237602 32 100.5 98.2372986596877 2.26270134031232 33 114.8 113.456773503574 1.34322649642551 34 116.5 113.523484667712 2.97651533228777 35 112.9 108.474739625328 4.42526037467166 36 102 101.618558024074 0.381441975926336 37 106 103.439350165013 2.56064983498662 38 105.3 103.969479250657 1.33052074934331 39 118.8 115.075206848775 3.72479315122533 40 106.1 106.214606132915 -0.114606132915115 41 109.3 105.744477047272 3.55552295272825 42 117.2 114.888553617304 2.31144638269621 43 92.5 88.2617757069594 4.23822429304057 44 104.2 100.783359988839 3.41664001116125 45 112.5 114.814672879122 -2.31467287912172 46 122.4 118.700476036986 3.69952396301392 47 113.3 109.450729801503 3.84927019849707 48 100 101.151780113729 -1.15178011372930 49 110.7 106.112714560622 4.587285439378 50 112.8 108.552389643129 4.24761035687137 51 109.8 117.027187201124 -7.22718720112383 52 117.3 114.362002386199 2.93799761380146 53 109.1 112.406670858550 -3.30667085855040 54 115.9 122.229697116356 -6.32969711635605 55 96 96.5364750267004 -0.536475026700412 56 99.8 104.857058115480 -5.05705811548047 57 116.8 118.082118251532 -1.28211825153227 58 115.7 115.857374219434 -0.157374219434048 59 99.4 105.716506518748 -6.31650651874801 60 94.3 97.9267690968046 -3.62676909680461 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.146336956591492 0.292673913182985 0.853663043408508 17 0.119266633278496 0.238533266556992 0.880733366721504 18 0.0607543078107421 0.121508615621484 0.939245692189258 19 0.0295361830596729 0.0590723661193457 0.970463816940327 20 0.0141338793317669 0.0282677586635338 0.985866120668233 21 0.0124680433774152 0.0249360867548305 0.987531956622585 22 0.0062764138267406 0.0125528276534812 0.99372358617326 23 0.0347707756395406 0.0695415512790811 0.96522922436046 24 0.0196498096215941 0.0392996192431881 0.980350190378406 25 0.0243025782125254 0.0486051564250507 0.975697421787475 26 0.0370477549266676 0.0740955098533352 0.962952245073332 27 0.0910802230625546 0.182160446125109 0.908919776937445 28 0.0722316470010767 0.144463294002153 0.927768352998923 29 0.311138089928458 0.622276179856917 0.688861910071542 30 0.234283772050270 0.468567544100541 0.76571622794973 31 0.189745109090494 0.379490218180987 0.810254890909506 32 0.148182909633626 0.296365819267252 0.851817090366374 33 0.103105109888041 0.206210219776082 0.89689489011196 34 0.111556083475186 0.223112166950372 0.888443916524814 35 0.135306828128730 0.270613656257461 0.86469317187127 36 0.0999533501807373 0.199906700361475 0.900046649819263 37 0.0924184695001448 0.184836939000290 0.907581530499855 38 0.0751393299797995 0.150278659959599 0.9248606700202 39 0.126912816599885 0.25382563319977 0.873087183400115 40 0.123233846745831 0.246467693491661 0.87676615325417 41 0.092680248985868 0.185360497971736 0.907319751014132 42 0.09160087731245 0.1832017546249 0.90839912268755 43 0.0942746167922112 0.188549233584422 0.905725383207789 44 0.583864316857628 0.832271366284743 0.416135683142372 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 5 0.172413793103448 NOK 10% type I error level 8 0.275862068965517 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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