month

*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: Tue, 28 Dec 2010 21:20:22 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293571115o8lo6twk5qrepu2.htm/, Retrieved Tue, 28 Dec 2010 22:18:46 +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/2010/Dec/28/t1293571115o8lo6twk5qrepu2.htm/}, year = {2010}, } @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 = {2010}, 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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12 -2 3 16 0 6 11 0 8 17 2 6 10 -2 3 23 3 7 9 -4 3 24 1 4 8 -4 7 27 1 3 7 -7 4 31 0 0 6 -9 -4 40 1 6 5 -13 -6 47 -1 3 4 -8 8 43 2 1 3 -13 2 60 2 6 2 -15 -1 64 0 5 1 -15 -2 65 1 7 12 -15 0 65 1 4 11 -10 10 55 3 3 10 -12 3 57 3 6 9 -11 6 57 1 6 8 -11 7 57 1 5 7 -17 -4 65 -2 2 6 -18 -5 69 1 3 5 -19 -7 70 1 -2 4 -22 -10 71 -1 -4 3 -24 -21 71 -4 0 2 -24 -22 73 -2 1 1 -20 -16 68 -1 4 12 -25 -25 65 -5 -3 11 -22 -22 57 -4 -3 10 -17 -22 41 -5 0 9 -9 -19 21 0 6 8 -11 -21 21 -2 -1 7 -13 -31 17 -4 0 6 -11 -28 9 -6 -1 5 -9 -23 11 -2 1 4 -7 -17 6 -2 -4 3 -3 -12 -2 -2 -1 2 -3 -14 0 1 -1 1 -6 -18 5 -2 0 12 -4 -16 3 0 3 11 -8 -22 7 -1 0 10 -1 -9 4 2 8 9 -2 -10 8 3 8 8 -2 -10 9 2 8 7 -1 0 14 3 8 6 1 3 12 4 11 5 2 2 12 5 13 4 2 4 7 5 5 3 -1 -3 15 4 12 2 1 0 14 5 13 1 -1 -1 19 6 9 12 -8 -7 39 4 11 11 1 2 12 6 7 10 2 3 11 6 12 9 -2 -3 17 3 11 8 -2 -5 16 5 10 7 -2 0 25 5 13 6 -2 -3 24 5 14 5 -6 -7 28 3 10 4 -4 -7 25 5 13 3 -5 -7 31 5 12 2 -2 -4 24 6 13 1 -1 -3 24 6 17

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 werkloosheid[t] = + 1.65540269135324 -0.123453483808698maand[t] -3.9315572647213indicator[t] + 1.00836927675496economie[t] + 1.00186866984164`financiën`[t] + 0.881370886951687spaarvermogen[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) 1.65540269135324 0.58071 2.8507 0.006167 0.003083 maand -0.123453483808698 0.045257 -2.7279 0.008583 0.004291 indicator -3.9315572647213 0.029371 -133.8573 0 0 economie 1.00836927675496 0.021528 46.8389 0 0 `financiën` 1.00186866984164 0.122679 8.1666 0 0 spaarvermogen 0.881370886951687 0.056269 15.6634 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.998842283514877 R-squared 0.997685907337214 Adjusted R-squared 0.997471639498067 F-TEST (value) 4656.25597994355 F-TEST (DF numerator) 5 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.16616746115089 Sum Squared Residuals 73.4371135621444 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16 16.3504085670663 -0.3504085670663 2 17 15.6563312448906 1.34366875510941 3 23 20.4842924311604 2.5157075688396 4 24 23.8230104438734 0.176989556126558 5 27 27.0985701477503 -0.0985701477502617 6 31 32.3456062647613 -1.34560626476128 7 40 38.5553140555247 1.44468594447534 8 47 47.7404080441703 -0.740408044170314 9 43 43.5661093145635 -0.566109314563477 10 60 61.7039878962074 -1.70398789620736 11 64 63.7803398525588 0.219660147441176 12 65 65.6600345033576 -0.660034503357571 13 65 63.6746720741167 1.32532792588326 14 55 55.3463984546001 -0.346398454600119 15 57 58.9184941914218 -1.91849419142177 16 57 56.1317609010908 0.868239098909232 17 57 56.3822127747027 0.617787225297262 18 65 63.3532291321547 1.64677086784528 19 69 70.2868475004064 -1.28684750040636 20 70 67.918265260668 2.08173473933200 21 71 73.0448035947891 -2.04480359478908 22 71 70.4591871020177 0.540812897982345 23 73 72.4593795357064 0.540620464293637 24 68 66.5528009518563 1.44719904814369 25 65 65.6002045747442 -0.600204574744149 26 57 57.9559627644954 -0.95596276449545 27 41 40.0638739157111 0.936126084288936 28 21 22.0575457829325 -1.05754578293253 29 21 19.8540416943288 1.14595830567117 30 17 16.6345504872989 0.365449512701052 31 9 9.03488904529497 -0.0348890452949698 32 11 12.1072908367058 -1.10729083670578 33 6 6.0109910168432 -0.010991016843202 34 -2 -1.90582551360345 -0.0941744863965514 35 0 -0.793504573779758 0.793504573779758 36 5 4.96690847459979 0.0330915254002124 37 3 2.41039417730975 0.589605822690246 38 7 8.5638797287772 -1.5638797287772 39 4 4.33180606248967 -0.331806062489669 40 8 8.38031620410634 -0.380316204106345 41 9 7.50190101807341 1.49809898192659 42 14 14.7793586745520 -0.77935867455204 43 12 13.7107867898797 -1.71078678987971 44 12 11.6589241759572 0.341075824042835 45 7 6.74814911766229 0.251850882337714 46 15 16.7754169971703 -1.77541699717034 47 14 13.9441033385946 0.055896661405361 48 19 18.3986871971259 0.601312802874138 49 39 38.2703885019696 0.729611498030369 50 12 10.5634038859578 1.43659611404221 51 11 12.1705238165586 -1.17052381655857 52 17 18.0830138022461 -1.08301380224613 53 16 17.3120951852765 -1.31209518527649 54 25 25.1215077137150 -0.121507713715047 55 24 23.1012242542106 0.898775745789445 56 28 29.3882088023946 -1.38820880239460 57 25 26.296397757299 -1.29639775729902 58 31 29.4700376188773 1.52996238112266 59 24 22.7071666955803 1.29283330441966 60 24 23.4329157392294 0.567084260770562 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0303930984716481 0.0607861969432962 0.969606901528352 10 0.0229701493477660 0.0459402986955319 0.977029850652234 11 0.116233853537892 0.232467707075784 0.883766146462108 12 0.207176153127824 0.414352306255648 0.792823846872176 13 0.341315369225906 0.682630738451812 0.658684630774094 14 0.280632252930967 0.561264505861934 0.719367747069033 15 0.693691361793178 0.612617276413644 0.306308638206822 16 0.690022627881167 0.619954744237666 0.309977372118833 17 0.641765037470802 0.716469925058396 0.358234962529198 18 0.756615541646242 0.486768916707516 0.243384458353758 19 0.727835263968283 0.544329472063435 0.272164736031717 20 0.887700942952494 0.224598114095012 0.112299057047506 21 0.950065021815382 0.0998699563692358 0.0499349781846179 22 0.92423387972417 0.151532240551661 0.0757661202758306 23 0.88956416495769 0.220871670084622 0.110435835042311 24 0.883321066260617 0.233357867478767 0.116678933739383 25 0.87920303213384 0.241593935732320 0.120796967866160 26 0.881363917892327 0.237272164215346 0.118636082107673 27 0.868497834263956 0.263004331472088 0.131502165736044 28 0.899444375222549 0.201111249554902 0.100555624777451 29 0.894870825436997 0.210258349126005 0.105129174563003 30 0.85906489005168 0.281870219896641 0.140935109948320 31 0.84365122302839 0.312697553943219 0.156348776971609 32 0.83160145511175 0.336797089776498 0.168398544888249 33 0.775946203641175 0.44810759271765 0.224053796358825 34 0.723817776207273 0.552364447585454 0.276182223792727 35 0.66751429408177 0.66497141183646 0.33248570591823 36 0.623395651608704 0.753208696782592 0.376604348391296 37 0.606497401690945 0.78700519661811 0.393502598309055 38 0.630690507578687 0.738618984842626 0.369309492421313 39 0.552120425704502 0.895759148590996 0.447879574295498 40 0.500126905391252 0.999746189217496 0.499873094608748 41 0.78410207657698 0.43179584684604 0.21589792342302 42 0.743649281206558 0.512701437586884 0.256350718793442 43 0.758226424350949 0.483547151298102 0.241773575649051 44 0.721961042006206 0.556077915987588 0.278038957993794 45 0.628822107700454 0.742355784599092 0.371177892299546 46 0.584530160117942 0.830939679764117 0.415469839882058 47 0.492221491841147 0.984442983682293 0.507778508158853 48 0.417463811402343 0.834927622804687 0.582536188597657 49 0.364997763918070 0.729995527836141 0.63500223608193 50 0.373081710022677 0.746163420045353 0.626918289977323 51 0.291105108052042 0.582210216104084 0.708894891947958 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 1 0.0232558139534884 OK 10% type I error level 3 0.0697674418604651 OK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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