Paper multiple intercept = dow jones

*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: Sun, 26 Dec 2010 14:51:59 +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/26/t12933751013u3xo8dv55fttkk.htm/, Retrieved Sun, 26 Dec 2010 15:51:44 +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/26/t12933751013u3xo8dv55fttkk.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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10554,27 2,08 83,9 61,2 10532,54 2,09 85,6 62 10324,31 2,07 87,5 65,1 10695,25 2,04 88,5 63,2 10827,81 2,35 91 66,3 10872,48 2,33 90,6 61,9 10971,19 2,37 91,2 62,1 11145,65 2,59 93,2 66,3 11234,68 2,62 90,1 72 11333,88 2,6 95 65,3 10997,97 2,83 95,4 67,6 11036,89 2,78 93,7 70,5 11257,35 3,01 93,9 74,2 11533,59 3,06 92,5 77,8 11963,12 3,33 89,2 78,5 12185,15 3,32 93,3 77,8 12377,62 3,6 93 81,4 12512,89 3,57 96,1 84,5 12631,48 3,57 96,7 88 12268,53 3,83 97,6 93,9 12754,8 3,84 102,6 98,9 13407,75 3,8 107,6 96,7 13480,21 4,07 103,5 98,9 13673,28 4,05 100,8 102,2 13239,71 4,272 94,5 105,4 13557,69 3,858 100,1 105,1 13901,28 4,067 97,4 116,6 13200,58 3,964 103 112 13406,97 3,782 100,2 108,8 12538,12 4,114 100,2 106,9 12419,57 4,009 99 109,5 12193,88 4,025 102,4 106,7 12656,63 4,082 99 118,9 12812,48 4,044 103,7 117,5 12056,67 3,916 103,4 113,7 11322,38 4,289 95,3 119,6 11530,75 4,296 93,6 120,6 11114,08 4,193 102,4 117,5 9181,73 3,48 110,5 120,3 8614,55 2,934 109,1 119,8 8595 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation DowJones[t] = + 4279.82100424418 + 1787.88911225167Eonia[t] + 68.489432676183deposits[t] -55.2692769688371`2JAAR`[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) 4279.82100424418 1566.40207 2.7323 0.00836 0.00418 Eonia 1787.88911225167 151.596251 11.7938 0 0 deposits 68.489432676183 15.151173 4.5204 3.2e-05 1.6e-05 `2JAAR` -55.2692769688371 7.630917 -7.2428 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.879003863462476 R-squared 0.772647791981959 Adjusted R-squared 0.7606818862968 F-TEST (value) 64.5707740234145 F-TEST (DF numerator) 3 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 803.298803039865 Sum Squared Residuals 36781471.1170209 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10554.27 10362.4140087666 191.855991233443 2 10532.54 10452.5095138635 80.0304861364707 3 10324.31 10375.5468950998 -51.2368950998476 4 10695.25 10495.4112806493 199.838719350728 5 10827.81 11049.5457285344 -221.735728534352 6 10872.48 11229.5769918817 -357.096991881728 7 10971.19 11331.1323605837 -359.942360583736 8 11145.65 11629.3158673624 -483.665867362354 9 11234.68 11155.6004207114 79.0795792886353 10 11333.88 11825.7450142708 -491.865014270838 11 10997.97 12137.2359461309 -1139.26594613087 12 11036.89 11771.1285517591 -734.238551759147 13 11257.35 11991.5446093276 -734.194609327569 14 11533.59 11786.0844621057 -252.494462105683 15 11963.12 12004.110900704 -40.9909007040433 16 12185.15 12305.7271774321 -120.577177432063 17 12377.62 12586.8199019719 -209.199901971862 18 12512.89 12574.1657112971 -61.2757112970847 19 12631.48 12421.8169015119 209.663098488135 20 12268.53 12622.2198259897 -353.689825989723 21 12754.8 12706.199495649 48.6005043510298 22 13407.75 13098.7235038713 309.026496128741 23 13480.21 13179.0544808754 301.155519124581 24 13673.28 12775.9866164075 897.293383592473 25 13239.71 12564.5528871672 675.157112832831 26 13557.69 12224.4884007723 1333.20159922775 27 13901.28 11777.6390718655 2123.64092813447 28 13200.58 12231.2659903469 969.314009653115 29 13406.97 11890.961446724 1516.00855327595 30 12538.12 12589.5522582324 -51.4322582323906 31 12419.57 12175.9364621156 243.633537884428 32 12193.88 12592.1607345234 -398.280734523365 33 12656.63 11786.9211638029 869.708836197126 34 12812.48 12118.2586988717 694.221301128257 35 12056.67 12078.8853151823 -22.2153151822548 36 11322.38 11864.9148152589 -542.534815258907 37 11530.75 11705.7287265263 -174.97872652632 38 11114.08 12295.6179141182 -1181.5379141182 39 9181.73 11420.8634062471 -2239.1334062471 40 8614.55 10376.4253836955 -1761.87538369545 41 8595.56 9192.2245669476 -596.664566947592 42 8396.2 8388.05782695522 8.14217304477612 43 7690.5 8531.23589767354 -840.735897673539 44 7235.47 8956.98546383657 -1721.51546383656 45 7992.12 8008.6314622422 -16.5114622421986 46 8398.37 8704.38332684428 -306.01332684428 47 8593 8651.41218212785 -58.4121821278535 48 8679.75 8202.47997386166 477.270026138341 49 9374.63 8684.10341343206 690.526586567935 50 9634.97 8963.37272802636 671.59727197364 51 9857.34 8553.45572732473 1303.88427267527 52 10238.83 9520.46184610933 718.36815389067 53 10433.44 9710.10152914819 723.338470851816 54 10471.24 9831.0370146019 640.202985398097 55 10214.51 9890.5988590032 323.9111409968 56 10677.52 10220.7455635073 456.774436492693 57 11052.15 10220.179984407 831.970015593016 58 10500.19 10924.0676559378 -423.877655937785 59 10159.27 11253.7519663967 -1094.48196639672 60 10222.24 10476.313825043 -254.073825042991 61 10350.4 10642.0703443668 -291.670344366798 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.00409041301413997 0.00818082602827994 0.99590958698586 8 0.000637461578571218 0.00127492315714244 0.999362538421429 9 0.000245544519533087 0.000491089039066174 0.999754455480467 10 4.14582375064148e-05 8.29164750128296e-05 0.999958541762494 11 0.000230989784606451 0.000461979569212902 0.999769010215394 12 8.11501798817786e-05 0.000162300359763557 0.999918849820118 13 2.09026893625446e-05 4.18053787250893e-05 0.999979097310637 14 8.27617871157461e-06 1.65523574231492e-05 0.999991723821288 15 4.44953888885106e-06 8.89907777770213e-06 0.999995550461111 16 5.54154676357724e-06 1.10830935271545e-05 0.999994458453236 17 2.63494195837061e-06 5.26988391674121e-06 0.999997365058042 18 2.96267804848661e-06 5.92535609697321e-06 0.999997037321952 19 2.35513237539404e-06 4.71026475078808e-06 0.999997644867625 20 5.75393214559303e-06 1.15078642911861e-05 0.999994246067854 21 2.17117375418409e-06 4.34234750836819e-06 0.999997828826246 22 8.49028004267934e-06 1.69805600853587e-05 0.999991509719957 23 4.6731678581454e-06 9.3463357162908e-06 0.999995326832142 24 4.43915064887655e-06 8.87830129775311e-06 0.99999556084935 25 2.12694186856094e-06 4.25388373712189e-06 0.999997873058131 26 1.56916146525482e-06 3.13832293050964e-06 0.999998430838535 27 2.94910819245613e-06 5.89821638491227e-06 0.999997050891808 28 9.673385092975e-06 1.934677018595e-05 0.999990326614907 29 1.82231591827324e-05 3.64463183654647e-05 0.999981776840817 30 0.000215530845022119 0.000431061690044237 0.999784469154978 31 0.00093496286716027 0.00186992573432054 0.99906503713284 32 0.00425043770393334 0.00850087540786668 0.995749562296067 33 0.0111151185045693 0.0222302370091386 0.98888488149543 34 0.080496735764732 0.160993471529464 0.919503264235268 35 0.258726644261554 0.517453288523108 0.741273355738446 36 0.549418680446177 0.901162639107647 0.450581319553823 37 0.583812868754316 0.832374262491367 0.416187131245684 38 0.772880490996264 0.454239018007472 0.227119509003736 39 0.924015742816485 0.151968514367029 0.0759842571835147 40 0.956156357933983 0.087687284132035 0.0438436420660175 41 0.961568048876645 0.07686390224671 0.038431951123355 42 0.99825105913077 0.00349788173846205 0.00174894086923103 43 0.999218702198084 0.00156259560383291 0.000781297801916454 44 0.998144554892708 0.00371089021458376 0.00185544510729188 45 0.997132181635495 0.00573563672900934 0.00286781836450467 46 0.998889698397665 0.00222060320467062 0.00111030160233531 47 0.998117823856906 0.0037643522861879 0.00188217614309395 48 0.998473863439584 0.00305227312083276 0.00152613656041638 49 0.997955167059816 0.00408966588036824 0.00204483294018412 50 0.996805929578 0.00638814084400003 0.00319407042200002 51 0.993927351441918 0.0121452971161649 0.00607264855808245 52 0.984500762968162 0.0309984740636767 0.0154992370318383 53 0.955812077913944 0.0883758441721113 0.0441879220860557 54 0.885344778129279 0.229310443741442 0.114655221870721 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 35 0.729166666666667 NOK 5% type I error level 38 0.791666666666667 NOK 10% type I error level 41 0.854166666666667 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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