paperMR3(werk)

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Tue, 21 Dec 2010 13:28:47 +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/21/t1292938092ws27c0ee7coboii.htm/, Retrieved Tue, 21 Dec 2010 14:28:24 +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/21/t1292938092ws27c0ee7coboii.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}, }

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Dataseries X:

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17972385,83 0 17637387,4 15213975,95 16471559,62 14731798,37 16896235,55 0 17972385,83 17637387,4 15213975,95 16471559,62 16697955,94 0 16896235,55 17972385,83 17637387,4 15213975,95 19691579,52 0 16697955,94 16896235,55 17972385,83 17637387,4 15930700,75 0 19691579,52 16697955,94 16896235,55 17972385,83 17444615,98 0 15930700,75 19691579,52 16697955,94 16896235,55 17699369,88 0 17444615,98 15930700,75 19691579,52 16697955,94 15189796,81 0 17699369,88 17444615,98 15930700,75 19691579,52 15672722,75 0 15189796,81 17699369,88 17444615,98 15930700,75 17180794,3 0 15672722,75 15189796,81 17699369,88 17444615,98 17664893,45 0 17180794,3 15672722,75 15189796,81 17699369,88 17862884,98 0 17664893,45 17180794,3 15672722,75 15189796,81 16162288,88 0 17862884,98 17664893,45 17180794,3 15672722,75 17463628,82 0 16162288,88 17862884,98 17664893,45 17180794,3 16772112,17 0 17463628,82 16162288,88 17862884,98 17664893,45 19106861,48 0 16772112,17 17463628,82 16162288,88 17862884,98 16721314,25 0 19106861,48 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 10 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 7058102.37766021 -2793503.20246403X[t] + 0.360299173377357Y1[t] + 0.152048144010289Y2[t] + 0.3745587444819Y3[t] -0.320617214160464Y4[t] -1277764.43976877M1[t] -301214.211190674M2[t] -613984.12257938M3[t] + 1702120.12956651M4[t] -697110.854102996M5[t] -310757.834273430M6[t] + 31032.2778017763M7[t] -794467.94169392M8[t] -1913826.67528654M9[t] + 447318.9919382M10[t] + 1871094.16661258M11[t] + 62686.6577060315t + 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) 7058102.37766021 1705473.86239 4.1385 0.000187 9.3e-05 X -2793503.20246403 626762.642767 -4.457 7.1e-05 3.6e-05 Y1 0.360299173377357 0.126369 2.8512 0.007004 0.003502 Y2 0.152048144010289 0.122565 1.2405 0.222379 0.111189 Y3 0.3745587444819 0.120063 3.1197 0.003448 0.001724 Y4 -0.320617214160464 0.110861 -2.8921 0.0063 0.00315 M1 -1277764.43976877 647489.781113 -1.9734 0.055753 0.027877 M2 -301214.211190674 675546.515769 -0.4459 0.658213 0.329106 M3 -613984.12257938 674823.388649 -0.9098 0.36864 0.18432 M4 1702120.12956651 668428.172544 2.5465 0.015057 0.007528 M5 -697110.854102996 621690.910914 -1.1213 0.26919 0.134595 M6 -310757.834273430 612045.124272 -0.5077 0.614573 0.307286 M7 31032.2778017763 721473.942765 0.043 0.965917 0.482958 M8 -794467.94169392 637796.661994 -1.2456 0.220521 0.11026 M9 -1913826.67528654 693698.412609 -2.7589 0.008872 0.004436 M10 447318.9919382 820443.485288 0.5452 0.588791 0.294395 M11 1871094.16661258 683553.738046 2.7373 0.009371 0.004685 t 62686.6577060315 16390.407887 3.8246 0.000473 0.000237 Multiple Linear Regression - Regression Statistics Multiple R 0.936477260038661 R-squared 0.876989658569518 Adjusted R-squared 0.821958716350618 F-TEST (value) 15.9363009828373 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 2.46369591394568e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 822642.663004327 Sum Squared Residuals 25716156137804.4 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 17972385.83 15957316.0405312 2015069.78946881 2 16896235.55 16456891.4315774 439344.118422616 3 16697955.94 17180920.9340329 -482964.994032918 4 19691579.52 18673134.3750347 1018445.14496525 5 15930700.75 16874554.3425273 -943853.592527275 6 17444615.98 16694492.3602775 750123.619722504 7 17699369.88 18257456.6449242 -558086.764924161 8 15189796.81 15448141.4209251 -258344.610925058 9 15672722.75 15298859.7618952 373862.988104766 10 17180794.3 17125146.9936770 55647.3063230449 11 17664893.45 18206732.7277884 -541839.277788402 12 17862884.98 17787541.6828714 75343.2971285835 13 16162288.88 17127433.4795061 -965144.599506103 14 17463628.82 17281861.1120908 181767.707909166 15 16772112.17 17161026.0204014 -388913.850401367 16 19106861.48 18788077.7426223 318783.737377711 17 16721314.25 18220266.4779752 -1498952.22797515 18 18161267.85 17488544.1653530 672723.684646968 19 18509941.2 19145329.9102478 -635388.710247796 20 17802737.97 17084996.9456764 717741.02432356 21 16409869.75 17130729.9860034 -720860.236003403 22 17967742.04 18614108.8445430 -646366.804542972 23 20286602.27 20073407.9154846 213194.354515382 24 19537280.81 19042385.9786602 494894.831339799 25 18021889.62 18939998.9055509 -918109.285550902 26 20194317.23 19688377.3642148 505939.865785151 27 19049596.62 18966474.1525072 83122.4674927592 28 20244720.94 20935779.0964159 -691058.156415871 29 21473302.24 20155346.6906513 1317955.54934873 30 19673603.19 20103476.8269737 -429873.636973670 31 21053177.29 20860988.4209119 192188.869088106 32 20159479.84 20398591.8058036 -239111.965803580 33 18203628.31 18161685.6284733 41942.6815267043 34 21289464.94 20838687.2638710 450777.676129021 35 20432335.71 19569029.2861691 863306.423830858 36 17180395.07 17474948.049778 -294552.979777997 37 15816786.32 16740780.5973217 -923994.277321695 38 15071819.75 15483841.2475146 -412021.497514609 39 14521120.61 13814780.5575235 706340.05247648 40 15668789.39 16413760.8053831 -744971.415383076 41 14346884.11 14565150.5055092 -218266.395509183 42 13881008.13 14744989.6391656 -863981.509165582 43 15465943.69 15387051.4355003 78892.2544997095 44 14238232.92 14261359.7187137 -23126.7987136971 45 13557713.21 13252658.6436281 305054.566371932 46 16127590.29 15987648.4679091 139941.822090906 47 16793894.2 17328555.7005578 -534661.50055784 48 16014007.43 16289692.5786904 -275685.148690384 49 16867867.15 16075688.7770901 792178.372909895 50 16014583.21 16729613.4046023 -715030.194602325 51 15878594.85 15796178.5255350 82416.324465046 52 18664899.14 18566098.450544 98800.6894559813 53 17962530.06 16619413.3933371 1343116.66666288 54 17332692.2 17461684.3582302 -128992.158230219 55 19542066.35 18619671.9984159 922394.351584143 56 17203555.19 17400712.8388812 -197157.648881226 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.82997349703611 0.340053005927782 0.170026502963891 22 0.83314792584259 0.333704148314821 0.166852074157411 23 0.787621552744803 0.424756894510394 0.212378447255197 24 0.757448683521364 0.485102632957272 0.242551316478636 25 0.663480249894047 0.673039500211906 0.336519750105953 26 0.666354737186291 0.667290525627417 0.333645262813709 27 0.632807094776176 0.734385810447648 0.367192905223824 28 0.511944058955326 0.976111882089348 0.488055941044674 29 0.879802087010773 0.240395825978454 0.120197912989227 30 0.898077144022206 0.203845711955589 0.101922855977794 31 0.891500414035321 0.216999171929357 0.108499585964679 32 0.818936660411113 0.362126679177775 0.181063339588887 33 0.812199403684684 0.375601192630632 0.187800596315316 34 0.685847504404318 0.628304991191365 0.314152495595682 35 0.610865026455625 0.77826994708875 0.389134973544375 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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