Downjones

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 02:50:10 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227779547qhgmeucu3ttyvlp.htm/, Retrieved Thu, 27 Nov 2008 09:52:37 +0000

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/2008/Nov/27/t1227779547qhgmeucu3ttyvlp.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Dataseries X:

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9492,49 0 9682,35 0 9762,12 0 10124,63 0 10540,05 0 10601,61 0 10323,73 0 10418,4 0 10092,96 0 10364,91 0 10152,09 0 10032,8 0 10204,59 0 10001,6 0 10411,75 0 10673,38 0 10539,51 0 10723,78 0 10682,06 0 10283,19 0 10377,18 0 10486,64 0 10545,38 0 10554,27 0 10532,54 0 10324,31 0 10695,25 0 10827,81 0 10872,48 0 10971,19 0 11145,65 0 11234,68 0 11333,88 0 10997,97 0 11036,89 0 11257,35 0 11533,59 0 11963,12 0 12185,15 0 12377,62 0 12512,89 0 12631,48 0 12268,53 0 12754,8 0 13407,75 1 13480,21 1 13673,28 1 13239,71 1 13557,69 1 13901,28 1 13200,58 1 13406,97 1 12538,12 1 12419,57 1 12193,88 1 12656,63 1 12812,48 1 12056,67 1 11322,38 1 11530,75 1 11114,08 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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation X[t] = + 9472.89548993289 + 619.911409395974Y[t] + 13.3641976137254M1[t] + 420.570489187174M2[t] + 452.505268456375M3[t] + 639.114047725578M4[t] + 513.13882699478M5[t] + 537.551606263982M6[t] + 346.292385533184M7[t] + 448.559164802386M8[t] + 415.383662192393M9[t] + 243.310441461596M10[t] + 67.5312207307977M11[t] + 44.5032207307978t + 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) 9472.89548993289 374.355088 25.3046 0 0 Y 619.911409395974 321.192125 1.93 0.05965 0.029825 M1 13.3641976137254 421.403118 0.0317 0.974835 0.487417 M2 420.570489187174 442.182481 0.9511 0.346407 0.173204 M3 452.505268456375 441.680678 1.0245 0.31084 0.15542 M4 639.114047725578 441.327719 1.4482 0.15421 0.077105 M5 513.13882699478 441.123961 1.1633 0.250599 0.125299 M6 537.551606263982 441.069609 1.2187 0.229023 0.114511 M7 346.292385533184 441.16472 0.785 0.436422 0.218211 M8 448.559164802386 441.409196 1.0162 0.314738 0.157369 M9 415.383662192393 439.875582 0.9443 0.349835 0.174918 M10 243.310441461596 439.500718 0.5536 0.582472 0.291236 M11 67.5312207307977 439.275646 0.1537 0.878478 0.439239 t 44.5032207307978 8.119686 5.4809 2e-06 1e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.855831238805228 R-squared 0.732447109314891 Adjusted R-squared 0.658443118274329 F-TEST (value) 9.89740011337272 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 1.67427827157951e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 694.437117668786 Sum Squared Residuals 22665416.7886182 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9492.49 9530.76290827739 -38.2729082773870 2 9682.35 9982.47242058166 -300.122420581655 3 9762.12 10058.9104205817 -296.790420581656 4 10124.63 10290.0224205817 -165.392420581656 5 10540.05 10208.5504205817 331.499579418343 6 10601.61 10277.4664205817 324.143579418343 7 10323.73 10130.7104205817 193.019579418343 8 10418.4 10277.4804205817 140.919579418343 9 10092.96 10288.8081387025 -195.848138702463 10 10364.91 10161.2381387025 203.671861297538 11 10152.09 10029.9621387025 122.127861297539 12 10032.8 10006.9341387025 25.8658612975377 13 10204.59 10064.8015570470 139.788442953015 14 10001.6 10516.5110693512 -514.911069351231 15 10411.75 10592.9490693512 -181.199069351231 16 10673.38 10824.0610693512 -150.681069351232 17 10539.51 10742.5890693512 -203.079069351230 18 10723.78 10811.5050693512 -87.7250693512302 19 10682.06 10664.7490693512 17.3109306487689 20 10283.19 10811.5190693512 -528.32906935123 21 10377.18 10822.8467874720 -445.666787472035 22 10486.64 10695.2767874720 -208.636787472036 23 10545.38 10564.0007874720 -18.6207874720366 24 10554.27 10540.9727874720 13.2972125279646 25 10532.54 10598.8402058166 -66.3002058165579 26 10324.31 11050.5497181208 -726.239718120807 27 10695.25 11126.9877181208 -431.737718120805 28 10827.81 11358.0997181208 -530.289718120806 29 10872.48 11276.6277181208 -404.147718120805 30 10971.19 11345.5437181208 -374.353718120805 31 11145.65 11198.7877181208 -53.1377181208052 32 11234.68 11345.5577181208 -110.877718120805 33 11333.88 11356.8854362416 -23.0054362416105 34 10997.97 11229.3154362416 -231.345436241611 35 11036.89 11098.0394362416 -61.1494362416104 36 11257.35 11075.0114362416 182.338563758390 37 11533.59 11132.8788545861 400.711145413867 38 11963.12 11584.5883668904 378.531633109621 39 12185.15 11661.0263668904 524.123633109621 40 12377.62 11892.1383668904 485.481633109621 41 12512.89 11810.6663668904 702.22363310962 42 12631.48 11879.5823668904 751.89763310962 43 12268.53 11732.8263668904 535.703633109621 44 12754.8 11879.5963668904 875.203633109621 45 13407.75 12510.8354944072 896.914505592842 46 13480.21 12383.2654944072 1096.94450559284 47 13673.28 12251.9894944072 1421.29050559284 48 13239.71 12228.9614944072 1010.74850559284 49 13557.69 12286.8289127517 1270.86108724832 50 13901.28 12738.5384250559 1162.74157494407 51 13200.58 12814.9764250559 385.603574944072 52 13406.97 13046.0884250559 360.881574944071 53 12538.12 12964.6164250559 -426.496425055927 54 12419.57 13033.5324250559 -613.962425055928 55 12193.88 12886.7764250559 -692.896425055928 56 12656.63 13033.5464250559 -376.916425055929 57 12812.48 13044.8741431767 -232.394143176733 58 12056.67 12917.3041431767 -860.634143176733 59 11322.38 12786.0281431767 -1463.64814317673 60 11530.75 12763.0001431767 -1232.25014317673 61 11114.08 12820.8675615213 -1706.78756152126 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0294015179009436 0.0588030358018872 0.970598482099056 18 0.0101046687599657 0.0202093375199313 0.989895331240034 19 0.00225087907457692 0.00450175814915385 0.997749120925423 20 0.00171330357346572 0.00342660714693145 0.998286696426534 21 0.000435528777402786 0.000871057554805571 0.999564471222597 22 0.000117718814150691 0.000235437628301382 0.99988228118585 23 2.59144719710438e-05 5.18289439420877e-05 0.999974085528029 24 6.73598592559919e-06 1.34719718511984e-05 0.999993264014074 25 1.73466331712772e-06 3.46932663425544e-06 0.999998265336683 26 6.65389174879873e-07 1.33077834975975e-06 0.999999334610825 27 2.15173813981221e-07 4.30347627962442e-07 0.999999784826186 28 9.52421135722889e-08 1.90484227144578e-07 0.999999904757886 29 4.89274717926636e-08 9.78549435853271e-08 0.999999951072528 30 3.28304958499332e-08 6.56609916998665e-08 0.999999967169504 31 1.69693394448795e-08 3.39386788897591e-08 0.99999998303066 32 1.17793483872920e-07 2.35586967745839e-07 0.999999882206516 33 9.87002225477729e-07 1.97400445095546e-06 0.999999012997774 34 1.33190139702299e-06 2.66380279404599e-06 0.999998668098603 35 2.18257402352637e-06 4.36514804705274e-06 0.999997817425976 36 8.61576777005778e-06 1.72315355401156e-05 0.99999138423223 37 0.000129444772825220 0.000258889545650439 0.999870555227175 38 0.0244910102548090 0.0489820205096181 0.97550898974519 39 0.0800445407918382 0.160089081583676 0.919955459208162 40 0.222159599643946 0.444319199287893 0.777840400356054 41 0.195408191647024 0.390816383294048 0.804591808352976 42 0.152231335199704 0.304462670399408 0.847768664800296 43 0.0886900481754073 0.177380096350815 0.911309951824593 44 0.0621446587456287 0.124289317491257 0.937855341254371 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 19 0.678571428571429 NOK 5% type I error level 21 0.75 NOK 10% type I error level 22 0.785714285714286 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal 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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