Multiple Regression analysis 3

*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, 15 Dec 2009 12:20:51 -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/Dec/15/t1260904891dv0f3hy0rs3r2py.htm/, Retrieved Tue, 15 Dec 2009 20:21:45 +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/Dec/15/t1260904891dv0f3hy0rs3r2py.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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103.34 98.60 96.33 102.60 96.90 96.33 100.69 95.10 95.05 105.67 97.00 96.84 123.61 112.70 96.92 113.08 102.90 97.44 106.46 97.40 97.78 123.38 111.40 97.69 109.87 87.40 96.67 95.74 96.80 98.29 123.06 114.10 98.20 123.39 110.30 98.71 120.28 103.90 98.54 115.33 101.60 98.20 110.40 94.60 100.80 114.49 95.90 101.33 132.03 104.70 101.88 123.16 102.80 101.85 118.82 98.10 102.04 128.32 113.90 102.22 112.24 80.90 102.63 104.53 95.70 102.65 132.57 113.20 102.54 122.52 105.90 102.37 131.80 108.80 102.68 124.55 102.30 102.76 120.96 99.00 102.82 122.60 100.70 103.31 145.52 115.50 103.23 118.57 100.70 103.60 134.25 109.90 103.95 136.70 114.60 103.93 121.37 85.40 104.25 111.63 100.50 104.38 134.42 114.80 104.36 137.65 116.50 104.32 137.86 112.90 104.58 119.77 102.00 104.68 130.69 106.00 104.92 128.28 105.30 105.46 147.45 118.80 105.23 128.42 106.10 105.58 136.90 109.30 105.34 143.95 117.20 105.28 135.64 92.50 105.70 122.48 104.20 105.67 136.83 112.50 105.71 153.04 122.40 106.19 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 8 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Uitvoer[t] = -331.141725919584 + 1.70620646635698TIP[t] + 2.72941331902169cons[t] + 3.85690559007311M1[t] + 5.18062213837092M2[t] + 7.79403001839284M3[t] + 5.82862661097081M4[t] + 3.69147814714131M5[t] + 4.56365482328583M6[t] + 6.54365000251388M7[t] + 1.06346039581490M8[t] + 32.5649038799904M9[t] + 3.02441373941592M10[t] -1.30786415664453M11[t] -0.303331431381686t + 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) -331.141725919584 63.565908 -5.2094 3e-06 1e-06 TIP 1.70620646635698 0.106402 16.0355 0 0 cons 2.72941331902169 0.650476 4.196 1e-04 5e-05 M1 3.85690559007311 3.131585 1.2316 0.223333 0.111667 M2 5.18062213837092 3.391212 1.5277 0.132328 0.066164 M3 7.79403001839284 3.395492 2.2954 0.025548 0.012774 M4 5.82862661097081 3.344886 1.7425 0.087002 0.043501 M5 3.69147814714131 3.039682 1.2144 0.229772 0.114886 M6 4.56365482328583 3.208112 1.4225 0.160518 0.080259 M7 6.54365000251388 3.26036 2.007 0.049671 0.024836 M8 1.06346039581490 3.018328 0.3523 0.725934 0.362967 M9 32.5649038799904 4.146076 7.8544 0 0 M10 3.02441373941592 3.492558 0.866 0.390274 0.195137 M11 -1.30786415664453 3.147305 -0.4156 0.679356 0.339678 t -0.303331431381686 0.153034 -1.9821 0.052471 0.026236 Multiple Linear Regression - Regression Statistics Multiple R 0.95760825351636 R-squared 0.917013567202651 Adjusted R-squared 0.895889747945144 F-TEST (value) 43.4113526547414 F-TEST (DF numerator) 14 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.97581886189116 Sum Squared Residuals 1361.73253404935 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 103.34 103.568190843264 -0.228190843264361 2 102.6 101.688024967374 0.91197503262612 3 100.69 97.4332807282237 3.25671927177627 4 105.67 103.291988016547 2.37801198345282 5 123.61 127.857302708662 -4.24730270866233 6 113.08 113.124619509018 -0.0446195090180273 7 106.46 106.345148220368 0.114851779631616 8 123.38 124.202870512573 -0.822870512573496 9 109.87 111.668025787398 -1.79802578739766 10 95.74 102.284194576012 -6.54419457601227 11 123.06 126.920309917834 -3.86030991783389 12 123.39 122.833258863641 0.556741136358738 13 120.28 115.003111373414 5.27688862658563 14 115.33 111.171221089242 4.15877891075796 15 110.4 108.634326902840 1.76567309716022 16 114.49 110.030249529382 4.45975047061833 17 132.03 124.105563863574 7.92443613642618 18 123.16 121.350734422688 1.80926557731227 19 118.82 115.526816309270 3.29318369072957 20 128.32 137.192651837054 -8.87265183705398 21 112.24 113.205009960866 -0.965009960866337 22 104.53 108.667632357374 -4.1376323573739 23 132.57 133.590400726087 -1.02040072608656 24 122.52 121.675625982710 0.844374017290252 25 131.8 131.023317022733 0.776682977266889 26 124.55 121.171713173851 3.37828682614939 27 120.96 118.015073082654 2.94492691734592 28 122.6 119.984301762978 2.61569823702211 29 145.52 142.577324504328 2.94267549567173 30 118.57 118.904196975046 -0.334196975045814 31 134.25 137.233254875034 -2.98325487503400 32 136.7 139.414315962451 -2.71431596245073 33 121.37 121.664611459708 -0.294611459707659 34 111.63 117.939331261215 -6.30933126121467 35 134.42 137.647886136297 -3.22788613629694 36 137.65 141.443793321606 -3.79379332160575 37 137.86 139.564671664358 -1.70467166435770 38 119.77 122.260347629885 -2.49034762988494 39 130.69 132.050309140518 -1.36030914051828 40 128.28 130.061112967536 -1.78111296753637 41 147.45 150.026655304769 -2.57665530476947 42 128.42 129.881973088456 -1.46197308845622 43 136.9 136.363438332080 0.53656166792029 44 143.95 143.895183579078 0.0548164209220768 45 135.64 134.096349506843 1.54365049315655 46 122.48 124.133261191693 -1.65326119169326 47 136.83 133.768342067775 3.0616579322251 48 153.04 152.974437203102 0.0655627968976957 49 142.71 143.021298374021 -0.311298374021242 50 123.46 122.741138281091 0.718861718909416 51 144.37 144.426683380549 -0.0566833805493852 52 146.15 148.088277575454 -1.93827757545398 53 147.61 142.194120405775 5.41587959422493 54 158.51 156.023514412449 2.48648558755102 55 147.4 145.647168592673 1.75283140732651 56 165.05 152.612205119809 12.4377948801906 57 154.64 151.494456483512 3.14554351648763 58 126.2 127.206218955245 -1.00621895524530 59 157.36 152.313061152008 5.0469388479923 60 154.15 151.822884628941 2.32711537105907 61 123.21 127.019410722209 -3.80941072220923 62 113.07 119.747554858558 -6.67755485855797 63 110.45 117.000326765215 -6.55032676521474 64 113.57 119.304070148103 -5.7340701481029 65 122.44 131.899033212891 -9.45903321289104 66 114.93 117.384961592343 -2.45496159234323 67 111.85 114.564173670574 -2.71417367057397 68 126.04 126.122772989034 -0.0827729890344382 69 121.34 122.971546801673 -1.63154680167253 70 124.36 104.709361658461 19.6506383415394 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0273629670689868 0.0547259341379737 0.972637032931013 19 0.00784315659593329 0.0156863131918666 0.992156843404067 20 0.0287670229057561 0.0575340458115123 0.971232977094244 21 0.0198251095484605 0.0396502190969209 0.98017489045154 22 0.00796201856509878 0.0159240371301976 0.992037981434901 23 0.00278198616206857 0.00556397232413713 0.997218013837931 24 0.0205162084541187 0.0410324169082374 0.979483791545881 25 0.0096926858079653 0.0193853716159306 0.990307314192035 26 0.00506209444038294 0.0101241888807659 0.994937905559617 27 0.00309362108050359 0.00618724216100719 0.996906378919496 28 0.00361448752320201 0.00722897504640402 0.996385512476798 29 0.00211572156057745 0.00423144312115491 0.997884278439423 30 0.00785526891751672 0.0157105378350334 0.992144731082483 31 0.0040970445608683 0.0081940891217366 0.995902955439132 32 0.00201022645932751 0.00402045291865502 0.997989773540672 33 0.00116720441268785 0.00233440882537569 0.998832795587312 34 0.000897991372070932 0.00179598274414186 0.99910200862793 35 0.000604123084927366 0.00120824616985473 0.999395876915073 36 0.000348411509173118 0.000696823018346236 0.999651588490827 37 0.000162090838077277 0.000324181676154554 0.999837909161923 38 0.000324140481687794 0.000648280963375588 0.999675859518312 39 0.000150880923397254 0.000301761846794508 0.999849119076603 40 9.4530091195643e-05 0.000189060182391286 0.999905469908804 41 4.29784748029952e-05 8.59569496059904e-05 0.999957021525197 42 1.68367976950450e-05 3.36735953900901e-05 0.999983163202305 43 9.16821561034247e-06 1.83364312206849e-05 0.99999083178439 44 9.71114826857995e-06 1.94222965371599e-05 0.999990288851731 45 7.81581813158614e-06 1.56316362631723e-05 0.999992184181868 46 3.50518976564998e-05 7.01037953129996e-05 0.999964948102343 47 1.48857957188906e-05 2.97715914377812e-05 0.999985114204281 48 1.86160176362112e-05 3.72320352724223e-05 0.999981383982364 49 7.97374001049162e-06 1.59474800209832e-05 0.99999202625999 50 3.96208025974011e-06 7.92416051948022e-06 0.99999603791974 51 1.1844501559729e-06 2.3689003119458e-06 0.999998815549844 52 5.85313431602017e-07 1.17062686320403e-06 0.999999414686568 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 26 0.742857142857143 NOK 5% type I error level 33 0.942857142857143 NOK 10% type I error level 35 1 NOK

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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