Multiple Regression analysis 3a

*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: Sat, 19 Dec 2009 04:06:13 -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/19/t12612208366khecw9sb35174r.htm/, Retrieved Sat, 19 Dec 2009 12:07:28 +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/19/t12612208366khecw9sb35174r.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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100.5 98.60 96.33 106.29 96.90 96.33 101.09 95.10 95.05 104.53 97.00 96.84 122.74 112.70 96.92 109.84 102.90 97.44 101.99 97.40 97.78 125.12 111.40 97.69 103.5 87.40 96.67 102.8 96.80 98.29 118.72 114.10 98.20 119.01 110.30 98.71 118.61 103.90 98.54 120.43 101.60 98.20 111.83 94.60 100.80 116.79 95.90 101.33 131.71 104.70 101.88 120.57 102.80 101.85 117.83 98.10 102.04 130.8 113.90 102.22 107.46 80.90 102.63 112.09 95.70 102.65 129.47 113.20 102.54 119.72 105.90 102.37 134.81 108.80 102.68 135.8 102.30 102.76 129.27 99.00 102.82 126.94 100.70 103.31 153.45 115.50 103.23 121.86 100.70 103.60 133.47 109.90 103.95 135.34 114.60 103.93 117.1 85.40 104.25 120.65 100.50 104.38 132.49 114.80 104.36 137.6 116.50 104.32 138.69 112.90 104.58 125.53 102.00 104.68 133.09 106.00 104.92 129.08 105.30 105.46 145.94 118.80 105.23 129.07 106.10 105.58 139.69 109.30 105.34 142.09 117.20 105.28 137.29 92.50 105.70 127.03 104.20 105.67 137.25 112.50 105.71 156.87 122.40 106.19 150. 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Invoer[t] = -565.364466748748 + 1.83716663011589TIP[t] + 4.96590613126583CONS[t] + 8.0960403885472M1[t] + 15.9374500609476M2[t] + 15.1165444156924M3[t] + 7.71488211793052M4[t] + 5.75852459637852M5[t] + 5.25941126185618M6[t] + 6.31099947214643M7[t] + 1.59723979471244M8[t] + 32.651378186831M9[t] + 10.4110003714842M10[t] -2.5694298043648M11[t] -0.658696536903804t + 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) -565.364466748748 72.554538 -7.7923 0 0 TIP 1.83716663011589 0.121448 15.1272 0 0 CONS 4.96590613126583 0.742457 6.6885 0 0 M1 8.0960403885472 3.574411 2.265 0.027473 0.013737 M2 15.9374500609476 3.870752 4.1174 0.00013 6.5e-05 M3 15.1165444156924 3.875636 3.9004 0.000264 0.000132 M4 7.71488211793052 3.817874 2.0207 0.048187 0.024094 M5 5.75852459637852 3.469512 1.6598 0.102657 0.051328 M6 5.25941126185618 3.66176 1.4363 0.156579 0.078289 M7 6.31099947214643 3.721396 1.6959 0.095565 0.047782 M8 1.59723979471244 3.445139 0.4636 0.644749 0.322374 M9 32.651378186831 4.732358 6.8996 0 0 M10 10.4110003714842 3.986428 2.6116 0.011593 0.005797 M11 -2.5694298043648 3.592354 -0.7152 0.47748 0.23874 t -0.658696536903804 0.174674 -3.771 0.000399 2e-04 Multiple Linear Regression - Regression Statistics Multiple R 0.958082962716787 R-squared 0.917922963448176 Adjusted R-squared 0.897030626871348 F-TEST (value) 43.9358690241597 F-TEST (DF numerator) 14 F-TEST (DF denominator) 55 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.67943181519843 Sum Squared Residuals 1774.07701589185 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.5 101.583244457159 -1.08324445715932 2 106.29 105.642774321459 0.647225678541308 3 101.09 94.4999123570707 6.59008764292927 4 104.53 98.8191420945912 5.71085790540882 5 122.74 125.444876619456 -2.70487661945604 6 109.84 108.865104961152 0.974895038847566 7 101.99 100.841988253532 1.14801174646808 8 125.12 120.742933309003 4.37706669099741 9 103.5 101.981151787545 1.51884821245507 10 102.8 104.396211691034 -1.5962116910343 11 118.72 122.093136127472 -3.3731361274724 12 119.01 119.555248327439 -0.545248327438574 13 118.61 114.390521704025 4.21947829597483 14 120.43 115.659343505625 4.77065649437517 15 111.83 114.230930853946 -2.40093085394575 16 116.79 111.190818888002 5.59918111199837 17 131.71 127.474079546762 4.2359204532382 18 120.57 122.676675894178 -2.10667589417751 19 117.83 115.378406570960 2.45159342904016 20 130.8 139.927046216081 -9.12704621608087 21 107.46 111.732010791290 -4.27201079129037 22 112.09 116.122320687380 -4.03232068738020 23 129.47 134.087360327216 -4.61736032721621 24 119.72 121.742573152516 -2.02257315251604 25 134.81 136.047131132188 -1.2371311321879 26 135.8 131.685533662433 4.11446633756749 27 129.27 124.441235968767 4.82876403123304 28 126.94 121.937354409619 5.0026455903814 29 153.45 146.115093986377 7.33490601362335 30 121.86 119.604603257804 2.25539674219629 31 133.47 138.637495074199 -5.16749507419939 32 135.34 141.800403898781 -6.46040389878094 33 117.1 120.139670116617 -3.03967011661687 34 120.65 125.627379676181 -4.97737967618063 35 132.49 138.160417651460 -5.67041765145974 36 137.6 142.995697944867 -5.39569794486709 37 138.69 145.110377522222 -6.42037752222244 38 125.53 132.764565002583 -7.23456500258252 39 133.09 139.825446812391 -6.7354468123908 40 129.08 133.160660647528 -4.0806606475275 41 145.94 154.205197685445 -8.26519768544508 42 129.07 131.453438757490 -2.38343875749020 43 139.69 136.533446175744 3.1565538242563 44 142.09 145.376651971445 -3.28665197144545 45 137.29 132.479758637929 4.81024136207053 46 127.03 130.926556674097 -3.89655667409672 47 137.25 132.734549236556 4.51545076344359 48 156.87 155.216867085172 1.65313291482771 49 150.89 149.610765139898 1.27923486010211 50 139.14 134.891774221799 4.24822577820124 51 158.3 155.105876495699 3.19412350430134 52 149 155.174246857165 -6.17424685716496 53 158.36 150.076895648434 8.28310435156636 54 168.06 163.542039545192 4.51796045480814 55 153.38 152.395958204827 0.984041795173183 56 173.86 161.601915650409 12.2580843495913 57 162.47 158.417285245077 4.0527147549232 58 145.17 140.811036002636 4.35896399736386 59 168.89 159.744536657295 9.14546334270474 60 166.64 160.329613490006 6.31038650999399 61 140.07 136.827960044507 3.24203995549272 62 128.84 135.386009286103 -6.54600928610268 63 123.41 128.886597512127 -5.4765975121271 64 120.3 126.357777103096 -6.05777710309612 65 129.67 138.553856513527 -8.88385651352679 66 118.1 121.358137584184 -3.25813758418428 67 113.91 116.482705720738 -2.57270572073833 68 131.09 128.851048954281 2.23895104571855 69 119.15 122.220123421542 -3.07012342154156 70 122.3 112.156495268672 10.1435047313280 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0140665019507201 0.0281330039014402 0.98593349804928 19 0.00878468933201034 0.0175693786640207 0.99121531066799 20 0.0320904649506883 0.0641809299013767 0.967909535049312 21 0.0184180738682762 0.0368361477365525 0.981581926131724 22 0.00749142093854755 0.0149828418770951 0.992508579061453 23 0.00280745728676688 0.00561491457353376 0.997192542713233 24 0.0106152281861401 0.0212304563722803 0.98938477181386 25 0.00536059937864248 0.0107211987572850 0.994639400621357 26 0.00333597863450473 0.00667195726900945 0.996664021365495 27 0.00206931125169387 0.00413862250338774 0.997930688748306 28 0.00404289023976252 0.00808578047952504 0.995957109760238 29 0.00606240343546542 0.0121248068709308 0.993937596564535 30 0.0131459551825405 0.0262919103650809 0.98685404481746 31 0.013116677749969 0.026233355499938 0.986883322250031 32 0.0261112153095249 0.0522224306190498 0.973888784690475 33 0.0183300268500785 0.0366600537001569 0.981669973149922 34 0.0131477002280862 0.0262954004561725 0.986852299771914 35 0.0133937109593199 0.0267874219186398 0.98660628904068 36 0.0097910585875835 0.019582117175167 0.990208941412416 37 0.0115931501103291 0.0231863002206582 0.988406849889671 38 0.0348901698499758 0.0697803396999517 0.965109830150024 39 0.0335073052597506 0.0670146105195013 0.96649269474025 40 0.0329182058190015 0.065836411638003 0.967081794180998 41 0.0483202569654224 0.096640513930845 0.951679743034578 42 0.0293236208090613 0.0586472416181225 0.97067637919094 43 0.0305326350172330 0.0610652700344661 0.969467364982767 44 0.0380340213785158 0.0760680427570316 0.961965978621484 45 0.0540840522107712 0.108168104421542 0.945915947789229 46 0.118100771207084 0.236201542414168 0.881899228792916 47 0.107749215244919 0.215498430489839 0.892250784755081 48 0.180758377003631 0.361516754007262 0.819241622996369 49 0.251139881022016 0.502279762044033 0.748860118977984 50 0.172095807577793 0.344191615155585 0.827904192422207 51 0.120862887463295 0.241725774926591 0.879137112536704 52 0.169923408875668 0.339846817751337 0.830076591124332 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 4 0.114285714285714 NOK 5% type I error level 18 0.514285714285714 NOK 10% type I error level 27 0.771428571428571 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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