3de model

*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: Fri, 20 Nov 2009 08:37:22 -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/Nov/20/t1258731534eozeykxx7p8s5eq.htm/, Retrieved Fri, 20 Nov 2009 16:39:06 +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/Nov/20/t1258731534eozeykxx7p8s5eq.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:

» Textbox « » Textfile « » CSV «

105.7 0 105.7 0 111.1 0 82.4 0 60 0 107.3 0 99.3 0 113.5 0 108.9 0 100.2 0 103.9 0 138.7 0 120.2 0 100.2 0 143.2 0 70.9 0 85.2 0 133 0 136.6 0 117.9 0 106.3 0 122.3 0 125.5 0 148.4 0 126.3 0 99.6 0 140.4 0 80.3 0 92.6 0 138.5 0 110.9 0 119.6 0 105 0 109 0 129.4 0 148.6 0 101.4 0 134.8 0 143.7 0 81.6 0 90.3 0 141.5 0 140.7 0 140.2 0 100.2 0 125.7 0 119.6 0 134.7 0 109 0 116.3 0 146.9 0 97.4 0 89.4 0 132.1 0 139.8 0 129 0 112.5 0 121.9 0 121.7 0 123.1 0 131.6 0 119.3 0 132.5 0 98.3 0 85.1 0 131.7 0 129.3 0 90.7 1 78.6 1 68.9 1 79.1 1 83.5 1 74.1 1 59.7 1 93.3 1 61.3 1 56.6 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 126.383760683761 -49.8978632478632X[t] -19.5698836657170M1[t] -24.5135158051825M2[t] + 0.285709198209129M3[t] -48.4007800841134M4[t] -50.5301265092932M5[t] -5.49975579975582M6[t] -10.3552927011260M7[t] -9.92785239451906M8[t] -26.7667226292227M9[t] -20.9555928639262M10[t] -16.0277964319631M11[t] + 0.272203568036901t + 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) 126.383760683761 4.924358 25.665 0 0 X -49.8978632478632 4.442725 -11.2314 0 0 M1 -19.5698836657170 5.841073 -3.3504 0.001367 0.000684 M2 -24.5135158051825 5.838375 -4.1987 8.6e-05 4.3e-05 M3 0.285709198209129 5.836432 0.049 0.961112 0.480556 M4 -48.4007800841134 5.835244 -8.2946 0 0 M5 -50.5301265092932 5.834812 -8.6601 0 0 M6 -5.49975579975582 6.084279 -0.9039 0.369477 0.184738 M7 -10.3552927011260 6.085009 -1.7018 0.093729 0.046864 M8 -9.92785239451906 6.060242 -1.6382 0.106367 0.053183 M9 -26.7667226292227 6.057693 -4.4186 4e-05 2e-05 M10 -20.9555928639262 6.055871 -3.4604 0.000974 0.000487 M11 -16.0277964319631 6.054778 -2.6471 0.010242 0.005121 t 0.272203568036901 0.066434 4.0973 0.000122 6.1e-05 Multiple Linear Regression - Regression Statistics Multiple R 0.917996846433517 R-squared 0.842718210061882 Adjusted R-squared 0.81026323753497 F-TEST (value) 25.9657656269178 F-TEST (DF numerator) 13 F-TEST (DF denominator) 63 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.4865511345852 Sum Squared Residuals 6927.96854599104 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.7 107.086080586081 -1.38608058608068 2 105.7 102.414652014652 3.28534798534793 3 111.1 127.486080586081 -16.3860805860806 4 82.4 79.0717948717949 3.32820512820513 5 60 77.2146520146519 -17.2146520146519 6 107.3 122.517226292226 -15.2172262922263 7 99.3 117.933892958893 -18.6338929588929 8 113.5 118.633536833537 -5.13353683353683 9 108.9 102.066870166870 6.83312983312984 10 100.2 108.150203500204 -7.95020350020353 11 103.9 113.350203500203 -9.45020350020345 12 138.7 129.650203500204 9.04979649979646 13 120.2 110.352523402523 9.84747659747661 14 100.2 105.681094831095 -5.48109483109483 15 143.2 130.752523402523 12.4474765974766 16 70.9 82.3382376882377 -11.4382376882377 17 85.2 80.4810948310949 4.71890516890516 18 133 125.783669108669 7.2163308913309 19 136.6 121.200335775336 15.3996642246642 20 117.9 121.899979649980 -3.99997964997965 21 106.3 105.333312983313 0.966687016687016 22 122.3 111.416646316646 10.8833536833537 23 125.5 116.616646316646 8.88335368335368 24 148.4 132.916646316646 15.4833536833537 25 126.3 113.618966218966 12.6810337810338 26 99.6 108.947537647538 -9.34753764753764 27 140.4 134.018966218966 6.3810337810338 28 80.3 85.6046805046805 -5.30468050468051 29 92.6 83.7475376475377 8.85246235246234 30 138.5 129.050111925112 9.44988807488808 31 110.9 124.466778591779 -13.5667785917786 32 119.6 125.166422466422 -5.56642246642248 33 105 108.599755799756 -3.5997557997558 34 109 114.683089133089 -5.68308913308913 35 129.4 119.883089133089 9.51691086691087 36 148.6 136.183089133089 12.4169108669108 37 101.4 116.885409035409 -15.485409035409 38 134.8 112.213980463980 22.5860195360196 39 143.7 137.285409035409 6.41459096459096 40 81.6 88.8711233211233 -7.27112332112333 41 90.3 87.0139804639805 3.28601953601952 42 141.5 132.316554741555 9.18344525844527 43 140.7 127.733221408221 12.9667785917786 44 140.2 128.432865282865 11.7671347171347 45 100.2 111.866198616199 -11.6661986161986 46 125.7 117.949531949532 7.75046805046806 47 119.6 123.149531949532 -3.54953194953197 48 134.7 139.449531949532 -4.74953194953197 49 109 120.151851851852 -11.1518518518518 50 116.3 115.480423280423 0.81957671957673 51 146.9 140.551851851852 6.34814814814816 52 97.4 92.1375661375661 5.26243386243387 53 89.4 90.2804232804233 -0.880423280423285 54 132.1 135.582997557998 -3.48299755799756 55 139.8 130.999664224664 8.80033577533578 56 129 131.699308099308 -2.6993080993081 57 112.5 115.132641432641 -2.63264143264143 58 121.9 121.215974765975 0.684025234025239 59 121.7 126.415974765975 -4.71597476597477 60 123.1 142.715974765975 -19.6159747659748 61 131.6 123.418294668295 8.18170533170535 62 119.3 118.746866096866 0.553133903133916 63 132.5 143.818294668295 -11.3182946682947 64 98.3 95.404008954009 2.89599104599105 65 85.1 93.5468660968661 -8.44686609686611 66 131.7 138.849440374440 -7.14944037444039 67 129.3 134.266107041107 -4.96610704110704 68 90.7 85.0678876678877 5.63211233211233 69 78.6 68.501221001221 10.098778998779 70 68.9 74.5845543345543 -5.68455433455433 71 79.1 79.7845543345543 -0.684554334554351 72 83.5 96.0845543345543 -12.5845543345543 73 74.1 76.7868742368742 -2.68687423687422 74 59.7 72.1154456654457 -12.4154456654457 75 93.3 97.1868742368742 -3.88687423687423 76 61.3 48.7725885225885 12.5274114774115 77 56.6 46.9154456654457 9.68455433455432 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.936205566026584 0.127588867946832 0.063794433973416 18 0.909276935731682 0.181446128536636 0.090723064268318 19 0.929897883358947 0.140204233282106 0.0701021166410528 20 0.908172739003429 0.183654521993143 0.0918272609965713 21 0.898499146723534 0.203001706552931 0.101500853276466 22 0.857172475096707 0.285655049806586 0.142827524903293 23 0.801693569986058 0.396612860027884 0.198306430013942 24 0.768737405293272 0.462525189413455 0.231262594706728 25 0.739463688146475 0.521072623707051 0.260536311853525 26 0.831656895042687 0.336686209914627 0.168343104957313 27 0.770544937344607 0.458910125310787 0.229455062655393 28 0.763795091389755 0.47240981722049 0.236204908610245 29 0.700959485460333 0.598081029079334 0.299040514539667 30 0.630014875015923 0.739970249968154 0.369985124984077 31 0.801586915352753 0.396826169294494 0.198413084647247 32 0.804671622556693 0.390656754886614 0.195328377443307 33 0.80171463809524 0.396570723809522 0.198285361904761 34 0.813239154403094 0.373521691193812 0.186760845596906 35 0.763168966568306 0.473662066863387 0.236831033431694 36 0.790843489228378 0.418313021543244 0.209156510771622 37 0.931828670354126 0.136342659291748 0.0681713296458738 38 0.975716776179814 0.0485664476403719 0.0242832238201859 39 0.963319041889111 0.0733619162217775 0.0366809581108887 40 0.982987331120944 0.0340253377581117 0.0170126688790559 41 0.97367078553315 0.0526584289337013 0.0263292144668507 42 0.962397988308342 0.0752040233833155 0.0376020116916578 43 0.951565924991817 0.0968681500163655 0.0484340750081828 44 0.94240329715319 0.115193405693622 0.0575967028468108 45 0.975612864034739 0.0487742719305228 0.0243871359652614 46 0.96594026399974 0.0681194720005217 0.0340597360002608 47 0.952976443141558 0.0940471137168832 0.0470235568584416 48 0.95810115548702 0.0837976890259592 0.0418988445129796 49 0.98232551334649 0.0353489733070188 0.0176744866535094 50 0.969244673624392 0.0615106527512166 0.0307553263756083 51 0.967277844378397 0.0654443112432055 0.0327221556216028 52 0.949310673439072 0.101378653121856 0.0506893265609278 53 0.927095179739313 0.145809640521373 0.0729048202606866 54 0.89874850574942 0.20250298850116 0.10125149425058 55 0.837881916765228 0.324236166469544 0.162118083234772 56 0.763610018973827 0.472779962052346 0.236389981026173 57 0.711645894391059 0.576708211217883 0.288354105608941 58 0.634250022010307 0.731499955979386 0.365749977989693 59 0.48983381856805 0.9796676371361 0.51016618143195 60 0.3963426819236 0.7926853638472 0.6036573180764 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 4 0.090909090909091 NOK 10% type I error level 13 0.295454545454545 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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