Model 5

*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 06:27:39 -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/t1258723845jhue3l8r48s8h41.htm/, Retrieved Fri, 20 Nov 2009 14:30:57 +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/t1258723845jhue3l8r48s8h41.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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96.92 148.3 98.2 98.54 99.06 152.2 96.92 98.2 99.65 169.4 99.06 96.92 99.82 168.6 99.65 99.06 99.99 161.1 99.82 99.65 100.33 174.1 99.99 99.82 99.31 179 100.33 99.99 101.1 190.6 99.31 100.33 101.1 190 101.1 99.31 100.93 181.6 101.1 101.1 100.85 174.8 100.93 101.1 100.93 180.5 100.85 100.93 99.6 196.8 100.93 100.85 101.88 193.8 99.6 100.93 101.81 197 101.88 99.6 102.38 216.3 101.81 101.88 102.74 221.4 102.38 101.81 102.82 217.9 102.74 102.38 101.72 229.7 102.82 102.74 103.47 227.4 101.72 102.82 102.98 204.2 103.47 101.72 102.68 196.6 102.98 103.47 102.9 198.8 102.68 102.98 103.03 207.5 102.9 102.68 101.29 190.7 103.03 102.9 103.69 201.6 101.29 103.03 103.68 210.5 103.69 101.29 104.2 223.5 103.68 103.69 104.08 223.8 104.2 103.68 104.16 231.2 104.08 104.2 103.05 244 104.16 104.08 104.66 234.7 103.05 104.16 104.46 250.2 104.66 103.05 104.95 265.7 104.46 104.66 105.85 287.6 104.95 104.46 106.23 283.3 105.85 104.95 104.86 295.4 106.23 105.85 107.44 312.3 104.86 106.23 108.23 33 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 15.8628084234176 + 0.00548846630286158X[t] + 0.547489113654386Y1[t] + 0.284804867258724Y2[t] -1.72061412426050M1[t] + 1.45033832307751M2[t] + 0.642970589035423M3[t] + 0.166916920944267M4[t] + 0.0931322767468709M5[t] -0.0145036866952044M6[t] -1.46494558899757M7[t] + 0.852531461568537M8[t] + 0.0488987753423475M9[t] -0.261059298752688M10[t] -0.0850382975186649M11[t] + 0.0230123622686391t + 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) 15.8628084234176 4.289639 3.6979 0.000638 0.000319 X 0.00548846630286158 0.000854 6.4234 0 0 Y1 0.547489113654386 0.137476 3.9824 0.000273 0.000136 Y2 0.284804867258724 0.128931 2.209 0.032822 0.016411 M1 -1.72061412426050 0.18075 -9.5193 0 0 M2 1.45033832307751 0.2932 4.9466 1.3e-05 7e-06 M3 0.642970589035423 0.341628 1.8821 0.066937 0.033468 M4 0.166916920944267 0.18071 0.9237 0.361062 0.180531 M5 0.0931322767468709 0.182659 0.5099 0.612876 0.306438 M6 -0.0145036866952044 0.182257 -0.0796 0.93696 0.46848 M7 -1.46494558899757 0.182619 -8.0218 0 0 M8 0.852531461568537 0.265256 3.214 0.002552 0.001276 M9 0.0488987753423475 0.270449 0.1808 0.857411 0.428705 M10 -0.261059298752688 0.195314 -1.3366 0.18872 0.09436 M11 -0.0850382975186649 0.190821 -0.4456 0.658198 0.329099 t 0.0230123622686391 0.00921 2.4985 0.016572 0.008286 Multiple Linear Regression - Regression Statistics Multiple R 0.998075693034228 R-squared 0.996155089025755 Adjusted R-squared 0.99474841427908 F-TEST (value) 708.163057153391 F-TEST (DF numerator) 15 F-TEST (DF denominator) 41 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.268481217752668 Sum Squared Residuals 2.95536873572417 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 96.92 96.8072487946755 0.112751205324474 2 99.06 99.2249989025177 -0.164998902517677 3 99.65 99.3421216242827 0.307878375717331 4 99.82 99.8171905384076 0.00280946159236502 5 99.99 99.9863627802113 0.00363721978870009 6 100.33 100.114579217730 0.215420782269713 7 99.31 98.948606288657 0.361393711342945 8 101.1 100.891156669545 0.208843330454502 9 101.1 100.796747814644 0.303252185356319 10 100.93 100.973499698266 -0.0434996982663469 11 100.85 101.042138341588 -0.192138341588327 12 100.93 101.089257302776 -0.159257302775590 13 99.6 99.502132281232 0.0978677187679605 14 101.88 101.974255560150 -0.0942555601504643 15 101.81 102.076947986224 -0.266947986224065 16 102.38 102.340864939441 0.0391350605591298 17 102.74 102.610216289732 0.129783710268405 18 102.82 102.865817911751 -0.0458179117511944 19 101.72 101.649481155397 0.0705188446032803 20 103.47 103.397893460096 0.0721065399042408 21 102.98 103.134761312822 -0.154761312822396 22 102.68 103.036242109106 -0.356242109106368 23 102.9 102.943548979422 -0.0435489794222405 24 103.03 103.134355440871 -0.104355440870793 25 101.29 101.478378100563 -0.188378100562836 26 103.69 103.816560767856 -0.126560767855689 27 103.68 103.899466149918 -0.219466149918047 28 104.2 104.195831696317 0.00416830368286885 29 104.08 104.428552244707 -0.348552244706930 30 104.16 104.466943131511 -0.306943131510678 31 103.05 103.119388505175 -0.0693885051748819 32 104.66 104.823906654617 -0.163906654617344 33 104.46 104.693681628681 -0.233681628680530 34 104.95 104.840845158104 0.109154841895856 35 105.85 105.371384625878 0.478615374121607 36 106.23 106.088129467809 0.141870532190897 37 104.86 104.921308391803 -0.0613083918033899 38 107.44 107.566194045780 -0.126194045780208 39 108.23 107.922179944602 0.307820055397856 40 108.45 108.712741277704 -0.262741277703879 41 109.39 109.202252999665 0.187747000334932 42 110.15 109.826100580762 0.32389941923794 43 109.13 109.118154373297 0.0118456267025193 44 110.28 110.837293654506 -0.557293654505717 45 110.17 110.17185542149 -0.00185542149005972 46 109.99 109.699413034523 0.290586965476859 47 109.26 109.502928053111 -0.242928053111039 48 109.11 108.988257788545 0.121742211455486 49 107.06 107.020932431726 0.0390675682737915 50 109.53 109.017990723696 0.512009276304038 51 108.92 109.049284294973 -0.129284294973075 52 109.24 109.023371548130 0.216628451869516 53 109.12 109.092615685685 0.0273843143148939 54 109 109.186559158246 -0.186559158245781 55 107.23 107.604369677474 -0.374369677473863 56 109.49 109.049749561236 0.440250438764319 57 109.04 108.952953822363 0.0870461776366666 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 19 0.226389869616353 0.452779739232706 0.773610130383647 20 0.129281386528889 0.258562773057778 0.870718613471111 21 0.0674370655506519 0.134874131101304 0.932562934449348 22 0.0306494993728678 0.0612989987457357 0.969350500627132 23 0.0150687756704923 0.0301375513409845 0.984931224329508 24 0.0055383444656031 0.0110766889312062 0.994461655534397 25 0.0034633024207615 0.006926604841523 0.996536697579238 26 0.00294244653348231 0.00588489306696462 0.997057553466518 27 0.00129864410512442 0.00259728821024883 0.998701355894876 28 0.000504184698360192 0.00100836939672038 0.99949581530164 29 0.00142932903598225 0.00285865807196451 0.998570670964018 30 0.00291100051538446 0.00582200103076891 0.997088999484615 31 0.00285637616665432 0.00571275233330863 0.997143623833346 32 0.00208153385334946 0.00416306770669893 0.99791846614665 33 0.00218872649522859 0.00437745299045719 0.997811273504771 34 0.00144898265082134 0.00289796530164267 0.998551017349179 35 0.00458966528560949 0.00917933057121898 0.99541033471439 36 0.0108611411270844 0.0217222822541689 0.989138858872916 37 0.0136346506818572 0.0272693013637143 0.986365349318143 38 0.00976812254880777 0.0195362450976155 0.990231877451192 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 11 0.55 NOK 5% type I error level 16 0.8 NOK 10% type I error level 17 0.85 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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