*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 00:44:37 -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/t1258703141manp4suvu65045z.htm/, Retrieved Fri, 20 Nov 2009 08:45:53 +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/t1258703141manp4suvu65045z.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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100.03 2 100.25 1.8 99.6 2.7 100.16 2.3 100.49 1.9 99.72 2 100.14 2.3 98.48 2.8 100.38 2.4 101.45 2.3 98.42 2.7 98.6 2.7 100.06 2.9 98.62 3 100.84 2.2 100.02 2.3 97.95 2.8 98.32 2.8 98.27 2.8 97.22 2.2 99.28 2.6 100.38 2.8 99.02 2.5 100.32 2.4 99.81 2.3 100.6 1.9 101.19 1.7 100.47 2 101.77 2.1 102.32 1.7 102.39 1.8 101.16 1.8 100.63 1.8 101.48 1.3 101.44 1.3 100.09 1.3 100.7 1.2 100.78 1.4 99.81 2.2 98.45 2.9 98.49 3.1 97.48 3.5 97.91 3.6 96.94 4.4 98.53 4.1 96.82 5.1 95.76 5.8 95.27 5.9 97.32 5.4 96.68 5.5 97.87 4.8 97.42 3.2 97.94 2.7 99.52 2.1 100.99 1.9 99.92 0.6 101.97 0.7 101.58 -0.2 99.54 -1 100.83 -1.7

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 Y[t] = + 101.473296893034 -0.89729709691884X[t] + 0.968511877494062M1[t] + 0.74987074493858M2[t] + 1.24112149625985M3[t] + 0.536858770135734M4[t] + 0.558163579518627M5[t] + 0.627684621148016M6[t] + 1.16477319828442M7[t] -0.123651702024567M8[t] + 1.26970716541995M9[t] + 1.41512009092609M10[t] -0.0756291577526306M11[t] -0.0152507513212727t + 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) 101.473296893034 0.556211 182.4368 0 0 X -0.89729709691884 0.092424 -9.7085 0 0 M1 0.968511877494062 0.640517 1.5121 0.137354 0.068677 M2 0.74987074493858 0.639196 1.1731 0.246776 0.123388 M3 1.24112149625985 0.638313 1.9444 0.05798 0.02899 M4 0.536858770135734 0.636233 0.8438 0.403143 0.201572 M5 0.558163579518627 0.635419 0.8784 0.384282 0.192141 M6 0.627684621148016 0.634317 0.9895 0.327574 0.163787 M7 1.16477319828442 0.634082 1.8369 0.072684 0.036342 M8 -0.123651702024567 0.633154 -0.1953 0.846022 0.423011 M9 1.26970716541995 0.632701 2.0068 0.050669 0.025334 M10 1.41512009092609 0.632323 2.238 0.030106 0.015053 M11 -0.0756291577526306 0.63218 -0.1196 0.905295 0.452648 t -0.0152507513212727 0.007606 -2.005 0.050866 0.025433 Multiple Linear Regression - Regression Statistics Multiple R 0.843822817706935 R-squared 0.712036947682871 Adjusted R-squared 0.630656085071508 F-TEST (value) 8.74943966965834 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 1.36955831120389e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.999274140497838 Sum Squared Residuals 45.9332451619139 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.03 100.631963825369 -0.601963825368862 2 100.25 100.577531360876 -0.327531360875884 3 99.6 100.245963973649 -0.645963973648927 4 100.16 99.885369334971 0.274630665028931 5 100.49 100.250342231800 0.239657768199771 6 99.72 100.214882812416 -0.494882812416457 7 100.14 100.467531509156 -0.327531509155934 8 98.48 98.7152073090663 -0.235207309066252 9 100.38 100.452234263957 -0.0722342639570395 10 101.45 100.672126147834 0.777873852166214 11 98.42 98.8072073090663 -0.387207309066256 12 98.6 98.8675857154976 -0.267585715497621 13 100.06 99.6413874222866 0.418612577713367 14 98.62 99.317765828718 -0.697765828717993 15 100.84 100.511603506253 0.328396493746934 16 100.02 99.7023603191158 0.317639680884203 17 97.95 99.259765828718 -1.30976582871799 18 98.32 99.3140361190261 -0.994036119026117 19 98.27 99.8358739448412 -1.56587394484124 20 97.22 99.0705765513623 -1.85057655136229 21 99.28 100.089765828718 -0.809765828717994 22 100.38 100.040468583519 0.339531416480898 23 99.02 98.8036577125948 0.216342287405244 24 100.32 98.953765828718 1.366234171282 25 99.81 99.9967566645827 -0.186756664582665 26 100.6 100.121783619473 0.478216380526545 27 101.19 100.777243038857 0.41275696114278 28 100.47 99.7885404323362 0.681459567663826 29 101.77 99.704864780706 2.06513521929409 30 102.32 100.118053909782 2.20194609021843 31 102.39 100.550162025905 1.83983797409519 32 101.16 99.2464863742746 1.91351362572545 33 100.63 100.624594490398 0.0054055096022002 34 101.48 101.203405213042 0.276594786957919 35 101.44 99.697405213042 1.74259478695791 36 100.09 99.7577836194734 0.332216380526557 37 100.7 100.800774455338 -0.100774455338116 38 100.78 100.387423152078 0.392576847922404 39 99.81 100.145585474543 -0.335585474542523 40 98.45 98.797964029254 -0.347964029253941 41 98.49 98.6245586679318 -0.134558667931802 42 97.48 98.3199101194724 -0.839910119472372 43 97.91 98.7520182355956 -0.842018235595627 44 96.94 96.7305049064303 0.209495093569705 45 98.53 98.3778021516292 0.152197848370811 46 96.82 97.6106672288952 -0.790667228895227 47 95.76 95.476559261052 0.283440738947971 48 95.27 95.4472079577915 -0.177207957791512 49 97.32 96.8491176324237 0.470882367576276 50 96.68 96.525496038855 0.154503961144927 51 97.87 97.6296040066983 0.240395993301737 52 97.42 98.345765884323 -0.925765884323018 53 97.94 98.800468490844 -0.860468490844063 54 99.52 99.3931170393035 0.126882960696515 55 100.99 100.094414284502 0.895585715497615 56 99.92 99.9572248588666 -0.0372248588666119 57 101.97 101.245603265298 0.724396734702024 58 101.58 102.183332826710 -0.603332826709803 59 99.54 101.395170504245 -1.85517050424487 60 100.83 102.083656878519 -1.25365687851942 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.271221434618069 0.542442869236138 0.728778565381931 18 0.156114203898486 0.312228407796972 0.843885796101514 19 0.177168749900818 0.354337499801636 0.822831250099182 20 0.390348023555196 0.780696047110392 0.609651976444804 21 0.367895274601237 0.735790549202475 0.632104725398763 22 0.260201350094769 0.520402700189538 0.73979864990523 23 0.242886073159631 0.485772146319261 0.757113926840369 24 0.315638318418779 0.631276636837558 0.684361681581221 25 0.262536951967122 0.525073903934244 0.737463048032878 26 0.226951376153116 0.453902752306233 0.773048623846884 27 0.161823785363718 0.323647570727435 0.838176214636282 28 0.106278569345358 0.212557138690716 0.893721430654642 29 0.312685870583488 0.625371741166976 0.687314129416512 30 0.50123960377891 0.99752079244218 0.49876039622109 31 0.538565801656229 0.922868396687541 0.461434198343771 32 0.590982668331706 0.818034663336589 0.409017331668294 33 0.582537218763222 0.834925562473556 0.417462781236778 34 0.626738711813289 0.746522576373422 0.373261288186711 35 0.812593798941816 0.374812402116367 0.187406201058184 36 0.859397910388936 0.281204179222127 0.140602089611064 37 0.815732424709654 0.368535150580692 0.184267575290346 38 0.787598951209153 0.424802097581694 0.212401048790847 39 0.705019396323322 0.589961207353356 0.294980603676678 40 0.724329704091617 0.551340591816766 0.275670295908383 41 0.929599789817204 0.140800420365591 0.0704002101827955 42 0.877188441099517 0.245623117800966 0.122811558900483 43 0.768436572039401 0.463126855921197 0.231563427960599 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 0 0 OK 10% type I error level 0 0 OK

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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