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R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 01 Dec 2008 09:17:50 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/01/t1228148380udsk4bghfo6q4o4.htm/, Retrieved Mon, 01 Dec 2008 16:19:40 +0000

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/2008/Dec/01/t1228148380udsk4bghfo6q4o4.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

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Dataseries X:

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14929387,5 0 14717825,3 0 15826281,2 0 16301309,6 0 15033016,9 0 16998460,6 0 14066462,7 0 13328937,3 0 17319718,2 0 17586426,8 0 15887037,4 0 17935679,1 0 15869489 0 15892510,9 0 17556558,1 0 16791643 0 15953688,5 0 18144913,6 0 14390881 0 13885708,7 0 17332571,5 0 17152595,8 0 16003877,1 0 16841467,1 0 14783398,1 0 14667847,5 0 17714362,2 0 16282088 0 15014866,2 0 17722582,4 1 13876509,4 0 15495489,6 0 17799521,1 0 17920079,1 0 17248022,4 0 18813782,4 1 16249688,3 1 17823358,5 1 20424438,3 1 17814218,7 1 19699959,6 1 19776328,1 1 15679833,1 1 17119266,5 1 20092613 1 20863688,3 1 20925203,1 1 21032593 1 20664684,3 1 19711511,4 1 22553293,4 1 19498332,9 1 20722827,8 1 21321275 1 17960847,7 1 17789654,9 1 20003708,5 1 21169851,7 1 20422839,4 1 19810562,3 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation x[t] = + 16924267.42 + 3270915.6y[t] -1733304.22000000M1[t] -1670022.94M2[t] + 582352.98M3[t] -895115.22M4[t] -947761.86M5[t] -94104.8399999996M6[t] -3037726.88M7[t] -2708822.26M8[t] + 276992.8M9[t] + 705894.68M10[t] -135237.780000001M11[t] + 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) 16924267.42 484445.00719 34.9354 0 0 y 3270915.6 269136.115105 12.1534 0 0 M1 -1733304.22000000 648165.596922 -2.6742 0.010272 0.005136 M2 -1670022.94 648165.596922 -2.5765 0.013181 0.00659 M3 582352.98 648165.596922 0.8985 0.373519 0.186759 M4 -895115.22 648165.596922 -1.381 0.173811 0.086906 M5 -947761.86 648165.596922 -1.4622 0.150335 0.075168 M6 -94104.8399999996 645926.676253 -0.1457 0.884789 0.442395 M7 -3037726.88 648165.596922 -4.6867 2.4e-05 1.2e-05 M8 -2708822.26 648165.596922 -4.1792 0.000126 6.3e-05 M9 276992.8 648165.596922 0.4273 0.671077 0.335538 M10 705894.68 648165.596922 1.0891 0.281678 0.140839 M11 -135237.780000001 648165.596922 -0.2086 0.835625 0.417813 Multiple Linear Regression - Regression Statistics Multiple R 0.915451082204775 R-squared 0.838050683909894 Adjusted R-squared 0.796701922354973 F-TEST (value) 20.2678545232066 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.22124532708767e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1021299.74921083 Sum Squared Residuals 49023499353690.8 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14929387.5 15190963.2 -261575.700000014 2 14717825.3 15254244.48 -536419.179999997 3 15826281.2 17506620.4 -1680339.2 4 16301309.6 16029152.2 272157.4 5 15033016.9 15976505.56 -943488.66 6 16998460.6 16830162.58 168298.020000001 7 14066462.7 13886540.54 179922.160000000 8 13328937.3 14215445.16 -886507.859999999 9 17319718.2 17201260.22 118457.979999999 10 17586426.8 17630162.1 -43735.3000000006 11 15887037.4 16789029.64 -901992.24 12 17935679.1 16924267.42 1011411.68000000 13 15869489 15190963.2 678525.800000003 14 15892510.9 15254244.48 638266.42 15 17556558.1 17506620.4 49937.7000000019 16 16791643 16029152.2 762490.8 17 15953688.5 15976505.56 -22817.0600000004 18 18144913.6 16830162.58 1314751.02 19 14390881 13886540.54 504340.46 20 13885708.7 14215445.16 -329736.46 21 17332571.5 17201260.22 131311.280000000 22 17152595.8 17630162.1 -477566.3 23 16003877.1 16789029.64 -785152.54 24 16841467.1 16924267.42 -82800.3199999987 25 14783398.1 15190963.2 -407565.099999997 26 14667847.5 15254244.48 -586396.98 27 17714362.2 17506620.4 207741.800000000 28 16282088 16029152.2 252935.800000001 29 15014866.2 15976505.56 -961639.36 30 17722582.4 20101078.18 -2378495.78000000 31 13876509.4 13886540.54 -10031.1399999990 32 15495489.6 14215445.16 1280044.44 33 17799521.1 17201260.22 598260.880000001 34 17920079.1 17630162.1 289917.000000001 35 17248022.4 16789029.64 458992.759999999 36 18813782.4 20195183.02 -1381400.62000000 37 16249688.3 18461878.8 -2212190.50000000 38 17823358.5 18525160.08 -701801.580000001 39 20424438.3 20777536 -353097.699999999 40 17814218.7 19300067.8 -1485849.1 41 19699959.6 19247421.16 452538.440000001 42 19776328.1 20101078.18 -324750.079999999 43 15679833.1 17157456.14 -1477623.04 44 17119266.5 17486360.76 -367094.26 45 20092613 20472175.82 -379562.82 46 20863688.3 20901077.7 -37389.3999999999 47 20925203.1 20059945.24 865257.860000002 48 21032593 20195183.02 837409.98 49 20664684.3 18461878.8 2202805.50000000 50 19711511.4 18525160.08 1186351.32000000 51 22553293.4 20777536 1775757.4 52 19498332.9 19300067.8 198265.099999999 53 20722827.8 19247421.16 1475406.64 54 21321275 20101078.18 1220196.82 55 17960847.7 17157456.14 803391.559999999 56 17789654.9 17486360.76 303294.139999999 57 20003708.5 20472175.82 -468467.32 58 21169851.7 20901077.7 268773.999999999 59 20422839.4 20059945.24 362894.159999999 60 19810562.3 20195183.02 -384620.719999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.462365009510181 0.924730019020362 0.537634990489819 17 0.348006745860095 0.69601349172019 0.651993254139905 18 0.313302354976189 0.626604709952378 0.686697645023811 19 0.205472200540617 0.410944401081234 0.794527799459383 20 0.134321630941482 0.268643261882963 0.865678369058518 21 0.0754062726795214 0.150812545359043 0.924593727320479 22 0.0433897812494111 0.0867795624988222 0.956610218750589 23 0.0249159893256726 0.0498319786513452 0.975084010674327 24 0.020140650417322 0.040281300834644 0.979859349582678 25 0.0121830392942485 0.0243660785884969 0.987816960705752 26 0.00777959225785263 0.0155591845157053 0.992220407742147 27 0.00677885627025519 0.0135577125405104 0.993221143729745 28 0.00340328229902907 0.00680656459805814 0.99659671770097 29 0.00314028496016481 0.00628056992032961 0.996859715039835 30 0.00437835688115855 0.0087567137623171 0.995621643118841 31 0.00218495350598424 0.00436990701196848 0.997815046494016 32 0.00708747451843895 0.0141749490368779 0.992912525481561 33 0.0042454503338358 0.0084909006676716 0.995754549666164 34 0.00228460471811996 0.00456920943623992 0.99771539528188 35 0.00215648666577098 0.00431297333154197 0.99784351333423 36 0.00221919831984543 0.00443839663969085 0.997780801680155 37 0.0345966513664192 0.0691933027328383 0.96540334863358 38 0.0792200249266755 0.158440049853351 0.920779975073324 39 0.207286077702461 0.414572155404923 0.792713922297539 40 0.247046697863839 0.494093395727678 0.752953302136161 41 0.345768765638637 0.691537531277274 0.654231234361363 42 0.387146311072656 0.774292622145312 0.612853688927344 43 0.788506982705897 0.422986034588207 0.211493017294103 44 0.710140908195031 0.579718183609938 0.289859091804969 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 8 0.275862068965517 NOK 5% type I error level 14 0.482758620689655 NOK 10% type I error level 16 0.551724137931034 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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