*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: Tue, 28 Dec 2010 18:23:34 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293560506uw1jnlr756bj2yf.htm/, Retrieved Tue, 28 Dec 2010 19:21:57 +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/2010/Dec/28/t1293560506uw1jnlr756bj2yf.htm/}, year = {2010}, } @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 = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

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No (this computation is public)

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Dataseries X:

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112,3 1 117,2 96,8 80 117,3 1 112,3 117,2 96,8 111,1 1 117,3 112,3 117,2 102,2 1 111,1 117,3 112,3 104,3 1 102,2 111,1 117,3 122,9 0 104,3 102,2 111,1 107,6 0 122,9 104,3 102,2 121,3 0 107,6 122,9 104,3 131,5 0 121,3 107,6 122,9 89 0 131,5 121,3 107,6 104,4 0 89 131,5 121,3 128,9 0 104,4 89 131,5 135,9 0 128,9 104,4 89 133,3 0 135,9 128,9 104,4 121,3 0 133,3 135,9 128,9 120,5 0 121,3 133,3 135,9 120,4 0 120,5 121,3 133,3 137,9 0 120,4 120,5 121,3 126,1 0 137,9 120,4 120,5 133,2 0 126,1 137,9 120,4 151,1 0 133,2 126,1 137,9 105 0 151,1 133,2 126,1 119 0 105 151,1 133,2 140,4 0 119 105 151,1 156,6 1 140,4 119 105 137,1 1 156,6 140,4 119 122,7 1 137,1 156,6 140,4 125,8 1 122,7 137,1 156,6 139,3 1 125,8 122,7 137,1 134,9 1 139,3 125,8 122,7 149,2 1 134,9 139,3 125,8 132,3 1 149,2 134,9 139,3 149 1 132,3 149,2 134,9 117,2 1 149 132,3 149,2 119,6 1 117,2 149 132,3 152 1 119,6 117,2 149 149,4 1 152 119,6 117,2 127,3 1 149,4 152 119,6 114,1 1 127,3 149,4 152 102,1 1 114,1 127,3 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message Warning: there are blank lines in the 'Data X' field. Please, use NA for missing data - blank lines are simply deleted and are NOT treated as missing values. Multiple Linear Regression - Estimated Regression Equation Y[t] = + 36.0412849947343 -1.07737500078825X[t] + 0.346066086990625Y1[t] + 0.308973906895185Y2[t] + 0.239167122050576Y3[t] + 0.549191143048674M1[t] -20.4478997908501M2[t] -35.6144987271497M3[t] -35.2010923362867M4[t] -21.6096098638476M5[t] -8.96826790774917M6[t] -16.9676387368805M7[t] -21.7652635983034M8[t] -5.96576558472508M9[t] -44.2213929649418M10[t] -30.1782647969586M11[t] -0.097245795559272t + 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) 36.0412849947343 10.58928 3.4036 0.00145 0.000725 X -1.07737500078825 2.990699 -0.3602 0.72043 0.360215 Y1 0.346066086990625 0.14722 2.3507 0.023395 0.011698 Y2 0.308973906895185 0.147592 2.0934 0.042245 0.021122 Y3 0.239167122050576 0.143192 1.6703 0.102133 0.051067 M1 0.549191143048674 9.21253 0.0596 0.95274 0.47637 M2 -20.4478997908501 9.710246 -2.1058 0.041098 0.020549 M3 -35.6144987271497 6.993079 -5.0928 7e-06 4e-06 M4 -35.2010923362867 5.966444 -5.8998 1e-06 0 M5 -21.6096098638476 5.739037 -3.7654 5e-04 0.00025 M6 -8.96826790774917 6.305878 -1.4222 0.16218 0.08109 M7 -16.9676387368805 7.694286 -2.2052 0.032835 0.016417 M8 -21.7652635983034 7.564488 -2.8773 0.006221 0.003111 M9 -5.96576558472508 6.261504 -0.9528 0.346033 0.173016 M10 -44.2213929649418 7.385429 -5.9877 0 0 M11 -30.1782647969586 8.339904 -3.6185 0.000775 0.000387 t -0.097245795559272 0.084068 -1.1567 0.253763 0.126881 Multiple Linear Regression - Regression Statistics Multiple R 0.936965555361769 R-squared 0.877904451934389 Adjusted R-squared 0.83247355032858 F-TEST (value) 19.3239495784548 F-TEST (DF numerator) 16 F-TEST (DF denominator) 43 p-value 1.32116539930394e-14 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 7.76399012700786 Sum Squared Residuals 2592.02033576785 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 112.3 125.016844688237 -12.7168446882366 2 117.3 112.547859483636 4.75214051636404 3 111.1 102.379382332776 8.72061766722434 4 102.2 100.922883825166 1.27711617483445 5 104.3 110.617329715332 -6.31732971533162 6 122.9 120.732835731259 2.16716426874133 7 107.6 117.593306142823 -9.9933061428234 8 121.3 113.652789979441 7.64721002055865 9 131.5 133.817355283876 -2.31735528387632 10 89 99.5680417524949 -10.5680417524949 11 104.4 105.234238850241 -0.834238850241086 12 128.9 129.952789193167 -1.05278919316651 13 135.9 133.476949150963 2.42305084903736 14 133.3 126.058109428950 7.24189057105015 15 121.3 117.916904709421 3.38309529057920 16 120.5 114.951109957264 5.54889004273647 17 120.4 123.838972364477 -3.43897236447719 18 137.9 133.231277326194 4.66872267380579 19 126.1 130.968586135510 -4.86858613550955 20 133.2 127.373262310499 5.82673768950126 21 151.1 146.072116280673 5.02788371932692 22 105 113.285368760788 -8.28536876078828 23 119 118.506324022927 0.493675977072679 24 140.4 143.469662619033 -3.06966261903265 25 156.6 143.550077597334 13.0499224026658 26 137.1 138.022392793389 -0.922392793389313 27 122.7 126.133813068798 -3.4338130687976 28 125.8 119.316138204199 6.4838617958005 29 139.3 124.770196611473 14.5298033885266 30 134.9 139.499997500233 -4.59999750023276 31 149.2 134.793255914225 14.4067440857748 32 132.3 136.716401258553 -4.41640125855294 33 149 149.936128138009 -0.936128138009019 34 117.2 115.560989433771 1.63901056622894 35 119.6 119.619910122388 -0.0199101223879989 36 152 144.700208431543 7.29979156845746 37 149.4 149.500717892868 -0.100717892868304 38 127.3 138.09136501356 -10.7913650135600 39 114.1 122.125142355720 -8.02514235571955 40 102.1 110.423072743032 -8.32307274303189 41 107.7 110.40046740769 -2.70046740769009 42 104.4 118.017840761567 -13.6178407615669 43 102.1 107.639454463813 -5.53945446381335 44 96 102.268353797482 -6.26835379748189 45 109.3 114.359711396232 -5.05971139623226 46 90 78.1746919646546 11.8253080353454 47 83.9 88.091932375357 -4.19193237535695 48 112 113.279674566309 -1.27967456630904 49 114.3 116.955410670598 -2.65541067059826 50 103.6 103.880273280465 -0.280273280464863 51 91.7 92.3447575332864 -0.644757533286418 52 80.8 85.7867952703395 -4.98679527033952 53 87.2 89.2730339010277 -2.0730339010277 54 109.2 97.8180486807475 11.3819513192525 55 102.7 96.7053973436285 5.9946026563715 56 95.1 97.889192654025 -2.78919265402508 57 117.5 114.214688901209 3.28531109879068 58 85.1 79.7109080882911 5.38909191170884 59 92.1 87.5475946290866 4.55240537091336 60 113.5 115.397665189949 -1.89766518994922 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.0190027095232591 0.0380054190465181 0.98099729047674 21 0.00615885435926884 0.0123177087185377 0.993841145640731 22 0.00155048730026150 0.00310097460052299 0.998449512699739 23 0.000293620813247382 0.000587241626494764 0.999706379186753 24 0.000366051462255277 0.000732102924510555 0.999633948537745 25 9.60663313403503e-05 0.000192132662680701 0.99990393366866 26 0.000693119275723665 0.00138623855144733 0.999306880724276 27 0.0285393753039088 0.0570787506078175 0.97146062469609 28 0.0965345141801375 0.193069028360275 0.903465485819863 29 0.109035517910172 0.218071035820345 0.890964482089828 30 0.145716396846631 0.291432793693262 0.854283603153369 31 0.372608277395624 0.745216554791248 0.627391722604376 32 0.28848768493992 0.57697536987984 0.71151231506008 33 0.293117477343783 0.586234954687566 0.706882522656217 34 0.204093135938671 0.408186271877342 0.795906864061329 35 0.158116712526663 0.316233425053326 0.841883287473337 36 0.259874600469556 0.519749200939111 0.740125399530444 37 0.343780462984237 0.687560925968474 0.656219537015763 38 0.461294575105482 0.922589150210965 0.538705424894518 39 0.442542451406579 0.885084902813157 0.557457548593421 40 0.386612535537560 0.773225071075121 0.61338746446244 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 5 0.238095238095238 NOK 5% type I error level 7 0.333333333333333 NOK 10% type I error level 8 0.380952380952381 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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