Verbetering_Model5

*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: Mon, 23 Nov 2009 11:40:20 -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/23/t1259001695609080u3v0mlc5r.htm/, Retrieved Mon, 23 Nov 2009 19:41:47 +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/23/t1259001695609080u3v0mlc5r.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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100.25 1.8 100.03 99.6 2.7 100.25 100.16 2.3 99.6 100.49 1.9 100.16 99.72 2 100.49 100.14 2.3 99.72 98.48 2.8 100.14 100.38 2.4 98.48 101.45 2.3 100.38 98.42 2.7 101.45 98.6 2.7 98.42 100.06 2.9 98.6 98.62 3 100.06 100.84 2.2 98.62 100.02 2.3 100.84 97.95 2.8 100.02 98.32 2.8 97.95 98.27 2.8 98.32 97.22 2.2 98.27 99.28 2.6 97.22 100.38 2.8 99.28 99.02 2.5 100.38 100.32 2.4 99.02 99.81 2.3 100.32 100.6 1.9 99.81 101.19 1.7 100.6 100.47 2 101.19 101.77 2.1 100.47 102.32 1.7 101.77 102.39 1.8 102.32 101.16 1.8 102.39 100.63 1.8 101.16 101.48 1.3 100.63 101.44 1.3 101.48 100.09 1.3 101.44 100.7 1.2 100.09 100.78 1.4 100.7 99.81 2.2 100.78 98.45 2.9 99.81 98.49 3.1 98.45 97.48 3.5 98.49 97.91 3.6 97.48 96.94 4.4 97.91 98.53 4.1 96.94 96.82 5.1 98.53 95.76 5.8 96.82 95.27 5.9 95.76 97.32 5.4 95.27 96.68 5.5 97.32 97.87 4.8 96.68 97.42 3.2 97.87 97.94 2.7 97.42 99.52 2.1 97.94 100.99 1.9 99.52 99.92 0.6 100.99 101.97 0.7 99.92 101.58 -0.2 101.97 99.54 -1 101.5 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 54.4671841739803 -0.510590757417604X[t] + 0.473872331863727Y1[t] -0.717448617283483M1[t] -0.141020655860973M2[t] -1.00988898244975M3[t] -0.72507879670461M4[t] -0.63690956869757M5[t] -0.199910499327358M6[t] -1.67235240181616M7[t] + 0.294576516509678M8[t] -0.215513166477157M9[t] -1.80210443582655M10[t] -0.967334170364718M11[t] -0.00660123971353016t + 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) 54.4671841739803 12.014833 4.5333 4.4e-05 2.2e-05 X -0.510590757417604 0.126577 -4.0338 0.000215 0.000108 Y1 0.473872331863727 0.118113 4.012 0.00023 0.000115 M1 -0.717448617283483 0.590856 -1.2143 0.231128 0.115564 M2 -0.141020655860973 0.587854 -0.2399 0.811529 0.405765 M3 -1.00988898244975 0.594107 -1.6998 0.09622 0.04811 M4 -0.72507879670461 0.58596 -1.2374 0.222494 0.111247 M5 -0.63690956869757 0.586093 -1.0867 0.283085 0.141542 M6 -0.199910499327358 0.5878 -0.3401 0.7354 0.3677 M7 -1.67235240181616 0.595058 -2.8104 0.007358 0.003679 M8 0.294576516509678 0.586924 0.5019 0.618241 0.309121 M9 -0.215513166477157 0.600171 -0.3591 0.721248 0.360624 M10 -1.80210443582655 0.60604 -2.9736 0.004762 0.002381 M11 -0.967334170364718 0.589491 -1.641 0.107935 0.053967 t -0.00660123971353016 0.007182 -0.9192 0.363025 0.181513 Multiple Linear Regression - Regression Statistics Multiple R 0.889364739685644 R-squared 0.790969640196113 Adjusted R-squared 0.724459980258513 F-TEST (value) 11.8925527650901 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 1.09689812788361e-10 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.869724287959638 Sum Squared Residuals 33.2824948309435 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 100.25 100.22552030996 0.0244796900400029 2 99.6 100.440067263003 -0.84006726300334 3 100.16 99.4608169839566 0.699183016043347 4 100.49 100.208630738799 0.28136926120101 5 99.72 100.395517520866 -0.675517520865765 6 100.14 100.307856427762 -0.167856427762095 7 98.48 98.7725442862337 -0.292544286233722 8 100.38 100.150480196919 0.229519803080704 9 101.45 100.585205780502 0.864794219498239 10 98.42 99.294820363566 -0.874820363565989 11 98.6 98.6871562237672 -0.0871562237672058 12 100.06 99.6310680226703 0.428931977329668 13 98.62 99.5478126944526 -0.9278126944526 14 100.84 99.843735864212 0.996264135788101 15 100.02 99.9692037989053 0.0507962010946843 16 97.95 99.6035420540999 -1.65354205409985 17 98.32 98.7041943154355 -0.384194315435464 18 98.27 99.3099249078817 -1.03992490788172 19 97.22 98.1135426035368 -0.893542603536754 20 99.28 99.3720680307251 -0.09206803072511 21 100.38 99.7294359601805 0.650564039819492 22 99.02 98.810680243393 0.209319756607038 23 100.32 99.0454419735483 1.27455802645164 24 99.81 100.673268011364 -0.863268011364142 25 100.6 99.9117795680837 0.688220431916318 26 101.19 100.958083583449 0.231916416551480 27 100.47 100.209021465721 0.260978534279466 28 101.77 100.094983257068 1.6750167429315 29 102.32 100.996821579752 1.3231784202481 30 102.39 101.636790116192 0.75320988380814 31 101.16 100.19091803722 0.969081962780007 32 100.63 101.56838274764 -0.93838274763992 33 101.48 101.055834867761 0.424165132239428 34 101.44 99.8654338407818 1.57456615921817 35 100.09 100.674647973256 -0.584647973255571 36 100.7 101.046712331632 -0.346712331632491 37 100.78 100.509606445589 0.270393554411168 38 99.81 100.708870347913 -0.898870347912826 39 98.45 99.0163310895104 -0.566331089510384 40 98.49 98.5479555127238 -0.0579555127238091 41 97.48 98.4442420913248 -0.964242091324815 42 97.91 98.3449697900574 -0.434969790057382 43 96.94 96.6612191446224 0.278780855377638 44 98.53 98.3150678885521 0.214932111447863 45 96.82 98.0412432160975 -1.22124321609750 46 95.76 95.2803154893553 0.479684510644732 47 95.27 95.5551207675863 -0.285120767586275 48 97.32 96.538951634333 0.781048365666965 49 96.68 96.735280981915 -0.0552809819148877 50 97.87 97.3592429414234 0.510757058576585 51 97.42 97.8646266619071 -0.444626661907113 52 97.94 98.1848884373088 -0.244888437308847 53 99.52 98.819224492622 0.700775507377942 54 100.99 100.100458758107 0.889541241893053 55 99.92 99.9817759283872 -0.0617759283871687 56 101.97 101.384001136164 0.585998863836462 57 101.58 102.298280175460 -0.718280175459655 58 99.54 100.928750062904 -1.38875006290395 59 100.83 101.147633061843 -0.317633061842588 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.264194454161243 0.528388908322486 0.735805545838757 19 0.502032030912094 0.995935938175812 0.497967969087906 20 0.372002866932961 0.744005733865921 0.62799713306704 21 0.248924636890084 0.497849273780167 0.751075363109916 22 0.224208480814764 0.448416961629528 0.775791519185236 23 0.26025796232125 0.5205159246425 0.73974203767875 24 0.315714155124867 0.631428310249733 0.684285844875133 25 0.269589643954673 0.539179287909346 0.730410356045327 26 0.184297417791826 0.368594835583652 0.815702582208174 27 0.120214247551822 0.240428495103644 0.879785752448178 28 0.365307127250607 0.730614254501214 0.634692872749393 29 0.445128920322775 0.89025784064555 0.554871079677225 30 0.384620295228626 0.769240590457252 0.615379704771374 31 0.360717729882443 0.721435459764886 0.639282270117557 32 0.462456267940862 0.924912535881724 0.537543732059138 33 0.504491613257794 0.99101677348441 0.495508386742206 34 0.800425631221686 0.399148737556627 0.199574368778314 35 0.823384280714955 0.353231438570091 0.176615719285045 36 0.756701839307065 0.48659632138587 0.243298160692935 37 0.786660160999019 0.426679678001963 0.213339839000981 38 0.698000435706552 0.603999128586896 0.301999564293448 39 0.632752075097222 0.734495849805555 0.367247924902778 40 0.830033164377217 0.339933671245565 0.169966835622783 41 0.94472911331322 0.110541773373562 0.0552708866867809 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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