Beste model

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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: Sat, 05 Dec 2009 08:17:52 -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/Dec/05/t1260026495e6u7oleieza9t73.htm/, Retrieved Sat, 05 Dec 2009 16:21:47 +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/Dec/05/t1260026495e6u7oleieza9t73.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}, }

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Dataseries X:

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6.3 3.1 6.3 6.1 6.1 6.3 6 3 6.3 6.3 6.1 6.1 6.2 2.8 6 6.3 6.3 6.1 6.4 2.5 6.2 6 6.3 6.3 6.8 1.9 6.4 6.2 6 6.3 7.5 1.9 6.8 6.4 6.2 6 7.5 1.8 7.5 6.8 6.4 6.2 7.6 2 7.5 7.5 6.8 6.4 7.6 2.6 7.6 7.5 7.5 6.8 7.4 2.5 7.6 7.6 7.5 7.5 7.3 2.5 7.4 7.6 7.6 7.5 7.1 1.6 7.3 7.4 7.6 7.6 6.9 1.4 7.1 7.3 7.4 7.6 6.8 0.8 6.9 7.1 7.3 7.4 7.5 1.1 6.8 6.9 7.1 7.3 7.6 1.3 7.5 6.8 6.9 7.1 7.8 1.2 7.6 7.5 6.8 6.9 8 1.3 7.8 7.6 7.5 6.8 8.1 1.1 8 7.8 7.6 7.5 8.2 1.3 8.1 8 7.8 7.6 8.3 1.2 8.2 8.1 8 7.8 8.2 1.6 8.3 8.2 8.1 8 8 1.7 8.2 8.3 8.2 8.1 7.9 1.5 8 8.2 8.3 8.2 7.6 0.9 7.9 8 8.2 8.3 7.6 1.5 7.6 7.9 8 8.2 8.3 1.4 7.6 7.6 7.9 8 8.4 1.6 8.3 7.6 7.6 7.9 8.4 1.7 8.4 8.3 7.6 7.6 8.4 1.4 8.4 8.4 8.3 7.6 8.4 1.8 8.4 8.4 8.4 8.3 8.6 1.7 8.4 8.4 8.4 8.4 8.9 1.4 8.6 8.4 8.4 8.4 8.8 1.2 8.9 8.6 8.4 8.4 8.3 1 8.8 8.9 8.6 8.4 7.5 1.7 8.3 8.8 8.9 8.6 7.2 2.4 7.5 8.3 8.8 8.9 7.4 2 7.2 7.5 8.3 8.8 8.8 2.1 7.4 7.2 7.5 8.3 9.3 2 8.8 7.4 7.2 7.5 9.3 1.8 9.3 8.8 7.4 7.2 8.7 2.7 9.3 9.3 8.8 7.4 8.2 2.3 8.7 9. 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 Werkl[t] = + 0.578720388686346 -0.0288976650552464Infl[t] + 1.30143214998577`Yt-1`[t] -0.500215742364641`Yt-2`[t] -0.406060070910419`Yt-3`[t] + 0.510605505838536`Yt-4`[t] -0.0090128947126465M1[t] + 0.00134048665666322M2[t] + 0.749204340383939M3[t] -0.00450670673461415M4[t] + 0.279500612908942M5[t] + 0.582882431043774M6[t] + 0.217843298407681M7[t] + 0.425664336820022M8[t] + 0.326808893226672M9[t] + 0.053531382937026M10[t] + 0.104634569514344M11[t] + 0.00124441197949185t + 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) 0.578720388686346 0.838499 0.6902 0.494164 0.247082 Infl -0.0288976650552464 0.053355 -0.5416 0.591165 0.295582 `Yt-1` 1.30143214998577 0.142453 9.1359 0 0 `Yt-2` -0.500215742364641 0.239085 -2.0922 0.042978 0.021489 `Yt-3` -0.406060070910419 0.239948 -1.6923 0.098568 0.049284 `Yt-4` 0.510605505838536 0.150148 3.4007 0.001564 0.000782 M1 -0.0090128947126465 0.107011 -0.0842 0.933309 0.466655 M2 0.00134048665666322 0.111548 0.012 0.990473 0.495237 M3 0.749204340383939 0.118082 6.3448 0 0 M4 -0.00450670673461415 0.145622 -0.0309 0.975469 0.487734 M5 0.279500612908942 0.145553 1.9203 0.062159 0.031079 M6 0.582882431043774 0.141407 4.122 0.00019 9.5e-05 M7 0.217843298407681 0.105199 2.0708 0.045044 0.022522 M8 0.425664336820022 0.103074 4.1297 0.000185 9.3e-05 M9 0.326808893226672 0.110542 2.9564 0.00526 0.00263 M10 0.053531382937026 0.122196 0.4381 0.663746 0.331873 M11 0.104634569514344 0.112827 0.9274 0.359429 0.179714 t 0.00124441197949185 0.004874 0.2553 0.79983 0.399915 Multiple Linear Regression - Regression Statistics Multiple R 0.98576974984865 R-squared 0.971741999716672 Adjusted R-squared 0.95942440984958 F-TEST (value) 78.8905954981365 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.152322251148176 Sum Squared Residuals 0.904880659599072 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.3 6.36892391499723 -0.068923914997231 2 6 6.18124722521091 -0.181247225210907 3 6.2 6.4644933647509 -0.264493364750907 4 6.4 6.23316828300267 0.166831716997327 5 6.8 6.81781991645622 -0.0178199164562220 6 7.5 7.30858219215828 0.191417807841719 7 7.5 7.67950253303701 -0.179502533037013 8 7.6 7.47233450356609 0.127665496433911 9 7.6 7.40752824061578 0.192471759384220 10 7.4 7.44578718866166 -0.0457871886616623 11 7.3 7.19724235013028 0.102757649869723 12 7.1 7.14082057520335 -0.04082057520335 13 6.9 7.00977878390264 -0.109778783902636 14 6.8 6.8169568006837 -0.0169568006836957 15 7.5 7.55744716394647 -0.0574471639464694 16 7.6 7.73931598803724 -0.139315988037242 17 7.8 7.74593458743248 0.054065412567522 18 8 7.92263330658082 0.0773666934191797 19 8.1 8.04167924745543 0.0583207525445709 20 8.2 8.24491376776363 -0.0449137677636313 21 8.3 8.25122323040303 0.048776769596967 22 8.2 8.10926780090956 0.0907321990904372 23 8 7.98901538721862 0.0109846127813844 24 7.9 7.69159445042693 0.208405549573066 25 7.6 7.76273105787617 -0.162731057876175 26 7.6 7.44673364503079 0.153266354969211 27 8.3 8.2872813058758 0.0127186941241927 28 8.4 8.51079511340501 -0.110795113405013 29 8.4 8.4199676221143 -0.0199676221143032 30 8.4 8.39899952787144 0.00100047212855698 31 8.4 8.34046358818868 0.059536411811323 32 8.6 8.60347935566989 -0.00347935566988855 33 8.9 8.77482405356976 0.125175946430242 34 8.8 8.79895698479346 0.00104301520654187 35 8.3 8.49566416447126 -0.195664164471265 36 7.5 7.7516542205359 -0.251654220535898 37 7.2 7.12640718230037 0.073592817699626 38 7.4 7.31127647543861 0.0887235245613888 39 8.8 8.53739143115547 0.262608568844532 40 9.3 9.22311004063138 0.076889959368616 41 9.3 9.23016167501423 0.0698383249857733 42 8.7 8.79230913728963 -0.0923091372896299 43 8.2 8.1710318653824 0.0289681346175983 44 8.3 8.2963725051415 0.00362749485850200 45 8.5 8.81975883574927 -0.319758835749268 46 8.6 8.64598802563532 -0.0459880256353168 47 8.5 8.41807809817984 0.0819219018201574 48 8.2 8.11593075383382 0.0840692461661811 49 8.1 7.83215906092358 0.267840939076416 50 7.9 7.943785853636 -0.0437858536359974 51 8.6 8.55338673427135 0.0466132657286517 52 8.7 8.69361057492369 0.00638942507631222 53 8.7 8.78611619898277 -0.08611619898277 54 8.5 8.67747583609983 -0.177475836099826 55 8.4 8.36732276593648 0.0326772340635212 56 8.5 8.5828998678589 -0.0828998678588934 57 8.7 8.74666563966216 -0.0466656396621606 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.789089283343986 0.421821433312029 0.210910716656015 22 0.697342321008158 0.605315357983684 0.302657678991842 23 0.571971889105435 0.85605622178913 0.428028110894565 24 0.59630045665869 0.80739908668262 0.40369954334131 25 0.665303061369886 0.669393877260229 0.334696938630114 26 0.613598686332359 0.772802627335283 0.386401313667641 27 0.75704702750172 0.485905944996561 0.242952972498281 28 0.673468243917435 0.65306351216513 0.326531756082565 29 0.668918345512874 0.662163308974253 0.331081654487126 30 0.702127914442173 0.595744171115655 0.297872085557827 31 0.654697507138478 0.690604985723045 0.345302492861522 32 0.570462406882262 0.859075186235476 0.429537593117738 33 0.522123436894398 0.955753126211204 0.477876563105602 34 0.564189295785025 0.87162140842995 0.435810704214975 35 0.464478537345776 0.928957074691551 0.535521462654224 36 0.827939637566508 0.344120724866985 0.172060362433492 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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