ws7 mini trend

*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, 23 Nov 2010 18:39:30 +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/Nov/23/t1290537507jhfyppf5y4s2lmg.htm/, Retrieved Tue, 23 Nov 2010 19:38:27 +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/Nov/23/t1290537507jhfyppf5y4s2lmg.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:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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73 2 71.91 5.11 50 3 28 6 6.06 3.53 48 5 40 5 8.1 4.52 63 11 79 3 79.38 3.72 113 13 75 3 65.34 5.99 128 11 21 3 34.62 3.15 52 7 16 2 26.26 3.17 104 1 81 2 60.92 3.5 40 1 90 2 39.56 3.39 89 11 87 5 65.61 4.15 97 3 99 3 56.49 4.5 29 9 54 3 56.19 3.31 36 5 53 5 80.3 3.09 114 11 6 4 61.2 5.31 49 9 71 5 58.2 4.24 57 7 93 6 75.91 5.06 82 4 82 3 73.66 4.72 34 10 32 4 73.87 4.58 36 13 93 4 87.21 5.3 89 9 24 4 64.29 5.11 69 5 96 5 71.82 4.05 35 8 88 4 89.31 4.62 65 12 83 2 1.41 4.66 70 8 23 6 35.17 4.66 60 5 23 5 34.68 2.76 57 9 20 5 41.08 5.1 127 11 33 3 30.57 4.97 96 8 88 2 68.84 2.87 61 9 42 6 7.17 5.14 127 10 98 2 71.05 4.98 36 1 34 4 23.32 4.55 55 9 59 3 61.39 5.45 75 2 26 6 8.41 4.36 42 3 64 4 65.88 4.78 64 4 13 1 64.06 4.74 83 3 6 2 26.8 5.44 56 1 49 4 12.78 5.78 114 5 3 5 23.84 2.92 33 4 87 6 42.69 4.22 91 2 77 2 54.94 3.93 127 2 70 4 89.99 3.01 45 10 76 4 5.68 3.22 80 6 82 4 72.64 5.12 40 9 12 2 45.92 3.04 115 7 44 3 24.96 5.82 33 1 63 5 18.17 3.11 127 13 35 1 29. 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 17 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation slaagkans[t] = + 26.8300788181571 -0.39718687633662verzekeraar[t] + 0.525635231419669kost[t] + 0.734765737056835grootte[t] + 0.0308685622071769snelheid[t] + 0.318502498855332maand[t] -0.144918874305115t + 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) 26.8300788181571 27.276257 0.9836 0.330794 0.165397 verzekeraar -0.39718687633662 2.82093 -0.1408 0.888685 0.444343 kost 0.525635231419669 0.165611 3.1739 0.002778 0.001389 grootte 0.734765737056835 4.48739 0.1637 0.870703 0.435351 snelheid 0.0308685622071769 0.135522 0.2278 0.820901 0.41045 maand 0.318502498855332 1.145549 0.278 0.782318 0.391159 t -0.144918874305115 0.287528 -0.504 0.616822 0.308411 Multiple Linear Regression - Regression Statistics Multiple R 0.484479983675251 R-squared 0.234720854581971 Adjusted R-squared 0.127937718012013 F-TEST (value) 2.19810788596003 F-TEST (DF numerator) 6 F-TEST (DF denominator) 43 p-value 0.0615615092501303 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 28.0290263146554 Sum Squared Residuals 33781.9315943488 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 73 69.9428042058524 3.05719579414758 2 28 33.0103958459621 -5.01039584596214 3 40 37.4364212260157 2.56357877398430 4 79 77.1457759184018 1.85422408159817 5 75 71.1148800534806 3.88511994651943 6 21 49.115691453555 -28.1156914535550 7 16 44.6824944773005 -28.6824944773005 8 81 61.0229774359705 19.9770225640295 9 90 54.26725032417 35.73274967583 10 87 64.8809190663154 22.1190809336846 11 99 60.80570140515 38.1942985948501 12 54 58.5707906743502 -4.57079067435021 13 53 74.4616778600394 -21.4616778600394 14 6 63.6620313370442 -57.6620313370442 15 71 60.3667640534394 10.6332359465606 16 93 69.55237271424 23.44762728576 17 82 69.5958388548387 12.4041611451613 18 32 70.0784939205875 -38.0784939205875 19 93 77.8366041656607 15.1633958343393 20 24 63.6131390576111 -39.6131390576111 21 96 66.1561912998012 29.8438087001988 22 88 78.2207028311218 9.77929716887822 23 83 31.5765443127978 51.4234556872022 24 23 46.3241302272365 -23.3241302272365 25 23 46.1041863742642 -23.1041863742642 26 20 53.840489157971 -33.840489157971 27 33 46.9575652833125 -13.9575652833125 28 88 65.0209883655595 22.9790116344405 29 42 34.895143091905 7.10485690809501 30 98 64.1234261375546 33.8765738624454 31 34 40.9141373207600 -6.91413732076005 32 59 60.2264814984457 -1.22648149844571 33 26 29.5407927271432 -3.54079272714323 34 64 61.7047168321768 2.29528316782319 35 13 62.0333120192965 -49.0333120192965 36 6 40.9499173845932 -34.9499173845932 37 49 35.9554257671481 13.0445742328519 38 3 36.3065596303886 -33.3065596303886 39 87 47.7812450604872 39.2187549395128 40 77 56.5622914521314 20.4377085478686 41 70 73.3873270981743 -3.38732709817425 42 76 28.8867923494887 47.1132076505113 43 82 65.0552284797315 16.9447715202685 44 12 51.8095344093154 -39.8095344093154 45 44 37.8505258630149 6.14947413698506 46 63 38.0746297010116 24.9253702989884 47 35 42.0273539798517 -7.02735397985172 48 69 49.0874186551782 19.9125813448218 49 10 28.2786005183774 -18.2786005183774 50 36 55.1853181217762 -19.1853181217762 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 10 0.409373249122097 0.818746498244194 0.590626750877903 11 0.296628931176052 0.593257862352104 0.703371068823948 12 0.318731295663219 0.637462591326437 0.681268704336781 13 0.319200961037059 0.638401922074119 0.680799038962941 14 0.7557064478902 0.488587104219601 0.244293552109800 15 0.692333428276687 0.615333143446626 0.307666571723313 16 0.658917773695881 0.682164452608237 0.341082226304119 17 0.565399285314007 0.869201429371986 0.434600714685993 18 0.608883126274927 0.782233747450147 0.391116873725073 19 0.532422381523346 0.935155236953307 0.467577618476654 20 0.568094044388775 0.86381191122245 0.431905955611225 21 0.57412547363144 0.85174905273712 0.42587452636856 22 0.491072043977387 0.982144087954773 0.508927956022613 23 0.685827839878086 0.628344320243827 0.314172160121914 24 0.65353888426076 0.692922231478481 0.346461115739240 25 0.603272556796338 0.793454886407324 0.396727443203662 26 0.631358118012329 0.737283763975343 0.368641881987671 27 0.557070731653681 0.885858536692639 0.442929268346319 28 0.527289578563128 0.945420842873744 0.472710421436872 29 0.452733039460211 0.905466078920423 0.547266960539789 30 0.549517815371967 0.900964369256067 0.450482184628033 31 0.454379057419053 0.908758114838105 0.545620942580948 32 0.36477232796456 0.72954465592912 0.63522767203544 33 0.271927901566851 0.543855803133703 0.728072098433149 34 0.193468072562519 0.386936145125038 0.806531927437481 35 0.25939847397099 0.51879694794198 0.74060152602901 36 0.2764425356142 0.5528850712284 0.7235574643858 37 0.233818336453229 0.467636672906458 0.766181663546771 38 0.44713614328225 0.8942722865645 0.55286385671775 39 0.374919712280864 0.749839424561727 0.625080287719136 40 0.376014540805878 0.752029081611756 0.623985459194122 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 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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Software written by Ed van Stee & Patrick Wessa

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