multiple lineair regression

*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: Wed, 26 Nov 2008 11:17:37 -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/Nov/26/t1227723493y5suqyegjjrvccu.htm/, Retrieved Wed, 26 Nov 2008 18:18:13 +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/Nov/26/t1227723493y5suqyegjjrvccu.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}, }

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IsPrivate?

No (this computation is public)

User-defined keywords:

multiple lineair regression

Dataseries X:

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147768 0 137507 0 136919 0 136151 0 133001 0 125554 0 119647 0 114158 0 116193 0 152803 0 161761 0 160942 0 149470 0 139208 0 134588 0 130322 0 126611 0 122401 0 117352 0 112135 0 112879 0 148729 0 157230 0 157221 0 146681 0 136524 0 132111 0 125326 0 122716 0 116615 0 113719 0 110737 0 112093 0 143565 0 149946 0 149147 0 134339 0 122683 0 115614 0 116566 0 111272 0 104609 0 101802 0 94542 0 93051 0 124129 0 130374 0 123946 0 114971 0 105531 0 104919 0 104782 0 101281 0 94545 0 93248 0 84031 0 87486 0 115867 0 120327 1 117008 1 108811 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 6 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation jonger_dan_25[t] = + 123953.758620690 -8571.75862068966economische_crisis[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) 123953.758620690 2518.335686 49.2205 0 0 economische_crisis -8571.75862068966 11355.804569 -0.7548 0.453351 0.226675 Multiple Linear Regression - Regression Statistics Multiple R 0.097800041724607 R-squared 0.00956484816133486 Adjusted R-squared -0.0072221883105068 F-TEST (value) 0.569775861116328 F-TEST (DF numerator) 1 F-TEST (DF denominator) 59 p-value 0.453350618851087 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 19179.0731879698 Sum Squared Residuals 21702374052.6207 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 123953.758620690 23814.2413793104 2 137507 123953.758620690 13553.2413793103 3 136919 123953.758620690 12965.2413793103 4 136151 123953.758620690 12197.2413793103 5 133001 123953.758620690 9047.24137931035 6 125554 123953.758620690 1600.24137931034 7 119647 123953.758620690 -4306.75862068965 8 114158 123953.758620690 -9795.75862068966 9 116193 123953.758620690 -7760.75862068966 10 152803 123953.758620690 28849.2413793103 11 161761 123953.758620690 37807.2413793103 12 160942 123953.758620690 36988.2413793103 13 149470 123953.758620690 25516.2413793103 14 139208 123953.758620690 15254.2413793103 15 134588 123953.758620690 10634.2413793103 16 130322 123953.758620690 6368.24137931035 17 126611 123953.758620690 2657.24137931035 18 122401 123953.758620690 -1552.75862068965 19 117352 123953.758620690 -6601.75862068966 20 112135 123953.758620690 -11818.7586206897 21 112879 123953.758620690 -11074.7586206897 22 148729 123953.758620690 24775.2413793103 23 157230 123953.758620690 33276.2413793103 24 157221 123953.758620690 33267.2413793103 25 146681 123953.758620690 22727.2413793103 26 136524 123953.758620690 12570.2413793103 27 132111 123953.758620690 8157.24137931035 28 125326 123953.758620690 1372.24137931034 29 122716 123953.758620690 -1237.75862068965 30 116615 123953.758620690 -7338.75862068966 31 113719 123953.758620690 -10234.7586206897 32 110737 123953.758620690 -13216.7586206897 33 112093 123953.758620690 -11860.7586206897 34 143565 123953.758620690 19611.2413793103 35 149946 123953.758620690 25992.2413793103 36 149147 123953.758620690 25193.2413793103 37 134339 123953.758620690 10385.2413793103 38 122683 123953.758620690 -1270.75862068965 39 115614 123953.758620690 -8339.75862068966 40 116566 123953.758620690 -7387.75862068966 41 111272 123953.758620690 -12681.7586206897 42 104609 123953.758620690 -19344.7586206897 43 101802 123953.758620690 -22151.7586206897 44 94542 123953.758620690 -29411.7586206897 45 93051 123953.758620690 -30902.7586206897 46 124129 123953.758620690 175.241379310345 47 130374 123953.758620690 6420.24137931035 48 123946 123953.758620690 -7.75862068965457 49 114971 123953.758620690 -8982.75862068966 50 105531 123953.758620690 -18422.7586206897 51 104919 123953.758620690 -19034.7586206897 52 104782 123953.758620690 -19171.7586206897 53 101281 123953.758620690 -22672.7586206897 54 94545 123953.758620690 -29408.7586206897 55 93248 123953.758620690 -30705.7586206897 56 84031 123953.758620690 -39922.7586206897 57 87486 123953.758620690 -36467.7586206897 58 115867 123953.758620690 -8086.75862068966 59 120327 115382 4945 60 117008 115382 1626 61 108811 115382 -6571 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.0460302105788377 0.0920604211576754 0.953969789421162 6 0.0463665911495413 0.0927331822990827 0.953633408850459 7 0.062496826663959 0.124993653327918 0.937503173336041 8 0.0913474977837089 0.182694995567418 0.908652502216291 9 0.0809252896251607 0.161850579250321 0.91907471037484 10 0.134576311093831 0.269152622187662 0.865423688906169 11 0.290448795338931 0.580897590677862 0.709551204661069 12 0.421120269315010 0.842240538630019 0.57887973068499 13 0.401494876386419 0.802989752772838 0.598505123613581 14 0.329150402570474 0.658300805140949 0.670849597429526 15 0.260577952099264 0.521155904198528 0.739422047900736 16 0.205447502968891 0.410895005937781 0.794552497031109 17 0.165759267122562 0.331518534245124 0.834240732877438 18 0.142476552452936 0.284953104905873 0.857523447547064 19 0.137936455813594 0.275872911627188 0.862063544186406 20 0.153980350894539 0.307960701789078 0.846019649105461 21 0.156742031219734 0.313484062439467 0.843257968780266 22 0.174093705050685 0.34818741010137 0.825906294949315 23 0.27975057194487 0.55950114388974 0.72024942805513 24 0.426292899458063 0.852585798916126 0.573707100541937 25 0.471055587655803 0.942111175311607 0.528944412344197 26 0.448841559040258 0.897683118080516 0.551158440959742 27 0.414436111822941 0.828872223645883 0.585563888177059 28 0.374676332105963 0.749352664211925 0.625323667894037 29 0.338500452072932 0.677000904145865 0.661499547927068 30 0.318696059762105 0.637392119524211 0.681303940237895 31 0.307271861259827 0.614543722519653 0.692728138740173 32 0.305376510742052 0.610753021484105 0.694623489257947 33 0.289023078548874 0.578046157097748 0.710976921451126 34 0.354021049906023 0.708042099812045 0.645978950093977 35 0.556858181504098 0.886283636991803 0.443141818495902 36 0.80503320051623 0.389933598967539 0.194966799483769 37 0.871394774715944 0.257210450568112 0.128605225284056 38 0.876264238772206 0.247471522455588 0.123735761227794 39 0.865925314215227 0.268149371569547 0.134074685784773 40 0.856760996549419 0.286478006901162 0.143239003450581 41 0.840214417593953 0.319571164812094 0.159785582406047 42 0.827995185143558 0.344009629712884 0.172004814856442 43 0.818428296755276 0.363143406489448 0.181571703244724 44 0.842295599383281 0.315408801233438 0.157704400616719 45 0.867080483707129 0.265839032585742 0.132919516292871 46 0.875426620574017 0.249146758851967 0.124573379425983 47 0.94371066492226 0.112578670155482 0.0562893350777409 48 0.974734592312654 0.0505308153746925 0.0252654076873463 49 0.980060195278243 0.039879609443514 0.019939804721757 50 0.970724799401986 0.0585504011960285 0.0292752005980142 51 0.957022447450988 0.0859551050980239 0.0429775525490119 52 0.939042276526528 0.121915446946944 0.0609577234734719 53 0.903965118931311 0.192069762137377 0.0960348810686886 54 0.840784515741535 0.318430968516930 0.159215484258465 55 0.745118715754952 0.509762568490096 0.254881284245048 56 0.7383431836128 0.5233136327744 0.2616568163872 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 1 0.0192307692307692 OK 10% type I error level 6 0.115384615384615 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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