voeding

*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: Sat, 20 Dec 2008 01:18:41 -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/Dec/20/t1229761215w5pbtvy40fiynul.htm/, Retrieved Sat, 20 Dec 2008 09:20:16 +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/2008/Dec/20/t1229761215w5pbtvy40fiynul.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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99.2 11554.5 93.6 13182.1 104.2 14800.1 95.3 12150.7 102.7 14478.2 103.1 13253.9 100 12036.8 107.2 12653.2 107 14035.4 119 14571.4 110.4 15400.9 101.7 14283.2 102.4 14485.3 98.8 14196.3 105.6 15559.1 104.4 13767.4 106.3 14634 107.2 14381.1 108.5 12509.9 106.9 12122.3 114.2 13122.3 125.9 13908.7 110.6 13456.5 110.5 12441.6 106.7 12953 104.7 13057.2 107.4 14350.1 109.8 13830.2 103.4 13755.5 114.8 13574.4 114.3 12802.6 109.6 11737.3 118.3 13850.2 127.3 15081.8 112.3 13653.3 114.9 14019.1 108.2 13962 105.4 13768.7 122.1 14747.1 113.5 13858.1 110 13188 125.3 13693.1 114.3 12970 115.6 11392.8 127.1 13985.2 123 14994.7 122.2 13584.7 126.4 14257.8 112.7 13553.4 105.8 14007.3 120.9 16535.8 116.3 14721.4 115.7 13664.6 127.9 16405.9 108.3 13829.4 121.1 13735.6 128.6 15870.5 123.1 15962.4 127.7 15744.1 126.6 16083.7 118.4 14863.9 110 15533.1 129.6 17473.1 115.8 15925.5 125.9 15573.7 128.4 17495 114 14155.8 125.6 14913.9 128.5 17250.4 136.6 15879.8 133.1 17647.8 124.6 17749.9

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 7 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Multiple Linear Regression - Estimated Regression Equation Voeding[t] = + 54.6615090162678 + 0.00424077980152477Invoer[t] -4.24170203087669M1[t] -10.8019810570597M2[t] -5.75580174684328M3[t] -5.02812449156892M4[t] -4.28035441481005M5[t] + 0.355880145944776M6[t] -0.106866011017156M7[t] + 5.56293735311408M8[t] + 3.6764790784733M9[t] + 7.26159013005267M10[t] + 1.47250192823431M11[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) 54.6615090162678 9.817276 5.5679 1e-06 0 Invoer 0.00424077980152477 0.000639 6.6417 0 0 M1 -4.24170203087669 3.827168 -1.1083 0.272224 0.136112 M2 -10.8019810570597 3.782844 -2.8555 0.005922 0.002961 M3 -5.75580174684328 3.776136 -1.5243 0.132787 0.066394 M4 -5.02812449156892 3.775473 -1.3318 0.188053 0.094026 M5 -4.28035441481005 3.762773 -1.1376 0.259906 0.129953 M6 0.355880145944776 3.743855 0.0951 0.924592 0.462296 M7 -0.106866011017156 3.907981 -0.0273 0.978276 0.489138 M8 5.56293735311408 3.965379 1.4029 0.165894 0.082947 M9 3.6764790784733 3.744641 0.9818 0.330209 0.165104 M10 7.26159013005267 3.747549 1.9377 0.057452 0.028726 M11 1.47250192823431 3.744497 0.3932 0.695556 0.347778 Multiple Linear Regression - Regression Statistics Multiple R 0.803984659839801 R-squared 0.64639133325772 Adjusted R-squared 0.57447092646268 F-TEST (value) 8.987592841345 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.78641912373934e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 6.48454499780201 Sum Squared Residuals 2480.91010588263 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.2 99.4198972021089 -0.219897202108887 2 93.6 99.7619113808878 -6.16191138088777 3 104.2 111.669672409971 -7.46967240997123 4 95.3 101.161827659086 -5.86182765908587 5 102.7 111.780012723894 -9.08001272389364 6 103.1 111.224260573642 -8.1242605736417 7 100 105.600061320244 -5.60006132024396 8 107.2 113.883881354035 -6.68388135403507 9 107 117.859028921062 -10.8590289210618 10 119 123.717197946258 -4.71719794625846 11 110.4 121.445836589805 -11.0458365898049 12 101.7 115.233415077406 -13.5334150774064 13 102.4 111.848774644418 -9.44877464441781 14 98.8 104.062910255594 -5.26291025559419 15 105.6 114.888424279329 -9.28842427932855 16 104.4 108.017896364211 -3.61789636421096 17 106.3 112.440726216971 -6.1407262169712 18 107.2 116.004467565920 -8.8044675659204 19 108.5 107.606374244345 0.893625755654673 20 106.9 111.632451357406 -4.73245135740556 21 114.2 113.986772884290 0.213227115710451 22 125.9 120.906833171788 4.993166828212 23 110.6 113.200064343720 -2.60006434372015 24 110.5 107.423594994918 3.07640500508165 25 106.7 105.350627754541 1.34937224545859 26 104.7 99.2322379836773 5.46776201632267 27 107.4 109.761321499285 -2.36132149928508 28 109.8 108.284217335747 1.51578266425327 29 103.4 108.715201161332 -5.31520116133168 30 114.8 112.583430500030 2.21656949996962 31 114.3 108.847650492252 5.45234950774837 32 109.6 109.999751133819 -0.399751133818532 33 118.3 117.073636501819 1.22636349818056 34 127.3 125.881691956957 1.41830804304328 35 112.3 114.034649808660 -1.73464980866022 36 114.9 114.113425131824 0.786574868176337 37 108.2 109.62957457428 -1.42957457427991 38 105.4 102.249552812462 3.1504471875378 39 122.1 111.444911080490 10.6550889195096 40 113.5 108.402535092209 5.09746490779074 41 110 106.308558623966 3.69144137603362 42 125.3 113.086811062471 12.2131889375286 43 114.3 109.557557031027 4.74244296897313 44 115.6 108.538802492193 7.06119750780676 45 127.1 117.646141775025 9.45385822497471 46 123 125.512320036244 -2.51232003624391 47 122.2 113.743732314276 8.45626768572438 48 126.4 115.125699270448 11.2743007295524 49 112.7 107.896791947377 4.80320805262312 50 105.8 103.261402873106 2.53859712689399 51 120.9 119.030393911478 1.86960608852223 52 116.3 112.063600294866 4.2363997051344 53 115.7 108.329714277373 7.37028572262692 54 127.9 124.591198508048 3.30880149195223 55 108.3 113.202083192457 -4.90208319245726 56 121.1 118.474101411205 2.62589858879451 57 128.6 125.64128393484 2.95871606516006 58 123.1 129.616122650179 -6.51612265017943 59 127.7 122.901272217688 4.79872778231179 60 126.6 122.868939110052 3.73106088994828 61 118.4 113.454333877275 4.94566612272491 62 110 109.731984694273 0.268015305727493 63 129.6 123.005276819447 6.59472318055306 64 115.8 117.169923253882 -1.36992325388158 65 125.9 116.425786996464 9.47421300353598 66 128.4 129.209831789888 -0.809831789888386 67 114 114.586273719675 -0.586273719674945 68 125.6 123.471012251342 2.12898774865788 69 128.5 131.493135982964 -2.99313598296397 70 136.6 129.265834238573 7.33416576142652 71 133.1 130.974444725851 2.12555527414909 72 124.6 129.934926415352 -5.33492641535229 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.183382695300946 0.366765390601892 0.816617304699054 17 0.120564857349307 0.241129714698614 0.879435142650693 18 0.0761674164981023 0.152334832996205 0.923832583501898 19 0.135097313196773 0.270194626393547 0.864902686803227 20 0.087258705172879 0.174517410345758 0.912741294827121 21 0.205036592255392 0.410073184510784 0.794963407744608 22 0.265744660258432 0.531489320516864 0.734255339741568 23 0.23136357042604 0.46272714085208 0.76863642957396 24 0.357847279931571 0.715694559863141 0.64215272006843 25 0.351628477503164 0.703256955006328 0.648371522496836 26 0.423179632136046 0.846359264272092 0.576820367863954 27 0.448154229458926 0.896308458917853 0.551845770541074 28 0.541127965640799 0.917744068718403 0.458872034359201 29 0.625523837521301 0.748952324957398 0.374476162478699 30 0.730966141864176 0.538067716271649 0.269033858135824 31 0.789762558502797 0.420474882994405 0.210237441497203 32 0.785294506206113 0.429410987587774 0.214705493793887 33 0.80482048017124 0.390359039657519 0.195179519828759 34 0.759326173463646 0.481347653072708 0.240673826536354 35 0.842795638354794 0.314408723290411 0.157204361645206 36 0.889353210147564 0.221293579704873 0.110646789852437 37 0.90200760795402 0.195984784091959 0.0979923920459795 38 0.881732903233273 0.236534193533455 0.118267096766727 39 0.947990418544388 0.104019162911224 0.0520095814556122 40 0.943068448053162 0.113863103893676 0.0569315519468382 41 0.963320823373025 0.0733583532539492 0.0366791766269746 42 0.979420564985026 0.0411588700299479 0.0205794350149739 43 0.977072091260282 0.0458558174794362 0.0229279087397181 44 0.9692140533809 0.0615718932382004 0.0307859466191002 45 0.971269436319485 0.0574611273610296 0.0287305636805148 46 0.963030692466932 0.0739386150661351 0.0369693075330676 47 0.95441046639488 0.0911790672102401 0.0455895336051201 48 0.97004025294986 0.0599194941002798 0.0299597470501399 49 0.953039721166177 0.0939205576676462 0.0469602788338231 50 0.918987115347263 0.162025769305474 0.0810128846527369 51 0.909682186231147 0.180635627537706 0.0903178137688528 52 0.863551815866534 0.272896368266932 0.136448184133466 53 0.852461978960427 0.295076042079146 0.147538021039573 54 0.762397840254382 0.475204319491236 0.237602159745618 55 0.677119813522234 0.645760372955532 0.322880186477766 56 0.532759270561666 0.934481458876668 0.467240729438334 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 2 0.0487804878048781 OK 10% type I error level 9 0.219512195121951 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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