ws7

*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: Fri, 20 Nov 2009 09:13:00 -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/20/t1258733750h66tyttjh8ttoza.htm/, Retrieved Fri, 20 Nov 2009 17:16:02 +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/20/t1258733750h66tyttjh8ttoza.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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3016,70 2756,76 3052,40 2849,27 3099,60 2921,44 3103,30 2981,85 3119,80 3080,58 3093,70 3106,22 3164,90 3119,31 3311,50 3061,26 3410,60 3097,31 3392,60 3161,69 3338,20 3257,16 3285,10 3277,01 3294,80 3295,32 3611,20 3363,99 3611,30 3494,17 3521,00 3667,03 3519,30 3813,06 3438,30 3917,96 3534,90 3895,51 3705,80 3801,06 3807,60 3570,12 3663,00 3701,61 3604,50 3862,27 3563,80 3970,10 3511,40 4138,52 3546,50 4199,75 3525,40 4290,89 3529,90 4443,91 3591,60 4502,64 3668,30 4356,98 3728,80 4591,27 3853,60 4696,96 3897,70 4621,40 3640,70 4562,84 3495,50 4202,52 3495,10 4296,49 3268,00 4435,23 3479,10 4105,18 3417,80 4116,68 3521,30 3844,49 3487,10 3720,98 3529,90 3674,40 3544,30 3857,62 3710,80 3801,06 3641,90 3504,37 3447,10 3032,60 3386,80 3047,03 3438,50 2962,34 3364,30 2197,82 3462,70 2014,45 3291,90 1862,83 3550,00 1905,41 3611,00 1810,99 3708,60 1670,07 3771,10 1864,44 4042,70 2052,02 3988,40 2029,60 3851,20 2070,83 3876,70 2293,41

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 'Gwilym Jenkins' @ 72.249.127.135 R Framework error message The field 'Names of X columns' contains a hard return which cannot be interpreted. Please, resubmit your request without hard returns in the 'Names of X columns'. Multiple Linear Regression - Estimated Regression Equation Zichtrekeningen[t] = + 3463.58138507922 + 0.0139554412607161`Bel20 `[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) 3463.58138507922 125.525559 27.5926 0 0 `Bel20 ` 0.0139554412607161 0.035976 0.3879 0.699525 0.349762 Multiple Linear Regression - Regression Statistics Multiple R 0.0513127948145063 R-squared 0.00263300291167562 Adjusted R-squared -0.0148646637039089 F-TEST (value) 0.150477373327623 F-TEST (DF numerator) 1 F-TEST (DF denominator) 57 p-value 0.69952451079962 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 232.257386984912 Sum Squared Residuals 3074779.14711637 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3016.7 3502.0531873291 -485.353187329097 2 3052.4 3503.34420520013 -450.944205200134 3 3099.6 3504.35136939592 -404.751369395921 4 3103.3 3505.19441760248 -401.89441760248 5 3119.8 3506.57223831815 -386.772238318151 6 3093.7 3506.93005583208 -413.230055832076 7 3164.9 3507.11273255818 -342.212732558178 8 3311.5 3506.30261919299 -194.802619192994 9 3410.6 3506.80571285044 -96.2057128504428 10 3392.6 3507.70416415881 -115.104164158808 11 3338.2 3509.03649013597 -170.836490135968 12 3285.1 3509.31350564499 -224.213505644993 13 3294.8 3509.56902977448 -214.769029774477 14 3611.2 3510.52734992585 100.672650074149 15 3611.3 3512.34406926917 98.9559307308297 16 3521 3514.7564068455 6.24359315450208 17 3519.3 3516.7943199328 2.50568006719989 18 3438.3 3518.25824572105 -79.9582457210493 19 3534.9 3517.94494606475 16.9550539352537 20 3705.8 3516.62685463767 189.173145362328 21 3807.6 3513.40398503292 294.196014967078 22 3663 3515.23898600429 147.761013995707 23 3604.5 3517.48106719724 87.0189328027598 24 3563.8 3518.98588242838 44.814117571617 25 3511.4 3521.33625784551 -9.9362578455129 26 3546.5 3522.19074951391 24.3092504860934 27 3525.4 3523.46264843041 1.93735156959178 28 3529.9 3525.59811005212 4.301889947877 29 3591.6 3526.41771311737 65.182286882635 30 3668.3 3524.38496354333 143.915036456671 31 3728.8 3527.6545838763 201.145416123698 32 3853.6 3529.12953446315 324.470465536853 33 3897.7 3528.07506132149 369.624938678512 34 3640.7 3527.25783068126 113.442169318740 35 3495.5 3522.2294060862 -26.7294060861988 36 3495.1 3523.54079890147 -28.4407989014684 37 3268 3525.47697682198 -257.47697682198 38 3479.1 3520.87098343388 -41.7709834338808 39 3417.8 3521.03147100838 -103.231471008379 40 3521.3 3517.23293945162 4.06706054837558 41 3487.1 3515.50930290151 -28.4093029015136 42 3529.9 3514.85925844759 15.0407415524107 43 3544.3 3517.41617439538 26.8838256046224 44 3710.8 3516.62685463767 194.173145362328 45 3641.9 3512.48641477003 129.413585229970 46 3447.1 3505.90265624646 -58.8026562464619 47 3386.8 3506.10403326385 -119.304033263854 48 3438.5 3504.92214694348 -66.4221469434839 49 3364.3 3494.25293299084 -129.952932990841 50 3462.7 3491.69392372686 -28.9939237268638 51 3291.9 3489.57799972291 -197.677999722914 52 3550 3490.17222241180 59.8277775882049 53 3611 3488.85454964796 122.145450352042 54 3708.6 3486.8879488655 221.712051134502 55 3771.1 3489.60046798334 281.499532016656 56 4042.7 3492.21822965503 550.481770344971 57 3988.4 3491.90534866196 496.494651338037 58 3851.2 3492.48073150514 358.719268494857 59 3876.7 3495.58693362095 381.113066379047 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.000570093347498656 0.00114018669499731 0.999429906652501 6 0.000345826608979264 0.000691653217958528 0.99965417339102 7 0.000139386525312424 0.000278773050624848 0.999860613474688 8 0.0168838463376311 0.0337676926752622 0.983116153662369 9 0.0778007625766571 0.155601525153314 0.922199237423343 10 0.0696561321669759 0.139312264333952 0.930343867833024 11 0.0424692629274156 0.0849385258548313 0.957530737072584 12 0.0325549833484845 0.0651099666969691 0.967445016651515 13 0.0243456829596272 0.0486913659192544 0.975654317040373 14 0.0445176681084051 0.0890353362168102 0.955482331891595 15 0.0278087891753847 0.0556175783507693 0.972191210824615 16 0.0280143590594912 0.0560287181189824 0.97198564094051 17 0.0338041716800477 0.0676083433600954 0.966195828319952 18 0.06184654774001 0.12369309548002 0.93815345225999 19 0.0430446850857256 0.0860893701714511 0.956955314914274 20 0.0394579792469901 0.0789159584939802 0.96054202075301 21 0.127531128201865 0.25506225640373 0.872468871798135 22 0.100617825340446 0.201235650680892 0.899382174659554 23 0.0707986585750734 0.141597317150147 0.929201341424927 24 0.0579406567843821 0.115881313568764 0.942059343215618 25 0.0714359779286133 0.142871955857227 0.928564022071387 26 0.0684546761543602 0.136909352308720 0.93154532384564 27 0.0703179451090773 0.140635890218155 0.929682054890923 28 0.073439138661559 0.146878277323118 0.926560861338441 29 0.0595633383256227 0.119126676651245 0.940436661674377 30 0.0414357935382785 0.082871587076557 0.958564206461721 31 0.0313673744288466 0.0627347488576933 0.968632625571153 32 0.0376660822855208 0.0753321645710415 0.96233391771448 33 0.0763176100122152 0.152635220024430 0.923682389987785 34 0.0735491981341154 0.147098396268231 0.926450801865885 35 0.058123384477809 0.116246768955618 0.94187661552219 36 0.0479016533513463 0.0958033067026926 0.952098346648654 37 0.115333025887190 0.230666051774381 0.88466697411281 38 0.0845893414536008 0.169178682907202 0.915410658546399 39 0.0680498165315993 0.136099633063199 0.9319501834684 40 0.0456509850538975 0.0913019701077951 0.954349014946102 41 0.0301288511456433 0.0602577022912867 0.969871148854357 42 0.0197088253014893 0.0394176506029785 0.98029117469851 43 0.0118803605615817 0.0237607211231633 0.988119639438418 44 0.0145184599228852 0.0290369198457704 0.985481540077115 45 0.0175125112083173 0.0350250224166347 0.982487488791683 46 0.0119562906638478 0.0239125813276957 0.988043709336152 47 0.00799701543603963 0.0159940308720793 0.99200298456396 48 0.00976640655553283 0.0195328131110657 0.990233593444467 49 0.0564973428258527 0.112994685651705 0.943502657174147 50 0.133884739310644 0.267769478621288 0.866115260689356 51 0.535016336631806 0.929967326736388 0.464983663368194 52 0.733378333413874 0.533243333172252 0.266621666586126 53 0.802167257748281 0.395665484503438 0.197832742251719 54 0.732482378568662 0.535035242862675 0.267517621431338 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.06 NOK 5% type I error level 12 0.24 NOK 10% type I error level 26 0.52 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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