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 11:24:48 -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/t1258741593cqf1yhpckcdkug4.htm/, Retrieved Fri, 20 Nov 2009 19:26:45 +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/t1258741593cqf1yhpckcdkug4.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 3 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] = + 3401.75544822108 + 0.0120969897239121`Bel20 `[t] -151.418552454816M1[t] -11.3744834589064M2[t] -52.9255465216977M3[t] + 2.59538220831397M4[t] + 23.0483785201583M5[t] + 45.5385969317301M6[t] + 105.120861282040M7[t] + 280.997123781110M8[t] + 306.783504033436M9[t] + 157.172944092784M10[t] + 98.271599657758M11[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) 3401.75544822108 161.661588 21.0424 0 0 `Bel20 ` 0.0120969897239121 0.033371 0.3625 0.718639 0.35932 M1 -151.418552454816 144.069161 -1.051 0.298743 0.149371 M2 -11.3744834589064 144.199956 -0.0789 0.93747 0.468735 M3 -52.9255465216977 144.127776 -0.3672 0.715144 0.357572 M4 2.59538220831397 144.061512 0.018 0.985704 0.492852 M5 23.0483785201583 144.028519 0.16 0.873561 0.43678 M6 45.5385969317301 144.110306 0.316 0.753433 0.376717 M7 105.120861282040 143.904262 0.7305 0.468794 0.234397 M8 280.997123781110 143.884393 1.9529 0.056927 0.028463 M9 306.783504033436 144.069505 2.1294 0.038604 0.019302 M10 157.172944092784 144.201474 1.09 0.28141 0.140705 M11 98.271599657758 144.138421 0.6818 0.498793 0.249396 Multiple Linear Regression - Regression Statistics Multiple R 0.560631926842463 R-squared 0.314308157395093 Adjusted R-squared 0.135432024541639 F-TEST (value) 1.75712741762252 F-TEST (DF numerator) 12 F-TEST (DF denominator) 46 p-value 0.0851778774134877 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 214.370510647222 Sum Squared Residuals 2113916.92841693 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3016.7 3283.68539315755 -266.985393157546 2 3052.4 3424.84855467282 -372.448554672823 3 3099.6 3384.17053135841 -284.570531358407 4 3103.3 3440.42223923764 -337.122239237640 5 3119.8 3462.06957134493 -342.269571344926 6 3093.7 3484.86995657302 -391.169956573019 7 3164.9 3544.61057051881 -379.710570518815 8 3311.5 3719.78460276441 -408.284602764412 9 3410.6 3746.00707949628 -335.407079496285 10 3392.6 3597.17532375406 -204.575323754059 11 3338.2 3539.42887892797 -201.228878927975 12 3285.1 3441.39740451624 -156.297404516236 13 3294.8 3290.20034794327 4.59965205673503 14 3611.2 3431.07511722352 180.124882776484 15 3611.3 3391.09884028298 220.201159717017 16 3521 3448.71085465667 72.2891453433299 17 3519.3 3470.9303743779 48.3696256221029 18 3438.3 3494.68956701151 -56.3895670115073 19 3534.9 3554.00025394252 -19.1002539425153 20 3705.8 3728.73395576216 -22.9339557621616 21 3807.6 3751.72665720765 55.8733427923526 22 3663 3603.70673044579 59.293269554207 23 3604.5 3546.74888837981 57.7511116201892 24 3563.8 3449.78170712398 114.018292876018 25 3511.4 3300.40052967847 210.999470321532 26 3546.5 3441.18529735517 105.314702644828 27 3525.4 3400.73675393582 124.663246064182 28 3529.9 3458.10876403338 71.7912359666171 29 3591.6 3479.27221655171 112.327783448287 30 3668.3 3500.0003874401 168.299612559901 31 3728.8 3562.41685551282 166.383144487176 32 3853.6 3739.57164885581 114.028351144185 33 3897.7 3764.4439805646 133.256019435398 34 3640.7 3614.12502090572 26.5749790942819 35 3495.5 3550.86488913337 -55.364889133372 36 3495.1 3453.73004359997 41.36995640003 37 3268 3303.98982749945 -35.9898274994498 38 3479.1 3440.04128503698 39.058714963018 39 3417.8 3398.62933735602 19.1706626439845 40 3521.3 3450.85758645308 70.4424135469246 41 3487.1 3469.81648356412 17.2835164358804 42 3529.9 3491.74322419435 38.1567758056487 43 3544.3 3553.54189900188 -9.2418990018762 44 3710.8 3728.73395576216 -17.9339557621616 45 3641.9 3750.9312801333 -109.0312801333 46 3447.1 3595.6137233506 -148.513723350599 47 3386.8 3536.88693847729 -150.086938477288 48 3438.5 3437.59084475981 0.909155240187502 49 3364.3 3276.92390172127 87.3760982787286 50 3462.7 3414.74974571151 47.9502542884928 51 3291.9 3371.36453706678 -79.4645370667762 52 3550 3427.40055561923 122.599444380768 53 3611 3446.71135416134 164.288645838655 54 3708.6 3467.49686478102 241.103135218977 55 3771.1 3529.43042102397 241.669578976031 56 4042.7 3707.57583685545 335.124163144550 57 3988.4 3733.09100259817 255.308997401834 58 3851.2 3583.97920154383 267.220798456168 59 3876.7 3527.77040508155 348.929594918446 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.394914189447886 0.789828378895772 0.605085810552114 17 0.315694571237868 0.631389142475737 0.684305428762132 18 0.354348853230789 0.708697706461578 0.645651146769211 19 0.280402483836056 0.560804967672111 0.719597516163945 20 0.198444691177214 0.396889382354428 0.801555308822786 21 0.153626273295907 0.307252546591814 0.846373726704093 22 0.0964382856308519 0.192876571261704 0.903561714369148 23 0.0647887910042704 0.129577582008541 0.93521120899573 24 0.0508285286549909 0.101657057309982 0.94917147134501 25 0.125998888652215 0.25199777730443 0.874001111347785 26 0.269503909424671 0.539007818849343 0.730496090575329 27 0.419776189907538 0.839552379815076 0.580223810092462 28 0.416804905987843 0.833609811975687 0.583195094012157 29 0.361124770109245 0.72224954021849 0.638875229890755 30 0.307171201299231 0.614342402598462 0.692828798700769 31 0.255819155554662 0.511638311109324 0.744180844445338 32 0.202500580648401 0.405001161296802 0.797499419351599 33 0.208252898109441 0.416505796218881 0.79174710189056 34 0.236153742605195 0.47230748521039 0.763846257394805 35 0.194700395386427 0.389400790772854 0.805299604613573 36 0.164931974269464 0.329863948538928 0.835068025730536 37 0.188178746118705 0.37635749223741 0.811821253881295 38 0.163920027001946 0.327840054003893 0.836079972998054 39 0.284812093883867 0.569624187767734 0.715187906116133 40 0.303385741692022 0.606771483384045 0.696614258307978 41 0.277919478834613 0.555838957669226 0.722080521165387 42 0.279830382150297 0.559660764300595 0.720169617849703 43 0.324463160660145 0.64892632132029 0.675536839339855 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 = 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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