verbetering

*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: Mon, 01 Dec 2008 12:24:25 -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/01/t1228159534ik5d8jqfhx7yuoi.htm/, Retrieved Mon, 01 Dec 2008 19:25:44 +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/Dec/01/t1228159534ik5d8jqfhx7yuoi.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

6.06 0 5.983 0 6.11 0 6.143 0 6.093 0 6.148 0 6.464 0 6.532 0 6.321 0 6.23 0 6.176 0 6.338 0 6.462 0 6.401 0 6.46 0 6.519 0 6.542 0 6.637 0 7.114 0 7.579 0 7.408 0 8.243 0 8.243 0 8.434 0 8.576 0 8.58 0 8.645 0 8.66 0 8.72 0 8.787 0 9.162 0 9.144 0 8.806 0 8.778 0 8.66 0 8.826 0 8.609 1 8.628 1 8.619 1 8.775 1 8.84 1 8.745 1 9.092 1 8.934 1 8.749 1 8.298 1 8.067 1 7.969 1 7.999 0 7.865 0 7.746 0 7.633 0 7.458 0 7.391 0 7.856 0 7.72 0 7.297 0 7.123 0 7.004 0 7.151 0

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Textiel[t] = + 7.50579583333333 + 1.18902083333333dummy[t] -0.2024M1[t] -0.252199999999998M2[t] -0.227599999999999M3[t] -0.197600000000000M4[t] -0.212999999999998M5[t] -0.201999999999999M6[t] + 0.194000000000001M7[t] + 0.238200000000001M8[t] -0.0273999999999989M9[t] -0.00919999999999873M10[t] -0.113599999999999M11[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) 7.50579583333333 0.460791 16.2889 0 0 dummy 1.18902083333333 0.329136 3.6125 0.000735 0.000368 M1 -0.2024 0.644973 -0.3138 0.755053 0.377526 M2 -0.252199999999998 0.644973 -0.391 0.697546 0.348773 M3 -0.227599999999999 0.644973 -0.3529 0.725754 0.362877 M4 -0.197600000000000 0.644973 -0.3064 0.760676 0.380338 M5 -0.212999999999998 0.644973 -0.3302 0.742681 0.371341 M6 -0.201999999999999 0.644973 -0.3132 0.755521 0.37776 M7 0.194000000000001 0.644973 0.3008 0.764903 0.382451 M8 0.238200000000001 0.644973 0.3693 0.71355 0.356775 M9 -0.0273999999999989 0.644973 -0.0425 0.966294 0.483147 M10 -0.00919999999999873 0.644973 -0.0143 0.98868 0.49434 M11 -0.113599999999999 0.644973 -0.1761 0.860947 0.430474 Multiple Linear Regression - Regression Statistics Multiple R 0.485732366547749 R-squared 0.235935931912077 Adjusted R-squared 0.0408557443151606 F-TEST (value) 1.20943051582244 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.305008961144369 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.01979161822021 Sum Squared Residuals 48.8788223958333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6.06 7.30339583333334 -1.24339583333334 2 5.983 7.25359583333333 -1.27059583333333 3 6.11 7.27819583333333 -1.16819583333333 4 6.143 7.30819583333333 -1.16519583333333 5 6.093 7.29279583333333 -1.19979583333333 6 6.148 7.30379583333333 -1.15579583333333 7 6.464 7.69979583333333 -1.23579583333333 8 6.532 7.74399583333333 -1.21199583333333 9 6.321 7.47839583333333 -1.15739583333333 10 6.23 7.49659583333333 -1.26659583333333 11 6.176 7.39219583333333 -1.21619583333333 12 6.338 7.50579583333333 -1.16779583333333 13 6.462 7.30339583333333 -0.841395833333333 14 6.401 7.25359583333333 -0.852595833333335 15 6.46 7.27819583333333 -0.818195833333333 16 6.519 7.30819583333333 -0.789195833333333 17 6.542 7.29279583333333 -0.750795833333334 18 6.637 7.30379583333333 -0.666795833333334 19 7.114 7.69979583333333 -0.585795833333334 20 7.579 7.74399583333333 -0.164995833333333 21 7.408 7.47839583333333 -0.070395833333333 22 8.243 7.49659583333333 0.746404166666667 23 8.243 7.39219583333333 0.850804166666667 24 8.434 7.50579583333333 0.928204166666668 25 8.576 7.30339583333333 1.27260416666667 26 8.58 7.25359583333333 1.32640416666667 27 8.645 7.27819583333333 1.36680416666667 28 8.66 7.30819583333333 1.35180416666667 29 8.72 7.29279583333333 1.42720416666667 30 8.787 7.30379583333333 1.48320416666667 31 9.162 7.69979583333333 1.46220416666667 32 9.144 7.74399583333333 1.40000416666667 33 8.806 7.47839583333333 1.32760416666667 34 8.778 7.49659583333333 1.28140416666667 35 8.66 7.39219583333333 1.26780416666667 36 8.826 7.50579583333333 1.32020416666667 37 8.609 8.49241666666667 0.116583333333334 38 8.628 8.44261666666667 0.185383333333332 39 8.619 8.46721666666667 0.151783333333333 40 8.775 8.49721666666667 0.277783333333334 41 8.84 8.48181666666667 0.358183333333332 42 8.745 8.49281666666667 0.252183333333332 43 9.092 8.88881666666667 0.203183333333333 44 8.934 8.93301666666667 0.000983333333332614 45 8.749 8.66741666666667 0.0815833333333335 46 8.298 8.68561666666667 -0.387616666666667 47 8.067 8.58121666666667 -0.514216666666667 48 7.969 8.69481666666667 -0.725816666666665 49 7.999 7.30339583333333 0.695604166666667 50 7.865 7.25359583333333 0.611404166666666 51 7.746 7.27819583333333 0.467804166666667 52 7.633 7.30819583333333 0.324804166666667 53 7.458 7.29279583333333 0.165204166666666 54 7.391 7.30379583333333 0.0872041666666665 55 7.856 7.69979583333333 0.156204166666666 56 7.72 7.74399583333333 -0.0239958333333335 57 7.297 7.47839583333333 -0.181395833333334 58 7.123 7.49659583333333 -0.373595833333333 59 7.004 7.39219583333333 -0.388195833333334 60 7.151 7.50579583333333 -0.354795833333332 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.0906382840816514 0.181276568163303 0.909361715918349 17 0.0615670759541935 0.123134151908387 0.938432924045806 18 0.0495036831288467 0.0990073662576935 0.950496316871153 19 0.0592056307568999 0.118411261513800 0.9407943692431 20 0.123402791614211 0.246805583228422 0.87659720838579 21 0.188287355214924 0.376574710429847 0.811712644785076 22 0.518240318837301 0.963519362325398 0.481759681162699 23 0.728135966238649 0.543728067522703 0.271864033761351 24 0.840800731646575 0.318398536706850 0.159199268353425 25 0.9327342335691 0.134531532861802 0.0672657664309009 26 0.967988967335643 0.0640220653287144 0.0320110326643572 27 0.98209713217355 0.0358057356529009 0.0179028678264505 28 0.98810053336081 0.0237989332783819 0.0118994666391910 29 0.992078379532938 0.0158432409341246 0.00792162046706231 30 0.994823255650575 0.0103534886988497 0.00517674434942486 31 0.99628258268853 0.00743483462294111 0.00371741731147055 32 0.997319071282426 0.00536185743514751 0.00268092871757376 33 0.99797221557378 0.00405556885244061 0.00202778442622031 34 0.999132350817223 0.00173529836555352 0.00086764918277676 35 0.99985274474243 0.000294510515141988 0.000147255257570994 36 0.999999970505215 5.8989568999894e-08 2.9494784499947e-08 37 0.999999965643897 6.87122051117157e-08 3.43561025558579e-08 38 0.99999993131221 1.37375580659605e-07 6.86877903298024e-08 39 0.999999796466867 4.07066265096903e-07 2.03533132548451e-07 40 0.999998051033568 3.89793286463067e-06 1.94896643231533e-06 41 0.999987320972186 2.53580556276438e-05 1.26790278138219e-05 42 0.999917600655659 0.000164798688682476 8.2399344341238e-05 43 0.999317696019518 0.00136460796096411 0.000682303980482054 44 0.994795794255112 0.0104084114897765 0.00520420574488825 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.448275862068966 NOK 5% type I error level 18 0.620689655172414 NOK 10% type I error level 20 0.689655172413793 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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