paper

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Mon, 27 Dec 2010 13:30:00 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/27/t12934565364ps16qui90zidh9.htm/, Retrieved Mon, 27 Dec 2010 14:29:05 +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/2010/Dec/27/t12934565364ps16qui90zidh9.htm/}, year = {2010}, } @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 = {2010}, 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:

» Textbox « » Textfile « » CSV «

921365 0 987921 0 1132614 0 1332224 0 1418133 0 1411549 0 1695920 0 1636173 0 1539653 0 1395314 0 1127575 0 1036076 0 989236 0 1008380 0 1207763 0 1368839 0 1469798 0 1498721 0 1761769 0 1653214 0 1599104 0 1421179 0 1163995 0 1037735 0 1015407 0 1039210 0 1258049 0 1469445 0 1552346 0 1549144 0 1785895 0 1662335 0 1629440 0 1467430 0 1202209 0 1076982 0 1039367 1 1063449 1 1335135 1 1491602 1 1591972 1 1641248 1 1898849 1 1798580 1 1762444 1 1622044 1 1368955 1 1262973 1 1195650 1 1269530 1 1479279 1 1607819 1 1712466 1 1721766 1 1949843 1 1821326 1 1757802 1 1590367 1 1260647 1 1149235 1 1016367 1 1027885 1 1262159 1 1520854 1 1544144 1 1564709 1 1821776 1 1741365 1 1623386 1 1498658 1 1241822 1 1136029 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation bewegingen[t] = + 1048875 + 135260.000000000dummy[t] -86939.6666666658M1[t] -50442.4999999994M2[t] + 162661.5M3[t] + 348625.5M4[t] + 431638.166666666M5[t] + 448017.833333333M6[t] + 702503.666666666M7[t] + 602327.166666667M8[t] + 535466.5M9[t] + 382660.333333333M10[t] + 111028.833333333M11[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) 1048875 26330.439832 39.8351 0 0 dummy 135260.000000000 14605.500142 9.2609 0 0 M1 -86939.6666666658 35776.022785 -2.4301 0.018155 0.009078 M2 -50442.4999999994 35776.022785 -1.41 0.163804 0.081902 M3 162661.5 35776.022785 4.5467 2.8e-05 1.4e-05 M4 348625.5 35776.022785 9.7447 0 0 M5 431638.166666666 35776.022785 12.065 0 0 M6 448017.833333333 35776.022785 12.5229 0 0 M7 702503.666666666 35776.022785 19.6362 0 0 M8 602327.166666667 35776.022785 16.8361 0 0 M9 535466.5 35776.022785 14.9672 0 0 M10 382660.333333333 35776.022785 10.696 0 0 M11 111028.833333333 35776.022785 3.1034 0.002935 0.001468 Multiple Linear Regression - Regression Statistics Multiple R 0.977983324636905 R-squared 0.956451383267854 Adjusted R-squared 0.947594037491824 F-TEST (value) 107.983972563910 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 61965.8891569034 Sum Squared Residuals 226546513721.333 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 921365 961935.333333329 -40570.3333333288 2 987921 998432.5 -10511.4999999999 3 1132614 1211536.5 -78922.4999999997 4 1332224 1397500.5 -65276.500000001 5 1418133 1480513.16666667 -62380.1666666667 6 1411549 1496892.83333333 -85343.833333334 7 1695920 1751378.66666667 -55458.6666666657 8 1636173 1651202.16666667 -15029.1666666667 9 1539653 1584341.5 -44688.4999999986 10 1395314 1431535.33333333 -36221.3333333345 11 1127575 1159903.83333333 -32328.8333333337 12 1036076 1048875 -12799.0000000002 13 989236 961935.333333334 27300.6666666657 14 1008380 998432.5 9947.49999999987 15 1207763 1211536.5 -3773.50000000014 16 1368839 1397500.5 -28661.4999999998 17 1469798 1480513.16666667 -10715.1666666668 18 1498721 1496892.83333333 1828.16666666676 19 1761769 1751378.66666667 10390.3333333330 20 1653214 1651202.16666667 2011.83333333326 21 1599104 1584341.5 14762.4999999995 22 1421179 1431535.33333333 -10356.3333333331 23 1163995 1159903.83333333 4091.16666666665 24 1037735 1048875 -11140.0000000001 25 1015407 961935.333333334 53471.6666666658 26 1039210 998432.5 40777.4999999999 27 1258049 1211536.5 46512.4999999999 28 1469445 1397500.5 71944.5000000001 29 1552346 1480513.16666667 71832.8333333333 30 1549144 1496892.83333333 52251.1666666668 31 1785895 1751378.66666667 34516.333333333 32 1662335 1651202.16666667 11132.8333333333 33 1629440 1584341.5 45098.4999999995 34 1467430 1431535.33333333 35894.6666666668 35 1202209 1159903.83333333 42305.1666666667 36 1076982 1048875 28106.9999999999 37 1039367 1097195.33333333 -57828.3333333341 38 1063449 1133692.5 -70243.5 39 1335135 1346796.5 -11661.5 40 1491602 1532760.5 -41158.4999999997 41 1591972 1615773.16666667 -23801.1666666666 42 1641248 1632152.83333333 9095.16666666682 43 1898849 1886638.66666667 12210.3333333332 44 1798580 1786462.16666667 12117.8333333334 45 1762444 1719601.5 42842.4999999998 46 1622044 1566795.33333333 55248.666666667 47 1368955 1295163.83333333 73791.1666666668 48 1262973 1184135 78838 49 1195650 1097195.33333333 98454.666666666 50 1269530 1133692.5 135837.5 51 1479279 1346796.5 132482.5 52 1607819 1532760.5 75058.5000000003 53 1712466 1615773.16666667 96692.8333333334 54 1721766 1632152.83333333 89613.1666666668 55 1949843 1886638.66666667 63204.3333333332 56 1821326 1786462.16666667 34863.8333333334 57 1757802 1719601.5 38200.4999999998 58 1590367 1566795.33333333 23571.6666666669 59 1260647 1295163.83333333 -34516.8333333332 60 1149235 1184135 -34899.9999999999 61 1016367 1097195.33333333 -80828.3333333341 62 1027885 1133692.5 -105807.5 63 1262159 1346796.5 -84637.5 64 1520854 1532760.5 -11906.4999999997 65 1544144 1615773.16666667 -71629.1666666666 66 1564709 1632152.83333333 -67443.8333333332 67 1821776 1886638.66666667 -64862.6666666668 68 1741365 1786462.16666667 -45097.1666666666 69 1623386 1719601.5 -96215.5000000002 70 1498658 1566795.33333333 -68137.333333333 71 1241822 1295163.83333333 -53341.8333333332 72 1136029 1184135 -48105.9999999999 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.308035248325923 0.616070496651847 0.691964751674077 17 0.222970867679562 0.445941735359124 0.777029132320438 18 0.247065229862631 0.494130459725262 0.752934770137369 19 0.206899898109013 0.413799796218026 0.793100101890987 20 0.127126748417722 0.254253496835444 0.872873251582278 21 0.0995672601035075 0.199134520207015 0.900432739896493 22 0.0616459787860611 0.123291957572122 0.93835402121394 23 0.038870871191036 0.077741742382072 0.961129128808964 24 0.0211445597512705 0.042289119502541 0.97885544024873 25 0.0189675436571608 0.0379350873143216 0.98103245634284 26 0.0125073633016509 0.0250147266033017 0.98749263669835 27 0.0184042264746623 0.0368084529493247 0.981595773525338 28 0.0424809904793458 0.0849619809586917 0.957519009520654 29 0.0620406401777593 0.124081280355519 0.93795935982224 30 0.0671784588286266 0.134356917657253 0.932821541171373 31 0.0514540320395802 0.102908064079160 0.94854596796042 32 0.0328674284236503 0.0657348568473005 0.96713257157635 33 0.0249575116077606 0.0499150232155212 0.97504248839224 34 0.0184724688906282 0.0369449377812564 0.981527531109372 35 0.0132029456652867 0.0264058913305735 0.986797054334713 36 0.0082794507897605 0.016558901579521 0.99172054921024 37 0.00505677277710599 0.0101135455542120 0.994943227222894 38 0.00329926045567471 0.00659852091134941 0.996700739544325 39 0.00251900526593503 0.00503801053187007 0.997480994734065 40 0.00153644590319314 0.00307289180638628 0.998463554096807 41 0.00081814432814387 0.00163628865628774 0.999181855671856 42 0.000523603213826054 0.00104720642765211 0.999476396786174 43 0.000291204933400391 0.000582409866800782 0.9997087950666 44 0.000147033638940910 0.000294067277881820 0.99985296636106 45 0.000104515783404011 0.000209031566808022 0.999895484216596 46 8.97854078716556e-05 0.000179570815743311 0.999910214592128 47 0.000111961600214814 0.000223923200429628 0.999888038399785 48 0.000147656621391933 0.000295313242783866 0.999852343378608 49 0.000441257939867382 0.000882515879734764 0.999558742060133 50 0.00596682985901515 0.0119336597180303 0.994033170140985 51 0.0410767539290701 0.0821535078581403 0.95892324607093 52 0.0364467793678997 0.0728935587357993 0.9635532206321 53 0.0850917660318956 0.170183532063791 0.914908233968105 54 0.177115021056818 0.354230042113635 0.822884978943182 55 0.257343187602907 0.514686375205815 0.742656812397093 56 0.222200572000411 0.444401144000823 0.777799427999589 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.292682926829268 NOK 5% type I error level 22 0.536585365853659 NOK 10% type I error level 27 0.658536585365854 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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