*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: Wed, 18 Nov 2009 09:45:27 -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/18/t1258562770l8elc9xg3roa6r8.htm/, Retrieved Wed, 18 Nov 2009 17:46:23 +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/18/t1258562770l8elc9xg3roa6r8.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:

WS7dummies

Dataseries X:

» Textbox « » Textfile « » CSV «

7291 4071 6820 4351 8031 4871 7862 4649 7357 4922 7213 4879 7079 4853 7012 4545 7319 4733 8148 5191 7599 4983 6908 4593 7878 4656 7407 4513 7911 4857 7323 4681 7179 4897 6758 4547 6934 4692 6696 4390 7688 5341 8296 5415 7697 4890 7907 5120 7592 4422 7710 4797 9011 5689 8225 5171 7733 4265 8062 5215 7859 4874 8221 4590 8330 4994 8868 4988 9053 5110 8811 5141 8120 4395 7953 4523 8878 5306 8601 5365 8361 5496 9116 5647 9310 5443 9891 5546 10147 5912 10317 5665 10682 5963 10276 5861 10614 5366 9413 5619 11068 6721 9772 6054 10350 6619 10541 6856 10049 6193 10714 6317 10759 6618 11684 6585 11462 6852 10485 6586 11056 6154 10184 6193 11082 7606 10554 6588 11315 7143 10847 7629 11104 7041 11026 7146 11073 7200 12073 7739 12328 7953 11172 7082

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation UitvEU[t] = + 451.553239016502 + 1.53708753063726`Uitvniet-EU`[t] + 861.294762576599M1[t] + 111.867166150947M2[t] -100.539563822509M3[t] -56.6601466758552M4[t] -277.315313434435M5[t] -603.577356158089M6[t] -207.628058011640M7[t] + 140.512474024717M8[t] -146.815220869077M9[t] + 330.415827205881M10[t] + 193.210709681371M11[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) 451.553239016502 460.575059 0.9804 0.330886 0.165443 `Uitvniet-EU` 1.53708753063726 0.070214 21.8915 0 0 M1 861.294762576599 323.025425 2.6663 0.00988 0.00494 M2 111.867166150947 321.102213 0.3484 0.728791 0.364396 M3 -100.539563822509 317.06776 -0.3171 0.752293 0.376147 M4 -56.6601466758552 317.730205 -0.1783 0.859076 0.429538 M5 -277.315313434435 317.20568 -0.8742 0.38553 0.192765 M6 -603.577356158089 317.004525 -1.904 0.06179 0.030895 M7 -207.628058011640 317.329276 -0.6543 0.515462 0.257731 M8 140.512474024717 317.709339 0.4423 0.659913 0.329956 M9 -146.815220869077 317.008872 -0.4631 0.644977 0.322489 M10 330.415827205881 317.282585 1.0414 0.301942 0.150971 M11 193.210709681371 317.375676 0.6088 0.54501 0.272505 Multiple Linear Regression - Regression Statistics Multiple R 0.948662711737977 R-squared 0.899960940642052 Adjusted R-squared 0.879614013315012 F-TEST (value) 44.2308033137781 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 549.011037290824 Sum Squared Residuals 17783374.0249617 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7291 7570.3313388174 -279.331338817402 2 6820 7251.28825097017 -431.288250970168 3 8031 7838.1670369281 192.832963071904 4 7862 7540.81302227328 321.186977726722 5 7357 7739.78275137867 -382.782751378671 6 7213 7347.42594483761 -134.425944837615 7 7079 7703.4109671875 -624.410967187495 8 7012 7578.12853978757 -566.128539787574 9 7319 7579.77330065359 -260.773300653586 10 8148 8760.99043776041 -612.990437760411 11 7599 8304.07111386335 -705.07111386335 12 6908 7511.39626723345 -603.396267233447 13 7878 8469.52754424019 -591.527544240193 14 7407 7500.29643093341 -93.2964309334127 15 7911 7816.64781149918 94.352188500825 16 7323 7589.99982325367 -266.999823253671 17 7179 7701.35556311274 -522.35556311274 18 6758 6837.11288466604 -79.1128846660435 19 6934 7455.9398747549 -521.939874754895 20 6696 7339.8799725388 -643.879972538798 21 7688 8514.32251928104 -826.322519281042 22 8296 9105.29804462316 -809.298044623157 23 7697 8161.12197351408 -464.121973514084 24 7907 8321.44139587928 -414.441395879284 25 7592 8109.84906207107 -517.849062071074 26 7710 7936.8292896344 -226.829289634395 27 9011 9095.50463698938 -84.504636989378 28 8225 8343.17271326593 -118.172713265929 29 7733 6729.91624374999 1003.08375625001 30 8062 7863.88735513174 198.112644868265 31 7859 7735.68980533088 123.310194669123 32 8221 7647.29747866625 573.702521333749 33 8330 7980.95314614991 349.046853850088 34 8868 8448.96166904105 419.038330958954 35 9053 8499.28123025428 553.718769745718 36 8811 8353.72023402267 457.279765977333 37 8120 8068.34769874387 51.6523012561326 38 7953 7515.66730623978 437.332693760215 39 8878 8506.8001127553 371.199887244694 40 8601 8641.36769420956 -40.3676942095584 41 8361 8622.07099396446 -261.070993964460 42 9116 8527.90916836703 588.090831632967 43 9310 8610.29261026348 699.70738973652 44 9891 9116.75315795547 774.246842044525 45 10147 9391.99949927492 755.00050072508 46 10317 9489.56992728247 827.430072717527 47 10682 9810.41689388787 871.583106112132 48 10276 9460.4232560815 815.576743918504 49 10614 9560.85969099265 1053.14030900735 50 9413 9200.31523981823 212.684760181774 51 11068 10681.7789686070 386.221031392967 52 9772 9700.42100281863 71.5789971813673 53 10350 10348.2202908701 1.77970912989292 54 10541 10386.2479929075 154.752007092516 55 10049 9763.10825824143 285.891741758573 56 10714 10301.8476440768 412.152355923195 57 10759 10477.1832959048 281.816704095173 58 11684 10903.6904554688 780.309544531245 59 11462 11176.8877086244 285.112291375605 60 10485 10574.8117157935 -89.811715793512 61 11056 10772.0846651348 283.915334865186 62 10184 10082.603482404 101.396517595985 63 11082 12042.101433221 -960.10143322101 64 10554 10521.2257441789 32.7742558210685 65 11315 11153.6541569240 161.345843075967 66 10847 11574.4166540901 -727.416654090089 67 11104 11066.5584842218 37.4415157781736 68 11026 11576.0932069751 -550.093206975096 69 11073 11371.7682387357 -298.768238735714 70 12073 12677.4894658242 -604.489465824157 71 12328 12869.2210798560 -541.221079856021 72 11172 11337.2071309896 -165.207130989595 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.152542003734813 0.305084007469627 0.847457996265187 17 0.0712121257849319 0.142424251569864 0.928787874215068 18 0.0278196024205625 0.0556392048411251 0.972180397579437 19 0.0114777862824931 0.0229555725649863 0.988522213717507 20 0.0056563236276161 0.0113126472552322 0.994343676372384 21 0.00463804793125554 0.00927609586251109 0.995361952068744 22 0.00307319604509236 0.00614639209018472 0.996926803954908 23 0.00238595926092484 0.00477191852184968 0.997614040739075 24 0.00441551297752071 0.00883102595504142 0.99558448702248 25 0.00460048376745545 0.0092009675349109 0.995399516232545 26 0.00336687409380543 0.00673374818761086 0.996633125906195 27 0.00157040897334304 0.00314081794668608 0.998429591026657 28 0.000755960546308565 0.00151192109261713 0.999244039453691 29 0.0841499452162938 0.168299890432588 0.915850054783706 30 0.107769994019761 0.215539988039523 0.892230005980239 31 0.200406853035100 0.400813706070199 0.7995931469649 32 0.470678998667246 0.941357997334492 0.529321001332754 33 0.568826383888752 0.862347232222496 0.431173616111248 34 0.688664247070665 0.62267150585867 0.311335752929335 35 0.809439761472041 0.381120477055917 0.190560238527959 36 0.853863480003057 0.292273039993887 0.146136519996943 37 0.955287824686031 0.0894243506279377 0.0447121753139688 38 0.957402784809873 0.085194430380253 0.0425972151901265 39 0.947479003512045 0.105041992975911 0.0525209964879554 40 0.95335760535678 0.0932847892864389 0.0466423946432195 41 0.997302589807113 0.00539482038577444 0.00269741019288722 42 0.99709134615263 0.00581730769474089 0.00290865384737044 43 0.997946687539392 0.00410662492121652 0.00205331246060826 44 0.997076485946172 0.00584702810765557 0.00292351405382778 45 0.99527356758924 0.00945286482152081 0.00472643241076040 46 0.996585431650325 0.00682913669935041 0.00341456834967520 47 0.994615822190143 0.0107683556197137 0.00538417780985686 48 0.989728289174672 0.0205434216506558 0.0102717108253279 49 0.982657915666609 0.0346841686667825 0.0173420843333912 50 0.974775491684425 0.0504490166311509 0.0252245083155755 51 0.979317736621805 0.0413645267563908 0.0206822633781954 52 0.970753469034655 0.0584930619306898 0.0292465309653449 53 0.980999590724845 0.0380008185503097 0.0190004092751549 54 0.960461140156467 0.0790777196870661 0.0395388598435331 55 0.967170069719773 0.065659860560454 0.032829930280227 56 0.916424675265494 0.167150649469013 0.0835753247345064 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 14 0.341463414634146 NOK 5% type I error level 21 0.51219512195122 NOK 10% type I error level 29 0.707317073170732 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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