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: Tue, 21 Dec 2010 10:08:50 +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/21/t1292926034d1ciq83aovfzcl8.htm/, Retrieved Tue, 21 Dec 2010 11:07:14 +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/21/t1292926034d1ciq83aovfzcl8.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:

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No (this computation is public)

User-defined keywords:

Dataseries X:

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695 0 638 0 762 0 635 0 721 0 854 0 418 0 367 0 824 0 687 0 601 0 676 0 740 0 691 0 683 0 594 0 729 0 731 0 386 0 331 0 707 0 715 0 657 0 653 0 642 0 643 0 718 0 654 0 632 0 731 0 392 1 344 1 792 1 852 1 649 1 629 1 685 1 617 1 715 1 715 1 629 1 916 1 531 1 357 1 917 1 828 1 708 1 858 1 775 1 785 1 1006 1 789 1 734 1 906 1 532 1 387 1 991 1 841 1 892 1 782 1 813 1 793 1 978 1 775 1 797 1 946 1 594 1 438 1 1022 1 868 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation MultipleLinearRegression[t] = + 655.02828685259 + 107.619521912351X[t] + 16.1619521912351M1[t] -14.3380478087649M2[t] + 101.495285524568M3[t] -15.1713811420983M4[t] -1.83804780876497M5[t] + 138.495285524568M6[t] -251.274634794157M7[t] -356.10796812749M8[t] + 148.725365205843M9[t] + 71.7253652058432M10[t] -18.2M11[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) 655.02828685259 33.839763 19.3568 0 0 X 107.619521912351 17.576628 6.1229 0 0 M1 16.1619521912351 43.572866 0.3709 0.712074 0.356037 M2 -14.3380478087649 43.572866 -0.3291 0.743317 0.371659 M3 101.495285524568 43.572866 2.3293 0.023409 0.011705 M4 -15.1713811420983 43.572866 -0.3482 0.728985 0.364492 M5 -1.83804780876497 43.572866 -0.0422 0.9665 0.48325 M6 138.495285524568 43.572866 3.1785 0.002393 0.001196 M7 -251.274634794157 43.553167 -5.7694 0 0 M8 -356.10796812749 43.553167 -8.1764 0 0 M9 148.725365205843 43.553167 3.4148 0.001182 0.000591 M10 71.7253652058432 43.553167 1.6468 0.105093 0.052546 M11 -18.2 45.473332 -0.4002 0.69048 0.34524 Multiple Linear Regression - Regression Statistics Multiple R 0.918933501019192 R-squared 0.844438779295389 Adjusted R-squared 0.811689048620734 F-TEST (value) 25.7846022516729 F-TEST (DF numerator) 12 F-TEST (DF denominator) 57 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 71.899651190645 Sum Squared Residuals 294664.910956175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 695 671.190239043824 23.8097609561755 2 638 640.690239043825 -2.69023904382466 3 762 756.523572377158 5.47642762284196 4 635 639.856905710491 -4.85690571049137 5 721 653.190239043825 67.8097609561753 6 854 793.523572377158 60.476427622842 7 418 403.753652058433 14.2463479415672 8 367 298.920318725100 68.0796812749004 9 824 803.753652058433 20.2463479415669 10 687 726.753652058433 -39.7536520584329 11 601 636.82828685259 -35.8282868525896 12 676 655.02828685259 20.9717131474104 13 740 671.190239043825 68.8097609561752 14 691 640.690239043825 50.3097609561753 15 683 756.523572377158 -73.523572377158 16 594 639.856905710491 -45.8569057104914 17 729 653.190239043825 75.8097609561753 18 731 793.523572377158 -62.523572377158 19 386 403.753652058433 -17.753652058433 20 331 298.920318725100 32.0796812749003 21 707 803.753652058433 -96.753652058433 22 715 726.753652058433 -11.7536520584329 23 657 636.82828685259 20.1717131474104 24 653 655.02828685259 -2.02828685258966 25 642 671.190239043825 -29.1902390438248 26 643 640.690239043825 2.30976095617528 27 718 756.523572377158 -38.5235723771581 28 654 639.856905710491 14.1430942895086 29 632 653.190239043825 -21.1902390438247 30 731 793.523572377158 -62.523572377158 31 392 511.373173970783 -119.373173970783 32 344 406.53984063745 -62.5398406374502 33 792 911.373173970783 -119.373173970783 34 852 834.373173970784 17.6268260292165 35 649 744.44780876494 -95.4478087649402 36 629 762.64780876494 -133.647808764940 37 685 778.809760956175 -93.8097609561753 38 617 748.309760956175 -131.309760956175 39 715 864.143094289509 -149.143094289509 40 715 747.476427622842 -32.476427622842 41 629 760.809760956175 -131.809760956175 42 916 901.143094289509 14.8569057104914 43 531 511.373173970784 19.6268260292164 44 357 406.53984063745 -49.5398406374502 45 917 911.373173970784 5.62682602921649 46 828 834.373173970783 -6.37317397078351 47 708 744.44780876494 -36.4478087649402 48 858 762.64780876494 95.3521912350598 49 775 778.809760956175 -3.80976095617534 50 785 748.309760956175 36.6902390438247 51 1006 864.143094289509 141.856905710491 52 789 747.476427622842 41.523572377158 53 734 760.809760956175 -26.8097609561753 54 906 901.143094289509 4.85690571049138 55 532 511.373173970784 20.6268260292164 56 387 406.53984063745 -19.5398406374502 57 991 911.373173970783 79.6268260292166 58 841 834.373173970784 6.62682602921647 59 892 744.44780876494 147.552191235060 60 782 762.64780876494 19.3521912350597 61 813 778.809760956175 34.1902390438246 62 793 748.309760956175 44.6902390438247 63 978 864.143094289509 113.856905710491 64 775 747.476427622842 27.5235723771580 65 797 760.809760956175 36.1902390438247 66 946 901.143094289509 44.8569057104914 67 594 511.373173970784 82.6268260292165 68 438 406.53984063745 31.4601593625498 69 1022 911.373173970783 110.626826029217 70 868 834.373173970784 33.6268260292164 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.206978812158947 0.413957624317895 0.793021187841053 17 0.102335649807685 0.204671299615371 0.897664350192315 18 0.194388059484226 0.388776118968453 0.805611940515773 19 0.115790269142844 0.231580538285688 0.884209730857156 20 0.0711060630490693 0.142212126098139 0.92889393695093 21 0.109325742828949 0.218651485657897 0.890674257171051 22 0.0654617442073544 0.130923488414709 0.934538255792646 23 0.0449134851368959 0.0898269702737918 0.955086514863104 24 0.0249308007066038 0.0498616014132076 0.975069199293396 25 0.0229971229930061 0.0459942459860123 0.977002877006994 26 0.0128423022233450 0.0256846044466901 0.987157697776655 27 0.00659128200060004 0.0131825640012001 0.9934087179994 28 0.003832851994908 0.007665703989816 0.996167148005092 29 0.00529155057240098 0.0105831011448020 0.9947084494276 30 0.00380717331910047 0.00761434663820093 0.9961928266809 31 0.00318528440994172 0.00637056881988344 0.996814715590058 32 0.00161990744076976 0.00323981488153951 0.99838009255923 33 0.00205914598263539 0.00411829196527078 0.997940854017365 34 0.00496400672750775 0.0099280134550155 0.995035993272492 35 0.00475793767172489 0.00951587534344978 0.995242062328275 36 0.0102289132943434 0.0204578265886868 0.989771086705657 37 0.0088584534161187 0.0177169068322374 0.991141546583881 38 0.0179442906093805 0.035888581218761 0.98205570939062 39 0.233218286061881 0.466436572123763 0.766781713938119 40 0.258504388570598 0.517008777141195 0.741495611429402 41 0.484612213435107 0.969224426870213 0.515387786564893 42 0.550171669679993 0.899656660640014 0.449828330320007 43 0.579179541835441 0.841640916329117 0.420820458164559 44 0.53497152580425 0.9300569483915 0.46502847419575 45 0.670497443669188 0.659005112661624 0.329502556330812 46 0.603386568348824 0.793226863302351 0.396613431651176 47 0.951941556170078 0.096116887659844 0.048058443829922 48 0.98305647899025 0.0338870420194986 0.0169435210097493 49 0.974053273675372 0.0518934526492561 0.0259467263246281 50 0.953999153856023 0.0920016922879542 0.0460008461439771 51 0.958695119593236 0.0826097608135284 0.0413048804067642 52 0.917386140959955 0.165227718080090 0.0826138590400452 53 0.90098147944786 0.19803704110428 0.09901852055214 54 0.827970918286829 0.344058163426342 0.172029081713171 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 7 0.179487179487179 NOK 5% type I error level 16 0.41025641025641 NOK 10% type I error level 21 0.538461538461538 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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