Experiment 2 SWS multiple regression

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Mon, 20 Dec 2010 18:30:47 +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/20/t12928698293ztmbmcurhyb3n2.htm/, Retrieved Mon, 20 Dec 2010 19:30:37 +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/20/t12928698293ztmbmcurhyb3n2.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 «

-999.0 38.6 6654.000 5712.000 645.0 3 5 3 6.3 4.5 1.000 6.600 42.0 3 1 3 -999.0 14.0 3.385 44.500 60.0 1 1 1 -999.0 -999.0 0.920 5.700 25.0 5 2 3 2.1 69.0 2547.000 4603.000 624.0 3 5 4 9.1 27.0 10.550 179.500 180.0 4 4 4 15.8 19.0 0.023 0.300 35.0 1 1 1 5.2 30.4 160.000 169.000 392.0 4 5 4 10.9 28.0 3.300 25.600 63.0 1 2 1 8.3 50.0 52.160 440.000 230.0 1 1 1 11.0 7.0 0.425 6.400 112.0 5 4 4 3.2 30.0 465.000 423.000 281.0 5 5 5 7.6 -999.0 0.550 2.400 -999.0 2 1 2 -999.0 40.0 187.100 419.000 365.0 5 5 5 6.3 0.075 1.200 42.0 1 1 1 8.6 50.0 3.000 25.000 28.0 2 2 2 6.6 6.0 0.785 3.500 42.0 2 2 2 9.5 10.4 0.200 5.000 120.0 2 2 2 4.8 34.0 1.410 17.500 -999.0 1 2 1 12.0 7.0 60.000 81.000 -999.0 1 1 1 -999.0 28.0 529.000 680.000 400.0 5 5 5 3.3 20.0 27.660 115.000 148.0 5 5 5 11.0 3.9 0.120 1.000 16.0 3 1 2 -999.0 39.3 207.000 406.000 252.0 1 4 1 4.7 41.0 85.000 325.000 310.0 1 3 1 -999.0 16.2 36.330 119.500 63.0 1 1 1 10.4 9.0 0.101 4.000 28.0 5 1 3 7.4 7.6 1.040 5.500 68.0 5 3 4 2.1 46.0 etc...

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 'RServer@AstonUniversity' @ vre.aston.ac.uk 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 SWS[t] = -59.3847183091035 + 0.669867333323824L[t] -0.15337634089585wb[t] + 0.112721445746871wbr[t] -0.677139476203819tg[t] + 1.9389991901035P[t] -2.07827048307807S[t] -0.0452853646947986`D `[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) -59.3847183091035 76.261547 -0.7787 0.439557 0.219778 L 0.669867333323824 0.200577 3.3397 0.001526 0.000763 wb -0.15337634089585 0.092404 -1.6598 0.102744 0.051372 wbr 0.112721445746871 0.097336 1.1581 0.251931 0.125966 tg -0.677139476203819 0.26466 -2.5585 0.013349 0.006674 P 1.9389991901035 34.87417 0.0556 0.955866 0.477933 S -2.07827048307807 39.641694 -0.0524 0.958382 0.479191 `D ` -0.0452853646947986 0.092015 -0.4922 0.624607 0.312304 Multiple Linear Regression - Regression Statistics Multiple R 0.535795288345291 R-squared 0.287076591013013 Adjusted R-squared 0.194660593551737 F-TEST (value) 3.10635170207737 F-TEST (DF numerator) 7 F-TEST (DF denominator) 54 p-value 0.00792978853301995 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 271.762779444885 Sum Squared Residuals 3988170.44774689 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -851.69428654829 -147.305713451711 2 6.3 -80.616717115525 86.916717115525 3 -999 -86.3225754506653 -912.677424549335 4 -999 -739.606666307289 -259.393333692711 5 2.1 -312.247127253683 314.347127253683 6 9.1 -145.306253541613 154.406253541613 7 15.8 -70.5113885228704 86.3113885228704 8 5.2 -312.766213373827 317.966213373827 9 10.9 -83.1715200314608 94.0715200314608 10 8.3 -140.220661639964 148.520661639964 11 11 -128.678263443339 139.678263443339 12 3.2 -254.126501376652 257.326501376652 13 7.6 -50.2245159219495 57.8245159219495 14 -999 -262.135144692566 -736.864855307434 15 6.3 -55.9900940523643 62.2900940523643 16 50 -59.9850292959584 109.985029295958 17 6 -56.7244214271685 62.7244214271685 18 10.4 -48.3412443461853 58.7412443461853 19 34 -173.153851591331 207.153851591331 20 7 -99.8012176624372 106.801217662437 21 28 231.536271959385 -203.536271959385 22 20 -46.391885959387 66.391885959387 23 3.9 -16.6630483126109 20.5630483126109 24 39.3 50.200575200491 -10.900575200491 25 41 30.9520093549327 10.0479906450673 26 16.2 -47.5628383064545 63.7628383064545 27 9 -64.79098793 73.79098793 28 7.6 -57.8434488554666 65.4434488554666 29 46 268.187090320988 -222.187090320987 30 22.4 39.2177426382429 -16.8177426382429 31 16.3 -41.8068307418467 58.1068307418467 32 2.6 -65.6107195377658 68.2107195377658 33 24 -54.8729429274673 78.8729429274673 34 100 -191.40083837081 291.40083837081 35 -999 -58.2554274535379 -940.744572546462 36 -999 -61.516407239374 -937.483592760626 37 3.2 -64.7824065302547 67.9824065302547 38 2 -63.6508436939277 65.6508436939277 39 5 -60.0006884016522 65.0006884016522 40 6.5 -1.42354454979917 7.92354454979917 41 23.6 77.7547527222564 -54.1547527222564 42 12 -47.7451880537365 59.7451880537365 43 20.2 -54.9662173185016 75.1662173185016 44 13 -61.9979345366113 74.9979345366113 45 27 50.9797512767833 -23.9797512767833 46 18 -14.9135133982689 32.9135133982689 47 13.7 -57.536075068997 71.236075068997 48 4.7 -63.7837625292743 68.4837625292743 49 9.8 -59.6132903874054 69.4132903874054 50 29 -63.7496172873854 92.7496172873854 51 7 -37.2612413344448 44.2612413344448 52 6 6.02007405756056 -0.0200740575605638 53 17 -51.8308925827682 68.8308925827682 54 20 9.13102282558435 10.8689771744157 55 12.7 -52.2188111788145 64.9188111788145 56 3.5 -174.775455644353 178.275455644353 57 4.5 -13.2289426554167 17.7289426554167 58 7.5 -45.0330897900245 52.5330897900245 59 2.3 -57.2625355064215 59.5625355064215 60 13 -47.6803747091688 60.6803747091688 61 3 -57.7756986638945 60.7756986638945 62 24 -10.7100973052437 34.7100973052437 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 11 0.988582482713334 0.0228350345733326 0.0114175172866663 12 0.977278081249274 0.0454438375014513 0.0227219187507256 13 0.990332149094973 0.0193357018100535 0.00966785090502674 14 0.999781392257102 0.000437215485795718 0.000218607742897859 15 0.999482006960507 0.00103598607898637 0.000517993039493184 16 0.998831722731426 0.00233655453714864 0.00116827726857432 17 0.997494692421333 0.00501061515733394 0.00250530757866697 18 0.994973873191816 0.0100522536163682 0.0050261268081841 19 0.991540892526383 0.016918214947234 0.00845910747361701 20 0.98966950391883 0.0206609921623403 0.0103304960811702 21 0.986444562152017 0.0271108756959652 0.0135554378479826 22 0.976660002161105 0.0466799956777896 0.0233399978388948 23 0.963481542562596 0.0730369148748081 0.036518457437404 24 0.943601189448303 0.112797621103394 0.0563988105516969 25 0.915005193324981 0.169989613350037 0.0849948066750187 26 0.879668573470983 0.240662853058033 0.120331426529017 27 0.835691702956024 0.328616594087952 0.164308297043976 28 0.779120820253572 0.441758359492856 0.220879179746428 29 0.732707909345737 0.534584181308526 0.267292090654263 30 0.659389581843036 0.681220836313927 0.340610418156964 31 0.583476968238078 0.833046063523844 0.416523031761922 32 0.509582393813886 0.980835212372227 0.490417606186114 33 0.432047209445807 0.864094418891615 0.567952790554193 34 0.386818762117626 0.773637524235251 0.613181237882374 35 0.982106069768338 0.0357878604633236 0.0178939302316618 36 1 1.32472315484048e-28 6.62361577420241e-29 37 1 7.84989336333282e-27 3.92494668166641e-27 38 1 4.54644866238322e-25 2.27322433119161e-25 39 1 2.43642976764696e-23 1.21821488382348e-23 40 1 1.17318784059787e-21 5.86593920298936e-22 41 1 8.7270408417218e-21 4.3635204208609e-21 42 1 4.68262465519563e-19 2.34131232759782e-19 43 1 2.48924425126588e-17 1.24462212563294e-17 44 1 8.73444492251409e-16 4.36722246125704e-16 45 0.999999999999994 1.219172961133e-14 6.09586480566502e-15 46 0.99999999999975 4.99725967885789e-13 2.49862983942895e-13 47 0.99999999999048 1.90392492282198e-11 9.51962461410988e-12 48 0.999999999497508 1.00498452117843e-09 5.02492260589217e-10 49 0.999999975570896 4.88582070777214e-08 2.44291035388607e-08 50 0.999999188354167 1.62329166666965e-06 8.11645833334826e-07 51 0.999965274773158 6.94504536832837e-05 3.47252268416419e-05 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.48780487804878 NOK 5% type I error level 29 0.707317073170732 NOK 10% type I error level 30 0.73170731707317 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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