*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: Tue, 21 Dec 2010 12:33:14 +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/t1292934809lnpmi29fo0gfo5v.htm/, Retrieved Tue, 21 Dec 2010 13:33:33 +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/t1292934809lnpmi29fo0gfo5v.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:

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-999,000 6654,000 3,000 6,300 1,000 3,000 -999,000 3,385 1,000 -999,000 0,920 3,000 2,100 2547,000 4,000 9,100 10,550 4,000 15,800 0,023 1,000 5,200 160,000 4,000 10,900 3,300 1,000 8,300 52,160 1,000 11,000 0,425 4,000 3,200 465,000 5,000 7,600 0,550 2,000 -999,000 187,100 5,000 6,300 0,075 1,000 8,600 3,000 2,000 6,600 0,785 2,000 9,500 0,200 2,000 4,800 1,410 1,000 12,000 60,000 1,000 -999,000 529,000 5,000 3,300 27,660 5,000 11,000 0,120 2,000 -999,000 207,000 1,000 4,700 85,000 1,000 -999,000 36,330 1,000 10,400 0,101 3,000 7,400 1,040 4,000 2,100 521,000 5,000 -999,000 100,000 1,000 -999,000 35,000 4,000 7,700 0,005 4,000 17,900 0,010 1,000 6,100 62,000 1,000 8,200 0,122 1,000 8,400 1,350 3,000 11,900 0,023 3,000 10,800 0,048 3,000 13,800 1,700 1,000 14,300 3,500 1,000 -999,000 250,000 5,000 15,200 0,480 2,000 10,000 10,000 4,000 11,900 1,620 2,000 6,500 192,000 4,000 7,500 2,500 5,000 -999,000 4,288 2,000 10,600 0,280 3,000 7,400 4,235 1,000 8,400 6,800 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] = -168.238379681585 -0.10521225774235Wb[t] -11.3714913118809`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) -168.238379681585 111.194934 -1.513 0.135617 0.067809 Wb -0.10521225774235 0.06038 -1.7425 0.086629 0.043315 `D ` -11.3714913118809 37.669185 -0.3019 0.763807 0.381903 Multiple Linear Regression - Regression Statistics Multiple R 0.231053471238133 R-squared 0.0533857065711905 Adjusted R-squared 0.0212970864549599 F-TEST (value) 1.66369592640063 F-TEST (DF numerator) 2 F-TEST (DF denominator) 59 p-value 0.198200709948458 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 420.224497616881 Sum Squared Residuals 10418729.0754442 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 -999 -902.435216634825 -96.5647833651751 2 6.3 -202.458065874969 208.758065874969 3 -999 -179.966014485923 -819.033985514077 4 -999 -202.44964889435 -796.55035110565 5 2.1 -481.699965398874 483.799965398874 6 9.1 -214.83433424829 223.93433424829 7 15.8 -179.612290875393 195.412290875393 8 5.2 -230.558306167884 235.758306167884 9 10.9 -179.957071444015 190.857071444015 10 8.3 -185.097742357306 193.397742357306 11 11 -213.769060138649 224.769060138649 12 3.2 -274.019536091182 277.219536091182 13 7.6 -191.039229047105 198.639229047105 14 -999 -244.781049664583 -754.218950335417 15 6.3 -179.617761912796 185.917761912796 16 8.6 -191.296999078573 199.896999078573 17 6.6 -191.063953927674 197.663953927674 18 9.5 -191.002404756895 200.502404756895 19 4.8 -179.758220276882 184.558220276882 20 12 -185.922606458006 197.922606458006 21 -999 -280.753120586692 -718.246879413308 22 3.3 -228.006007290143 231.306007290143 23 11 -190.993987776275 201.993987776275 24 -999 -201.388808346132 -797.611191653868 25 4.7 -188.552912901565 193.252912901565 26 -999 -183.432232317245 -815.567767682755 27 10.4 -202.363480055259 212.763480055259 28 7.4 -213.83376567716 221.23376567716 29 2.1 -279.911422524754 282.011422524754 30 -999 -190.1310967677 -808.8689032323 31 -999 -217.40677395009 -781.59322604991 32 7.7 -213.724870990397 221.424870990397 33 17.9 -179.610923116043 197.510923116043 34 6.1 -186.133030973491 192.233030973491 35 8.2 -179.62270688891 187.82270688891 36 8.4 -202.494890165179 210.894890165179 37 11.9 -202.355273499155 214.255273499155 38 10.8 -202.357903805599 213.157903805599 39 13.8 -179.788731831627 193.588731831627 40 14.3 -179.978113895564 194.278113895564 41 -999 -251.398900676577 -747.601099323423 42 15.2 -191.031864189063 206.231864189063 43 10 -214.776467506532 224.776467506532 44 11.9 -191.151806162889 203.051806162889 45 6.5 -233.925098415639 240.425098415639 46 7.5 -225.358866885345 232.858866885345 47 -999 -191.432512466546 -807.567487533454 48 10.6 -202.382313049395 212.982313049395 49 7.4 -180.055444905004 187.455444905004 50 8.4 -191.696805657994 200.096805657994 51 5.7 -191.060271498653 196.760271498653 52 4.9 -202.7316177451 207.6316177451 53 -999 -226.656134023308 -772.343865976692 54 3.2 -230.93511654569 234.13511654569 55 -999 -191.128659466186 -807.871340533814 56 8.1 -190.987675040811 199.087675040811 57 11 -191.076053337314 202.076053337314 58 4.9 -202.563278132712 207.463278132712 59 13.2 -190.992304380152 204.192304380152 60 9.7 -214.165184289049 223.865184289049 61 12.8 -179.978113895564 192.778113895564 62 -999 -180.035980637322 -818.964019362678 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.71114518999704 0.57770962000592 0.28885481000296 7 0.896605088154537 0.206789823690927 0.103394911845463 8 0.828496105607924 0.343007788784153 0.171503894392076 9 0.830563029555752 0.338873940888496 0.169436970444248 10 0.796965370127127 0.406069259745747 0.203034629872873 11 0.714214206883604 0.571571586232791 0.285785793116396 12 0.660165087796958 0.679669824406083 0.339834912203041 13 0.586942604816815 0.826114790366371 0.413057395183185 14 0.813189516968097 0.373620966063806 0.186810483031903 15 0.759578072391122 0.480843855217757 0.240421927608879 16 0.698083215219669 0.603833569560662 0.301916784780331 17 0.629978675344477 0.740042649311046 0.370021324655523 18 0.5582596935854 0.883480612829199 0.4417403064146 19 0.483704248760647 0.967408497521293 0.516295751239353 20 0.417234527865807 0.834469055731614 0.582765472134193 21 0.491674981169681 0.983349962339362 0.508325018830319 22 0.44499349365032 0.88998698730064 0.55500650634968 23 0.378424687216704 0.756849374433408 0.621575312783296 24 0.564650840505204 0.870698318989592 0.435349159494796 25 0.503584829665034 0.992830340669933 0.496415170334966 26 0.68580101037887 0.628397979242259 0.314198989621129 27 0.631450266137559 0.737099467724882 0.368549733862441 28 0.574694749666144 0.850610500667712 0.425305250333856 29 0.626487702000998 0.747024595998005 0.373512297999002 30 0.746366671760497 0.507266656479006 0.253633328239503 31 0.869827697857281 0.260344604285438 0.130172302142719 32 0.834092260427167 0.331815479145666 0.165907739572833 33 0.793412677253671 0.413174645492658 0.206587322746329 34 0.75451365893002 0.490972682139962 0.245486341069981 35 0.702235694273925 0.595528611452149 0.297764305726075 36 0.644346254407287 0.711307491185427 0.355653745592713 37 0.582838775720932 0.834322448558136 0.417161224279068 38 0.518775901574743 0.962448196850514 0.481224098425257 39 0.455585395899697 0.911170791799394 0.544414604100303 40 0.395105545513549 0.790211091027098 0.604894454486451 41 0.509725292695475 0.98054941460905 0.490274707304525 42 0.448420459750153 0.896840919500305 0.551579540249847 43 0.385613425161156 0.771226850322311 0.614386574838844 44 0.327758316966057 0.655516633932114 0.672241683033943 45 0.262389458527199 0.524778917054397 0.737610541472801 46 0.211249784700867 0.422499569401735 0.788750215299133 47 0.374801257484331 0.749602514968662 0.625198742515669 48 0.312273705336935 0.624547410673869 0.687726294663065 49 0.243597052399364 0.487194104798729 0.756402947600636 50 0.187576052300543 0.375152104601086 0.812423947699457 51 0.14173873658554 0.28347747317108 0.85826126341446 52 0.105824136659187 0.211648273318374 0.894175863340813 53 0.311649787191496 0.623299574382993 0.688350212808504 54 0.254051009688121 0.508102019376243 0.745948990311879 55 0.639959702292036 0.720080595415929 0.360040297707964 56 0.471691151158574 0.943382302317148 0.528308848841426 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

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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