*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, 17 Dec 2008 03:49:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Dec/17/t1229511532phfecwtfraeza19.htm/, Retrieved Wed, 17 Dec 2008 11:59:35 +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/2008/Dec/17/t1229511532phfecwtfraeza19.htm/}, year = {2008}, } @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 = {2008}, 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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147768 0 1 0 137507 0 2 0 136919 0 3 0 136151 0 4 0 133001 0 5 0 125554 0 6 0 119647 0 7 0 114158 0 8 0 116193 0 9 0 152803 0 10 0 161761 0 11 0 160942 0 12 0 149470 0 13 0 139208 0 14 0 134588 0 15 0 130322 0 16 0 126611 0 17 0 122401 0 18 0 117352 0 19 0 112135 0 20 0 112879 0 21 0 148729 0 22 0 157230 0 23 0 157221 0 24 0 146681 0 25 0 136524 0 26 0 132111 1 0 27 125326 1 0 28 122716 1 0 29 116615 1 0 30 113719 1 0 31 110737 1 0 32 112093 1 0 33 143565 1 0 34 149946 1 0 35 149147 1 0 36 134339 1 0 37 122683 1 0 38 115614 1 0 39 116566 1 0 40 111272 1 0 41 104609 1 0 42 101802 1 0 43 94542 1 0 44 93051 1 0 45 124129 1 0 46 130374 1 0 47 123946 1 0 48 114971 1 0 49 105531 1 0 50 104919 0 51 0 104782 0 52 0 101281 0 53 0 94545 0 54 0 93248 0 55 0 84031 0 56 0 87486 0 57 0 115867 0 58 0 120327 0 59 0 117008 0 60 0 108811 0 61 0

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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation y[t] = + 167137.818656418 + 27869.9247953111d[t] -710.61975416534t1[t] -1368.39817229571t2[t] -11297.0905491941M1[t] -19942.1748071491M2[t] -25586.1800927574M3[t] -26813.2489713399M4[t] -29492.7178499224M5[t] -34750.3867285049M6[t] -37367.8556070874M7[t] -42427.1244856699M8[t] -40233.5933642525M9[t] -6581.66224283496M10[t] + 1301.06887858251M11[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) 167137.818656418 2103.675723 79.4504 0 0 d 27869.9247953111 5022.079829 5.5495 1e-06 1e-06 t1 -710.61975416534 32.893486 -21.6037 0 0 t2 -1368.39817229571 125.374364 -10.9145 0 0 M1 -11297.0905491941 2451.342923 -4.6085 3.2e-05 1.6e-05 M2 -19942.1748071491 2581.565338 -7.7248 0 0 M3 -25586.1800927574 2600.62134 -9.8385 0 0 M4 -26813.2489713399 2591.117749 -10.3481 0 0 M5 -29492.7178499224 2582.703187 -11.4193 0 0 M6 -34750.3867285049 2575.388327 -13.4933 0 0 M7 -37367.8556070874 2569.182564 -14.5446 0 0 M8 -42427.1244856699 2564.09395 -16.5466 0 0 M9 -40233.5933642525 2560.129146 -15.7155 0 0 M10 -6581.66224283496 2557.29338 -2.5737 0.01335 0.006675 M11 1301.06887858251 2555.59041 0.5091 0.613111 0.306555 Multiple Linear Regression - Regression Statistics Multiple R 0.982719960893569 R-squared 0.965738521538657 Adjusted R-squared 0.955311115050422 F-TEST (value) 92.61540946239 F-TEST (DF numerator) 14 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4039.84528855188 Sum Squared Residuals 750736097.950002 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 147768 155130.108353058 -7362.10835305808 2 137507 145774.404340938 -8267.40434093833 3 136919 139419.779301165 -2500.77930116461 4 136151 137482.090668417 -1331.09066841675 5 133001 134092.002035669 -1091.00203566894 6 125554 128123.713402921 -2569.71340292106 7 119647 124795.624770173 -5148.62477017326 8 114158 119025.736137425 -4867.73613742539 9 116193 120508.647504678 -4315.64750467755 10 152803 153449.958871930 -646.958871929662 11 161761 160622.070239182 1138.92976081813 12 160942 158610.381606434 2331.61839356598 13 149470 146602.671303075 2867.32869692549 14 139208 137246.967290954 1961.03270904579 15 134588 130892.342251181 3695.65774881942 16 130322 128954.653618433 1367.34638156727 17 126611 125564.564985685 1046.43501431513 18 122401 119596.276352937 2804.72364706298 19 117352 116268.187720189 1083.81227981084 20 112135 110498.299087441 1636.70091255868 21 112879 111981.210454693 897.789545306526 22 148729 144922.521821946 3806.47817805437 23 157230 152094.633189198 5135.36681080224 24 157221 150082.94455645 7138.05544355008 25 146681 138075.234253090 8605.76574690954 26 136524 128719.53024097 7804.46975902986 27 132111 132474.812706987 -363.812706987501 28 125326 129879.345656109 -4553.34565610927 29 122716 125831.478605231 -3115.47860523105 30 116615 119205.411554353 -2590.41155435283 31 113719 115219.544503475 -1500.54450347459 32 110737 108791.877452596 1945.12254740363 33 112093 109617.010401718 2475.98959828185 34 143565 141900.54335084 1664.45664916007 35 149946 148414.876299962 1531.12370003831 36 149147 145745.409249083 3401.59075091654 37 134339 133079.920527594 1259.07947240637 38 122683 123066.438097343 -383.438097342939 39 115614 116054.034639439 -440.034639438937 40 116566 113458.567588561 3107.43241143928 41 111272 109410.700537682 1861.29946231752 42 104609 102784.633486804 1824.36651319574 43 101802 98798.766435926 3003.23356407398 44 94542 92371.0993850478 2170.90061495220 45 93051 93196.2323341696 -145.232334169567 46 124129 125479.765283291 -1350.76528329136 47 130374 131994.098232413 -1620.09823241312 48 123946 129324.631181535 -5378.63118153489 49 114971 116659.142460045 -1688.14246004506 50 105531 106645.660029794 -1114.66002979437 51 104919 105310.031101228 -391.031101228376 52 104782 103372.342468481 1409.65753151947 53 101281 99982.2538357327 1298.74616426733 54 94545 94013.9652029848 531.03479701517 55 93248 90685.876570237 2562.12342976303 56 84031 84915.9879374891 -884.987937489114 57 87486 86398.8993047413 1087.10069525873 58 115867 119340.210671993 -3473.21067199343 59 120327 126512.322039246 -6185.32203924556 60 117008 124500.633406498 -7492.63340649771 61 108811 112492.923103138 -3681.92310313825 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.585463390595084 0.829073218809832 0.414536609404916 19 0.459816009253334 0.919632018506667 0.540183990746666 20 0.367182674369014 0.734365348738027 0.632817325630986 21 0.374779821147826 0.749559642295652 0.625220178852174 22 0.323480689297551 0.646961378595102 0.676519310702449 23 0.265758721814982 0.531517443629963 0.734241278185018 24 0.180660914331118 0.361321828662236 0.819339085668882 25 0.142107425247782 0.284214850495564 0.857892574752218 26 0.129725123582457 0.259450247164913 0.870274876417543 27 0.0818639796887055 0.163727959377411 0.918136020311294 28 0.0944509663666725 0.188901932733345 0.905549033633327 29 0.128979974817757 0.257959949635514 0.871020025182243 30 0.181940845292076 0.363881690584153 0.818059154707924 31 0.59421319808297 0.81157360383406 0.40578680191703 32 0.666455747425266 0.667088505149468 0.333544252574734 33 0.6743263253764 0.651347349247199 0.325673674623599 34 0.683808991772058 0.632382016455884 0.316191008227942 35 0.691932772109784 0.616134455780433 0.308067227890216 36 0.977932429638407 0.0441351407231851 0.0220675703615926 37 0.977470191825204 0.0450596163495917 0.0225298081747958 38 0.962697863171768 0.074604273656465 0.0373021368282325 39 0.950510494100102 0.098979011799796 0.049489505899898 40 0.915765750665963 0.168468498668074 0.0842342493340371 41 0.837900306970826 0.324199386058349 0.162099693029174 42 0.719152819331943 0.561694361336115 0.280847180668057 43 0.566477459420532 0.867045081158936 0.433522540579468 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 2 0.0769230769230769 NOK 10% type I error level 4 0.153846153846154 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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