dioxine

*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: Mon, 01 Dec 2008 09:30:23 -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/01/t1228149175nem4gjrl1k1bwze.htm/, Retrieved Mon, 01 Dec 2008 16:33:05 +0000

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/01/t1228149175nem4gjrl1k1bwze.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}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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14929387.5 0 14717825.3 0 15826281.2 0 16301309.6 0 15033016.9 0 16998460.6 0 14066462.7 0 13328937.3 0 17319718.2 0 17586426.8 0 15887037.4 0 17935679.1 0 15869489 0 15892510.9 0 17556558.1 0 16791643 0 15953688.5 0 18144913.6 0 14390881 0 13885708.7 0 17332571.5 0 17152595.8 0 16003877.1 0 16841467.1 0 14783398.1 0 14667847.5 0 17714362.2 0 16282088 0 15014866.2 0 17722582.4 1 13876509.4 1 15495489.6 1 17799521.1 1 17920079.1 1 17248022.4 1 18813782.4 1 16249688.3 1 17823358.5 0 20424438.3 0 17814218.7 0 19699959.6 0 19776328.1 0 15679833.1 0 17119266.5 0 20092613 0 20863688.3 0 20925203.1 0 21032593 0 20664684.3 0 19711511.4 0 22553293.4 0 19498332.9 0 20722827.8 0 21321275 0 17960847.7 0 17789654.9 0 20003708.5 0 21169851.7 0 20422839.4 0 19810562.3 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation x[t] = + 15686151.7530378 -1008053.78878749y[t] -1347903.07244676M1[t] -1580740.21089092M2[t] + 577128.048422425M3[t] -994847.812264233M4[t] -1142002.11295089M5[t] + 472941.124119949M6[t] -3219371.69656671M7[t] -2984974.73725337M8[t] -93667.3379400267M9[t] + 240726.881373318M10[t] -694913.239313342M11[t] + 94507.660686658t + 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) 15686151.7530378 520436.866799 30.1404 0 0 y -1008053.78878749 389173.999703 -2.5902 0.012804 0.006402 M1 -1347903.07244676 627702.975277 -2.1474 0.037068 0.018534 M2 -1580740.21089092 631245.257239 -2.5042 0.015883 0.007941 M3 577128.048422425 630433.851961 0.9154 0.364732 0.182366 M4 -994847.812264233 629710.487874 -1.5798 0.120994 0.060497 M5 -1142002.11295089 629075.468688 -1.8154 0.07599 0.037995 M6 472941.124119949 623893.382923 0.758 0.452289 0.226144 M7 -3219371.69656671 623398.675531 -5.1642 5e-06 3e-06 M8 -2984974.73725337 622993.622745 -4.7913 1.8e-05 9e-06 M9 -93667.3379400267 622678.399524 -0.1504 0.881086 0.440543 M10 240726.881373318 622453.142345 0.3867 0.700733 0.350366 M11 -694913.239313342 622317.948901 -1.1167 0.269942 0.134971 t 94507.660686658 7489.657116 12.6184 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.923521868842376 R-squared 0.852892642230114 Adjusted R-squared 0.81131882372993 F-TEST (value) 20.5151384452770 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 6.88338275267597e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 983899.810144435 Sum Squared Residuals 44530706474503.8 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 14929387.5 14432756.3412777 496631.1587223 2 14717825.3 14294426.8635202 423398.436479794 3 15826281.2 16546802.7835202 -720521.583520209 4 16301309.6 15069334.5835202 1231975.01647979 5 15033016.9 15016687.9435202 16328.9564797894 6 16998460.6 16726138.8412777 272321.758722294 7 14066462.7 13128333.6812777 938129.018722295 8 13328937.3 13457238.3012777 -128301.001277705 9 17319718.2 16443053.3612777 876664.838722289 10 17586426.8 16871955.2412777 714471.558722298 11 15887037.4 16030822.7812777 -143785.381277706 12 17935679.1 16820243.6812777 1115435.41872230 13 15869489 15566848.2695176 302640.730482396 14 15892510.9 15428518.7917601 463992.108239894 15 17556558.1 17680894.7117601 -124336.611760103 16 16791643 16203426.5117601 588216.488239895 17 15953688.5 16150779.8717601 -197091.371760105 18 18144913.6 17860230.7695176 284682.830482399 19 14390881 14262425.6095176 128455.390482398 20 13885708.7 14591330.2295176 -705621.529517602 21 17332571.5 17577145.2895176 -244573.789517601 22 17152595.8 18006047.1695176 -853451.369517603 23 16003877.1 17164914.7095176 -1161037.60951760 24 16841467.1 17954335.6095176 -1112868.5095176 25 14783398.1 16700940.1977575 -1917542.0977575 26 14667847.5 16562610.72 -1894763.22 27 17714362.2 18814986.64 -1100624.44000000 28 16282088 17337518.44 -1055430.44 29 15014866.2 17284871.8 -2270005.6 30 17722582.4 17986268.90897 -263686.508970015 31 13876509.4 14388463.7489700 -511954.348970013 32 15495489.6 14717368.36897 778121.231029987 33 17799521.1 17703183.42897 96337.6710299895 34 17920079.1 18132085.3089700 -212006.208970013 35 17248022.4 17290952.84897 -42930.4489700140 36 18813782.4 18080373.74897 733408.651029986 37 16249688.3 16826978.3372099 -577290.037209909 38 17823358.5 17696702.6482399 126655.851760104 39 20424438.3 19949078.5682399 475359.731760106 40 17814218.7 18471610.3682399 -657391.668239896 41 19699959.6 18418963.7282399 1280995.87176011 42 19776328.1 20128414.6259974 -352086.525997391 43 15679833.1 16530609.4659974 -850776.365997393 44 17119266.5 16859514.0859974 259752.414002609 45 20092613 19845329.1459974 247283.854002610 46 20863688.3 20274231.0259974 589457.274002608 47 20925203.1 19433098.5659974 1492104.53400261 48 21032593 20222519.4659974 810073.53400261 49 20664684.3 18969124.0542373 1695560.24576271 50 19711511.4 18830794.5764798 880716.823520207 51 22553293.4 21083170.4964798 1470122.90352021 52 19498332.9 19605702.2964798 -107369.396479791 53 20722827.8 19553055.6564798 1169772.14352021 54 21321275 21262506.5542373 58768.445762712 55 17960847.7 17664701.3942373 296146.305762712 56 17789654.9 17993606.0142373 -203951.114237289 57 20003708.5 20979421.0742373 -975712.574237287 58 21169851.7 21408322.9542373 -238471.25423729 59 20422839.4 20567190.4942373 -144351.094237289 60 19810562.3 21356611.3942373 -1546049.09423729 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0633771686266333 0.126754337253267 0.936622831373367 18 0.0206969209546319 0.0413938419092638 0.979303079045368 19 0.0183641290301438 0.0367282580602877 0.981635870969856 20 0.00764245035869804 0.0152849007173961 0.992357549641302 21 0.00938289149456628 0.0187657829891326 0.990617108505434 22 0.0175929537967543 0.0351859075935086 0.982407046203246 23 0.00964389117787957 0.0192877823557591 0.99035610882212 24 0.0296819353434250 0.05936387068685 0.970318064656575 25 0.0421537821753024 0.0843075643506047 0.957846217824698 26 0.0513978393489656 0.102795678697931 0.948602160651034 27 0.0481433980846755 0.096286796169351 0.951856601915325 28 0.0323803344737013 0.0647606689474026 0.967619665526299 29 0.181753328136211 0.363506656272423 0.818246671863789 30 0.121482071031319 0.242964142062637 0.878517928968682 31 0.0814808959253955 0.162961791850791 0.918519104074604 32 0.147487784896153 0.294975569792306 0.852512215103847 33 0.110684370096415 0.22136874019283 0.889315629903585 34 0.0691708407916919 0.138341681583384 0.930829159208308 35 0.0498027168996353 0.0996054337992706 0.950197283100365 36 0.132182940642238 0.264365881284476 0.867817059357762 37 0.0833871103296476 0.166774220659295 0.916612889670352 38 0.20254163875183 0.40508327750366 0.79745836124817 39 0.393125229264288 0.786250458528577 0.606874770735712 40 0.352427237742128 0.704854475484256 0.647572762257872 41 0.437391732813441 0.874783465626883 0.562608267186559 42 0.390512709002684 0.781025418005369 0.609487290997316 43 0.722944427414568 0.554111145170864 0.277055572585432 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 6 0.222222222222222 NOK 10% type I error level 11 0.407407407407407 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = 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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