*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, 30 Nov 2009 11:53:33 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/30/t1259607313bq68yb9dset0eft.htm/, Retrieved Mon, 30 Nov 2009 19:55:25 +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/2009/Nov/30/t1259607313bq68yb9dset0eft.htm/}, year = {2009}, } @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 = {2009}, 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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254844 281818 258863 264777 267366 267413 254868 287854 254844 258863 264777 267366 277267 316263 254868 254844 258863 264777 285351 325412 277267 254868 254844 258863 286602 326011 285351 277267 254868 254844 283042 328282 286602 285351 277267 254868 276687 317480 283042 286602 285351 277267 277915 317539 276687 283042 286602 285351 277128 313737 277915 276687 283042 286602 277103 312276 277128 277915 276687 283042 275037 309391 277103 277128 277915 276687 270150 302950 275037 277103 277128 277915 267140 300316 270150 275037 277103 277128 264993 304035 267140 270150 275037 277103 287259 333476 264993 267140 270150 275037 291186 337698 287259 264993 267140 270150 292300 335932 291186 287259 264993 267140 288186 323931 292300 291186 287259 264993 281477 313927 288186 292300 291186 287259 282656 314485 281477 288186 292300 291186 280190 313218 282656 281477 288186 292300 280408 309664 280190 282656 281477 288186 276836 302963 280408 280190 282656 281477 275216 298989 276836 280408 280190 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 7218.81321367391 + 0.168547715381535X[t] + 0.979872427652679Y1[t] + 0.137046798716369Y2[t] + 0.0699500275999237Y3[t] -0.406984626398871Y4[t] -1804.08726665933M1[t] + 1408.97397886702M2[t] + 18831.5706048898M3[t] -822.813077601211M4[t] -8320.63177610417M5[t] -14608.2217206370M6[t] -4583.64714859553M7[t] + 5149.13242714079M8[t] + 5625.48810387275M9[t] + 1211.36402069791M10[t] -3453.02634995847M11[t] + 72.3725529323416t + 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) 7218.81321367391 13548.296059 0.5328 0.596779 0.29839 X 0.168547715381535 0.096425 1.748 0.087291 0.043645 Y1 0.979872427652679 0.13895 7.052 0 0 Y2 0.137046798716369 0.202669 0.6762 0.502368 0.251184 Y3 0.0699500275999237 0.208433 0.3356 0.738733 0.369367 Y4 -0.406984626398871 0.142958 -2.8469 0.006629 0.003314 M1 -1804.08726665933 2222.876655 -0.8116 0.421293 0.210647 M2 1408.97397886702 2207.660013 0.6382 0.526565 0.263282 M3 18831.5706048898 4106.988387 4.5853 3.6e-05 1.8e-05 M4 -822.813077601211 5548.036122 -0.1483 0.882763 0.441382 M5 -8320.63177610417 4502.43792 -1.848 0.071177 0.035588 M6 -14608.2217206370 3618.16973 -4.0375 0.000208 0.000104 M7 -4583.64714859553 2233.34681 -2.0524 0.045978 0.022989 M8 5149.13242714079 2384.700257 2.1592 0.0362 0.0181 M9 5625.48810387275 2819.12521 1.9955 0.052067 0.026033 M10 1211.36402069791 2713.917192 0.4464 0.657483 0.328742 M11 -3453.02634995847 2233.000971 -1.5464 0.129022 0.064511 t 72.3725529323416 68.622167 1.0547 0.297214 0.148607 Multiple Linear Regression - Regression Statistics Multiple R 0.985779580101678 R-squared 0.97176138054544 Adjusted R-squared 0.961093457640385 F-TEST (value) 91.0919013189444 F-TEST (DF numerator) 17 F-TEST (DF denominator) 45 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3446.92213769629 Sum Squared Residuals 534657250.050334 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 254844 252795.7141966 2048.28580340013 2 254868 252187.927606741 2680.07239325895 3 277267 274583.893420713 2683.10657928659 4 285351 280621.154888941 4729.84511105919 5 286602 285925.018788635 676.981211364627 6 283042 283983.32302366 -941.323023660072 7 276687 280392.144806243 -3705.14480624268 8 277915 280289.709133675 -2374.70913367484 9 277128 279771.810018893 -2643.8100188928 10 277103 275585.276989321 1517.7230106786 11 275037 273046.932306098 1990.06769390194 12 270150 272904.044975779 -2754.0449757791 13 267140 265975.148489936 1164.85151006359 14 264993 266133.905387976 -1140.90538797611 15 287259 286573.775342432 685.224657568355 16 291186 291005.35695062 180.643049380156 17 292300 291256.539599500 1043.46040050027 18 288186 287079.645045988 1106.35495401205 19 281477 282824.689859679 -1347.68985967947 20 282656 284065.812669368 -1409.81266936802 21 280190 283895.658275904 -3705.65827590387 22 280408 277905.140952128 2502.85904787243 23 276836 274872.270618276 1963.72938172408 24 275216 273605.301148200 1610.69885180037 25 274352 270720.137124471 3631.86287552912 26 271311 273139.062255319 -1828.06225531923 27 289802 293618.182413021 -3816.18241302057 28 290726 293233.44804961 -2507.44804960997 29 292300 288127.907274778 4172.09272522187 30 278506 282995.099444134 -4489.09944413378 31 269826 270105.143575825 -279.143575824519 32 265861 268489.656677261 -2628.65667726102 33 269034 262379.882691043 6654.11730895658 34 264176 264453.743995432 -277.743995432311 35 255198 257409.033204932 -2211.03320493236 36 253353 252648.156566013 704.843433987028 37 246057 244968.557189578 1088.44281042175 38 235372 241916.096192795 -6544.09619279472 39 258556 257115.130442461 1440.86955753896 40 260993 260171.443948526 821.556051474032 41 254663 257734.617413691 -3071.61741369118 42 250643 249840.099068033 802.900931967098 43 243422 244179.406639836 -757.406639836445 44 247105 245046.237912857 2058.76208714311 45 248541 250716.211528677 -2175.21152867679 46 245039 248429.74814862 -3390.74814861993 47 237080 242623.015177727 -5543.01517772657 48 237085 236069.377646962 1015.62235303814 49 225554 230845.648026832 -5291.64802683159 50 226839 224870.770037319 1968.22996268103 51 247934 250290.670379149 -2356.67037914903 52 248333 251557.596162303 -3224.59616230341 53 246969 249789.916923396 -2820.91692339559 54 245098 241576.833418185 3521.1665818147 55 246263 240173.615118417 6089.38488158311 56 255765 251410.583606839 4354.41639316078 57 264319 262448.437485483 1870.56251451689 58 268347 268699.089914499 -352.089914498789 59 273046 269245.748692967 3800.25130703291 60 273963 274540.119663046 -577.119663046446 61 267430 270071.794972583 -2641.79497258300 62 271993 267128.23851985 4864.76148015008 63 292710 291346.348002224 1363.65199777570 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.319239655639428 0.638479311278856 0.680760344360572 22 0.169675826861434 0.339351653722867 0.830324173138566 23 0.0899781845661812 0.179956369132362 0.910021815433819 24 0.0780361291502273 0.156072258300455 0.921963870849773 25 0.0515962612508533 0.103192522501707 0.948403738749147 26 0.0240126202165777 0.0480252404331554 0.975987379783422 27 0.0110439884566817 0.0220879769133634 0.988956011543318 28 0.0139006034451061 0.0278012068902123 0.986099396554894 29 0.00731535419282779 0.0146307083856556 0.992684645807172 30 0.556400584084393 0.887198831831213 0.443599415915607 31 0.72967165242256 0.54065669515488 0.27032834757744 32 0.824730249431538 0.350539501136924 0.175269750568462 33 0.746839168014795 0.50632166397041 0.253160831985205 34 0.744707248963615 0.51058550207277 0.255292751036385 35 0.774218277962092 0.451563444075816 0.225781722037908 36 0.762960051580608 0.474079896838784 0.237039948419392 37 0.82216189163896 0.35567621672208 0.17783810836104 38 0.988037698876924 0.023924602246151 0.0119623011230755 39 0.989658288967638 0.0206834220647247 0.0103417110323624 40 0.977987681743668 0.0440246365126648 0.0220123182563324 41 0.941904380331292 0.116191239337415 0.0580956196687076 42 0.874895047389138 0.250209905221723 0.125104952610861 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 7 0.318181818181818 NOK 10% type I error level 7 0.318181818181818 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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