*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, 14 Dec 2009 02:49:06 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t1260784246ugjwdl5ffsp66sy.htm/, Retrieved Mon, 14 Dec 2009 10:50:59 +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/Dec/14/t1260784246ugjwdl5ffsp66sy.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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95,1 121,8 97,0 127,6 112,7 129,9 102,9 128,0 97,4 123,5 111,4 124,0 87,4 127,4 96,8 127,6 114,1 128,4 110,3 131,4 103,9 135,1 101,6 134,0 94,6 144,5 95,9 147,3 104,7 150,9 102,8 148,7 98,1 141,4 113,9 138,9 80,9 139,8 95,7 145,6 113,2 147,9 105,9 148,5 108,8 151,1 102,3 157,5 99,0 167,5 100,7 172,3 115,5 173,5 100,7 187,5 109,9 205,5 114,6 195,1 85,4 204,5 100,5 204,5 114,8 201,7 116,5 207,0 112,9 206,6 102,0 210,6 106,0 211,1 105,3 215,0 118,8 223,9 106,1 238,2 109,3 238,9 117,2 229,6 92,5 232,2 104,2 222,1 112,5 221,6 122,4 227,3 113,3 221,0 100,0 213,6 110,7 243,4 112,8 253,8 109,8 265,3 117,3 268,2 109,1 268,5 115,9 266,9 96,0 268,4 99,8 250,8 116,8 231,2 115,7 192,0 99,4 171,4 94,3 160,0

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TIP[t] = + 83.408897026977 + 0.126899884441892Grondstofprijzen[t] -0.98910911627775M1[t] -0.276741620859989M2[t] + 9.14070186993543M3[t] + 2.26829735148621M4[t] + 1.04095437311572M5[t] + 11.6277006898408M6[t] -14.8286700435465M7[t] -3.16253168984288M8[t] + 12.3753847077728M9[t] + 13.0351249944528M10[t] + 7.22349736433458M11[t] -0.155392855225834t + 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) 83.408897026977 2.880361 28.9578 0 0 Grondstofprijzen 0.126899884441892 0.024603 5.158 5e-06 3e-06 M1 -0.98910911627775 2.462033 -0.4017 0.689732 0.344866 M2 -0.276741620859989 2.482158 -0.1115 0.911711 0.455855 M3 9.14070186993543 2.504392 3.6499 0.000668 0.000334 M4 2.26829735148621 2.528222 0.8972 0.374289 0.187144 M5 1.04095437311572 2.516602 0.4136 0.681064 0.340532 M6 11.6277006898408 2.45557 4.7352 2.1e-05 1.1e-05 M7 -14.8286700435465 2.462255 -6.0224 0 0 M8 -3.16253168984288 2.413232 -1.3105 0.196534 0.098267 M9 12.3753847077728 2.37708 5.2061 4e-06 2e-06 M10 13.0351249944528 2.348482 5.5504 1e-06 1e-06 M11 7.22349736433458 2.334763 3.0939 0.003355 0.001678 t -0.155392855225834 0.066589 -2.3336 0.024042 0.012021 Multiple Linear Regression - Regression Statistics Multiple R 0.932262038977343 R-squared 0.869112509318194 Adjusted R-squared 0.832122566299422 F-TEST (value) 23.4959137103061 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 4.44089209850063e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.68742900677967 Sum Squared Residuals 625.468103281846 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 97.720800980496 -2.62080098049592 2 97 99.0137949504508 -2.01379495045078 3 112.7 108.567715320237 4.13228467976325 4 102.9 101.298808166122 1.60119183387791 5 97.4 99.3450228525372 -1.94502285253724 6 111.4 109.839826256257 1.56017374374258 7 87.4 83.6595222747467 3.74047772525329 8 96.8 95.195647750113 1.60435224988709 9 114.1 110.679691200056 3.42030879994366 10 110.3 111.564738284836 -1.26473828483611 11 103.9 106.067247371927 -2.16724737192705 12 101.6 98.5487672794806 3.05123272051942 13 94.6 98.7367140946169 -4.13671409461686 14 95.9 99.649008411246 -3.74900841124607 15 104.7 109.367898630806 -4.66789863080648 16 102.8 102.060921511359 0.739078488640739 17 98.1 99.7518165213371 -1.65181652133713 18 113.9 109.865920271732 4.0340797282684 19 80.9 83.3683665791162 -2.46836657911617 20 95.7 95.615131407357 0.0848685926430376 21 113.2 111.289524683963 1.9104753160368 22 105.9 111.870012046082 -5.97001204608245 23 108.8 106.232931260287 2.56706873971267 24 102.3 99.666200301155 2.63379969884497 25 99 99.7906971740704 -0.790697174070369 26 100.7 100.956791259583 -0.256791259583379 27 115.5 110.371121756483 5.12887824351677 28 100.7 105.119922764995 -4.41992276499467 29 109.9 106.021384851352 3.87861514864760 30 114.6 115.132979514656 -0.532979514655955 31 85.4 89.7140748397966 -4.3140748397966 32 100.5 101.224820338274 -0.724820338274414 33 114.8 116.252024204227 -1.45202420422701 34 116.5 117.428941023223 -0.928941023223155 35 112.9 111.411160584102 1.48883941589766 36 102 104.539869902310 -2.5398699023095 37 106 103.458817873027 2.54118212697313 38 105.3 104.510702062542 0.789297937457823 39 118.8 114.902161669645 3.89783833035539 40 106.1 109.689032643489 -3.58903264348861 41 109.3 108.395126729002 0.904873270998387 42 117.2 117.646311265191 -0.446311265191223 43 92.5 91.364487376127 1.13551262387299 44 104.2 101.593544041742 2.60645595825829 45 112.5 116.912617641911 -4.41261764191065 46 122.4 118.140294414684 4.25970558531645 47 113.3 111.373804657356 1.92619534264442 48 100 103.055855292925 -3.05585529292517 49 110.7 105.69296987779 5.00703012221002 50 112.8 107.569703316178 5.23029668382241 51 109.8 118.291102622829 -8.49110262282894 52 117.3 111.631314914035 5.66868508596463 53 109.1 110.286649045772 -1.18664904577162 54 115.9 120.514962692164 -4.61496269216380 55 96 94.0935489302135 1.90645106978650 56 99.8 103.370856462514 -3.57085646251401 57 116.8 116.266142269843 0.533857730157193 58 115.7 111.796014231175 3.90398576882526 59 99.4 103.214856126328 -3.8148561263277 60 94.3 94.3893072241297 -0.0893072241297221 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.314821135364290 0.629642270728581 0.68517886463571 18 0.184562239126081 0.369124478252163 0.815437760873919 19 0.288153696615991 0.576307393231982 0.711846303384009 20 0.177357784277629 0.354715568555257 0.822642215722371 21 0.108961671394219 0.217923342788438 0.891038328605781 22 0.0988242482004231 0.197648496400846 0.901175751799577 23 0.153564094985955 0.307128189971910 0.846435905014045 24 0.115546226819754 0.231092453639508 0.884453773180246 25 0.122921198454368 0.245842396908737 0.877078801545632 26 0.0968489495920677 0.193697899184135 0.903151050407932 27 0.146156351821527 0.292312703643054 0.853843648178473 28 0.235675446187106 0.471350892374212 0.764324553812894 29 0.238396270501140 0.476792541002279 0.76160372949886 30 0.232401305168858 0.464802610337716 0.767598694831142 31 0.265977556716744 0.531955113433489 0.734022443283256 32 0.189885254548521 0.379770509097042 0.810114745451479 33 0.141134727657323 0.282269455314646 0.858865272342677 34 0.145997332452485 0.29199466490497 0.854002667547515 35 0.10337880768839 0.20675761537678 0.89662119231161 36 0.0820952965938037 0.164190593187607 0.917904703406196 37 0.0831326833531806 0.166265366706361 0.91686731664682 38 0.078312406275977 0.156624812551954 0.921687593724023 39 0.209187355768769 0.418374711537538 0.790812644231231 40 0.477217972097041 0.954435944194081 0.522782027902959 41 0.346219486843502 0.692438973687003 0.653780513156498 42 0.261902864088580 0.523805728177159 0.73809713591142 43 0.163899196205749 0.327798392411499 0.83610080379425 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 = 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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