*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, 06 Dec 2010 14:48:47 +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/06/t1291646802gwkx0tk9bv46dhf.htm/, Retrieved Mon, 06 Dec 2010 15:46:53 +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/06/t1291646802gwkx0tk9bv46dhf.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?

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User-defined keywords:

Dataseries X:

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3484.74 13830.14 9349.44 7977 -5.6 6 1 2.77 3411.13 14153.22 9327.78 8241 -6.2 3 1 2.76 3288.18 15418.03 9753.63 8444 -7.1 2 1.2 2.76 3280.37 16666.97 10443.5 8490 -1.4 2 1.2 2.46 3173.95 16505.21 10853.87 8388 -0.1 2 0.8 2.46 3165.26 17135.96 10704.02 8099 -0.9 -8 0.7 2.47 3092.71 18033.25 11052.23 7984 0 0 0.7 2.71 3053.05 17671 10935.47 7786 0.1 -2 0.9 2.8 3181.96 17544.22 10714.03 8086 2.6 3 1.2 2.89 2999.93 17677.9 10394.48 9315 6 5 1.3 3.36 3249.57 18470.97 10817.9 9113 6.4 8 1.5 3.31 3210.52 18409.96 11251.2 9023 8.6 8 1.9 3.5 3030.29 18941.6 11281.26 9026 6.4 9 1.8 3.51 2803.47 19685.53 10539.68 9787 7.7 11 1.9 3.71 2767.63 19834.71 10483.39 9536 9.2 13 2.2 3.71 2882.6 19598.93 10947.43 9490 8.6 12 2.1 3.71 2863.36 17039.97 10580.27 9736 7.4 13 2.2 4.21 2897.06 16969.28 10582.92 9694 8.6 15 2.7 4.21 3012.61 16973.38 10654.41 9647 6.2 13 2.8 4.21 3142.95 16329.89 11014.51 9753 6 16 2.9 4.5 3032.93 16153.34 10967.87 10070 6.6 10 3.4 4.51 3045.78 15311.7 10433.56 10137 5.1 14 3 4.51 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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = + 623.189281438361 -0.0829840213057002Nikkei[t] + 0.265839363241114DJ_Indust[t] + 0.132169504408610Goudprijs[t] -13.1225855069165Conjunct_Seizoenzuiver[t] + 6.30504688723916Cons_vertrouw[t] -96.5668153338558Alg_consumptie_index_BE[t] + 146.912916190512Gem_rente_kasbon_1j[t] -38.0890581388965t + 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) 623.189281438361 412.103204 1.5122 0.137967 0.068984 Nikkei -0.0829840213057002 0.01802 -4.605 3.8e-05 1.9e-05 DJ_Indust 0.265839363241114 0.029041 9.1538 0 0 Goudprijs 0.132169504408610 0.039368 3.3573 0.001681 0.000841 Conjunct_Seizoenzuiver -13.1225855069165 7.195252 -1.8238 0.075306 0.037653 Cons_vertrouw 6.30504688723916 4.62649 1.3628 0.180204 0.090102 Alg_consumptie_index_BE -96.5668153338558 34.504521 -2.7987 0.007716 0.003858 Gem_rente_kasbon_1j 146.912916190512 57.895144 2.5376 0.014963 0.007481 t -38.0890581388965 3.739189 -10.1864 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.981850693082498 R-squared 0.964030783506582 Adjusted R-squared 0.957179504174502 F-TEST (value) 140.708141761599 F-TEST (DF numerator) 8 F-TEST (DF denominator) 42 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 89.244763913917 Sum Squared Residuals 334514.371214133 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 3398.88362648317 85.8563735168272 2 3411.13 3350.60804077742 60.5219592225808 3 3288.18 3333.78998188425 -45.609981884249 4 3280.37 3262.66064665118 17.7093533488226 5 3173.95 3355.17365881682 -181.223658816820 6 3165.26 3145.28282411202 19.9771758879848 7 3092.71 3183.99061319034 -91.2806131903363 8 3053.05 3098.7399979097 -45.6899979096969 9 3181.96 3034.9259252443 147.034074755697 10 2999.93 3090.61660765886 -90.6866076588616 11 3249.57 3059.58597261872 189.984027381280 12 3210.52 3090.26975014272 120.250249857276 13 3030.29 3062.75125238686 -32.4612523868644 14 2803.47 2881.64436346083 -78.1743634608296 15 2767.63 2746.99327657409 20.6367234259085 16 2882.6 2856.97567784456 25.6243221554399 17 2863.36 3051.99945440042 -188.639454400418 18 2897.06 2963.5094753543 -66.4494753542997 19 3012.61 2947.10050200769 65.5094979923125 20 3142.95 3126.6372758342 16.3127241658018 21 3032.93 3040.17992052018 -7.24992052017943 22 3045.78 3022.27905263790 23.5009473620975 23 3110.52 3067.00371838154 43.5162816184595 24 3013.24 3053.80418161965 -40.564181619646 25 2987.1 2988.24224979404 -1.14224979404267 26 2995.55 3001.00016312287 -5.45016312286636 27 2833.18 2851.06729829201 -17.8872982920094 28 2848.96 2788.07523590685 60.8847640931478 29 2794.83 2861.07581437834 -66.2458143783382 30 2845.26 3001.61193750129 -156.351937501293 31 2915.02 2958.71293227000 -43.6929322700043 32 2892.63 2865.19645504366 27.4335449563381 33 2604.42 2632.64244626349 -28.2224462634878 34 2641.65 2562.38950740884 79.260492591162 35 2659.81 2630.68239361239 29.1276063876141 36 2638.53 2681.71771730455 -43.1877173045495 37 2720.25 2625.50871373891 94.7412862610935 38 2745.88 2766.48891100244 -20.6089110024444 39 2735.7 2733.32559676584 2.37440323415940 40 2811.7 2701.7225280674 109.977471932601 41 2799.43 2649.06185162075 150.368148379246 42 2555.28 2529.49512565271 25.7848743472864 43 2304.98 2174.81502799308 130.164972006921 44 2214.95 2176.28711181467 38.6628881853331 45 2065.81 2048.38384461464 17.4261553853613 46 1940.49 2029.32362410187 -88.8336241018684 47 2042 2133.7607444843 -91.7607444843025 48 1995.37 2047.39602214434 -52.0260221443377 49 1946.81 2046.50916225015 -99.6991622501483 50 1765.9 1743.50952226729 22.3904777327094 51 1635.25 1677.14226607157 -41.8922660715677 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 12 0.871827040003008 0.256345919993984 0.128172959996992 13 0.795357544249061 0.409284911501877 0.204642455750939 14 0.842298420441598 0.315403159116804 0.157701579558402 15 0.849617741887723 0.300764516224554 0.150382258112277 16 0.785629767982804 0.428740464034391 0.214370232017196 17 0.844368393956662 0.311263212086677 0.155631606043338 18 0.821382080873025 0.357235838253951 0.178617919126975 19 0.858105772684601 0.283788454630798 0.141894227315399 20 0.856197613852305 0.28760477229539 0.143802386147695 21 0.809177738742812 0.381644522514376 0.190822261257188 22 0.813647797400158 0.372704405199684 0.186352202599842 23 0.770166746730189 0.459666506539622 0.229833253269811 24 0.7051387219687 0.5897225560626 0.2948612780313 25 0.617283049264262 0.765433901471475 0.382716950735738 26 0.518662659728251 0.962674680543498 0.481337340271749 27 0.461573451283702 0.923146902567405 0.538426548716298 28 0.378268864588856 0.756537729177712 0.621731135411144 29 0.337119073868308 0.674238147736616 0.662880926131692 30 0.860606205319787 0.278787589360425 0.139393794680213 31 0.957610029964452 0.0847799400710962 0.0423899700355481 32 0.935477820158575 0.129044359682850 0.0645221798414249 33 0.924670451324092 0.150659097351815 0.0753295486759075 34 0.886069000749422 0.227861998501156 0.113930999250578 35 0.818383865526791 0.363232268946418 0.181616134473209 36 0.938605981953897 0.122788036092206 0.0613940180461028 37 0.883860481162872 0.232279037674256 0.116139518837128 38 0.846297481779944 0.307405036440112 0.153702518220056 39 0.958974134460182 0.0820517310796369 0.0410258655398184 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 2 0.0714285714285714 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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