invoer-textiel

*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: Fri, 19 Dec 2008 12:19:44 -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/19/t1229714481w4ipy3jqv5uxpod.htm/, Retrieved Fri, 19 Dec 2008 20:21:31 +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/19/t1229714481w4ipy3jqv5uxpod.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:

» Textbox « » Textfile « » CSV «

101,3 163095 102 159044 109,2 155511 88,6 153745 94,3 150569 98,3 150605 86,4 179612 80,6 194690 104,1 189917 108,2 184128 93,4 175335 71,9 179566 94,1 181140 94,9 177876 96,4 175041 91,1 169292 84,4 166070 86,4 166972 88 206348 75,1 215706 109,7 202108 103 195411 82,1 193111 68 195198 96,4 198770 94,3 194163 90 190420 88 189733 76,1 186029 82,5 191531 81,4 232571 66,5 243477 97,2 227247 94,1 217859 80,7 208679 70,5 213188 87,8 216234 89,5 213586 99,6 209465 84,2 204045 75,1 200237 92 203666 80,8 241476 73,1 260307 99,8 243324 90 244460 83,1 233575 72,4 237217 78,8 235243 87,3 230354 91 227184 80,1 221678 73,6 217142 86,4 219452 74,5 256446 71,2 265845 92,4 248624 81,5 241114 85,3 229245 69,9 231805 84,2 219277 90,7 219313 100,3 212610 79,4 214771 84,8 211142 92,9 211457 81,6 240048 76 240636 98,7 230580 89,1 208795 88,7 197922 67,1 194596

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation textiel[t] = + 119.587170651848 -0.000157525651470813invoer[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) 119.587170651848 8.568266 13.957 0 0 invoer -0.000157525651470813 4.1e-05 -3.8404 0.000267 0.000133 Multiple Linear Regression - Regression Statistics Multiple R 0.417169352043602 R-squared 0.174030268284479 Adjusted R-squared 0.162230700688543 F-TEST (value) 14.7488682843275 F-TEST (DF numerator) 1 F-TEST (DF denominator) 70 p-value 0.000266815784297769 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.66788048947954 Sum Squared Residuals 6542.75392112014 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 101.3 93.8955245252155 7.40447547478451 2 102 94.533660939324 7.46633906067591 3 109.2 95.0901990659705 14.1098009340295 4 88.6 95.368389366468 -6.76838936646795 5 94.3 95.8686908355393 -1.56869083553925 6 98.3 95.8630199120863 2.43698008791370 7 86.4 91.2936733398724 -4.89367333987242 8 80.6 88.9185015669955 -8.31850156699551 9 104.1 89.6703715014657 14.4296284985343 10 108.2 90.5822874978302 17.6177125021698 11 93.4 91.9674105512131 1.43258944878691 12 71.9 91.30091951984 -19.4009195198401 13 94.1 91.052974144425 3.04702585557497 14 94.9 91.5671378708258 3.33286212917425 15 96.4 92.0137230927455 4.38627690725449 16 91.1 92.9193380630512 -1.81933806305122 17 84.4 93.4268857120902 -9.02688571209017 18 86.4 93.2847975744635 -6.8847975744635 19 88 87.0820675221488 0.91793247785123 20 75.1 85.6079424756849 -10.5079424756849 21 109.7 87.749976284385 21.950023715615 22 103 88.804925572285 14.1950744277149 23 82.1 89.1672345706679 -7.06723457066793 24 68 88.8384785360483 -20.8384785360483 25 96.4 88.2757969089946 8.12420309100541 26 94.3 89.0015175853206 5.29848241467937 27 90 89.5911360987759 0.408863901224119 28 88 89.6993562213363 -1.69935622133633 29 76.1 90.2828312343842 -14.1828312343842 30 82.5 89.4161250999918 -6.91612509999181 31 81.4 82.9512723636296 -1.55127236362964 32 66.5 81.233297608689 -14.7332976086890 33 97.2 83.7899389320603 13.4100610679398 34 94.1 85.2687897480682 8.83121025193175 35 80.7 86.7148752285703 -6.0148752285703 36 70.5 86.0045920660884 -15.5045920660884 37 87.8 85.5247689317083 2.27523106829168 38 89.5 85.941896856803 3.55810314319697 39 99.6 86.5910600665142 13.0089399334857 40 84.2 87.444849097486 -3.24484909748605 41 75.1 88.0447067782869 -12.9447067782869 42 92 87.5045513193935 4.49544868060651 43 80.8 81.548506437282 -0.748506437282053 44 73.1 78.5821408944352 -5.48214089443518 45 99.8 81.257399033364 18.542600966636 46 90 81.0784498932931 8.92155010670685 47 83.1 82.793116609553 0.30688339044705 48 72.4 82.2194081868962 -9.81940818689624 49 78.8 82.5303638228996 -3.73036382289963 50 87.3 83.3005067329404 3.99949326705956 51 91 83.7998630481029 7.20013695189709 52 80.1 84.6671992851012 -4.56719928510121 53 73.6 85.3817356401728 -11.7817356401728 54 86.4 85.0178513852752 1.38214861472477 55 74.5 79.190347434764 -4.69034743476398 56 71.2 77.7097638365898 -6.5097638365898 57 92.4 80.4225130805687 11.9774869194313 58 81.5 81.6055307231145 -0.105530723114485 59 85.3 83.4752026804216 1.82479731957843 60 69.9 83.0719370126563 -13.1719370126563 61 84.2 85.0454183742826 -0.845418374282626 62 90.7 85.0397474508297 5.66025254917032 63 100.3 86.0956418926385 14.2043581073615 64 79.4 85.7552289598101 -6.3552289598101 65 84.8 86.3268895489977 -1.52688954899770 66 92.9 86.2772689687844 6.62273103121562 67 81.6 81.7734530675824 -0.173453067582377 68 76 81.6808279845175 -5.68082798451753 69 98.7 83.264905935708 15.4350940642920 70 89.1 86.6966022529997 2.40339774700030 71 88.7 88.4093786614418 0.290621338558162 72 67.1 88.9333089782338 -21.8333089782338 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.441437726854991 0.882875453709983 0.558562273145009 6 0.289731546636518 0.579463093273035 0.710268453363482 7 0.356119907264102 0.712239814528205 0.643880092735898 8 0.252699714521562 0.505399429043125 0.747300285478438 9 0.478517095258312 0.957034190516623 0.521482904741688 10 0.619643599514412 0.760712800971176 0.380356400485588 11 0.525417322998815 0.94916535400237 0.474582677001185 12 0.825339714159902 0.349320571680196 0.174660285840098 13 0.762670639400259 0.474658721199482 0.237329360599741 14 0.692712659275566 0.614574681448869 0.307287340724434 15 0.622731038024096 0.754537923951808 0.377268961975904 16 0.549614842793713 0.900770314412574 0.450385157206287 17 0.551265766590414 0.897468466819171 0.448734233409586 18 0.514537937567737 0.970924124864525 0.485462062432263 19 0.433808867737925 0.86761773547585 0.566191132262075 20 0.429439604531466 0.858879209062933 0.570560395468534 21 0.73014589617468 0.539708207650641 0.269854103825321 22 0.782646745376907 0.434706509246187 0.217353254623093 23 0.762037457350626 0.475925085298749 0.237962542649374 24 0.904942636340231 0.190114727319537 0.0950573636597687 25 0.896562475110124 0.206875049779753 0.103437524889876 26 0.874649457838927 0.250701084322145 0.125350542161073 27 0.83662271366692 0.326754572666161 0.163377286333080 28 0.791856715913694 0.416286568172611 0.208143284086306 29 0.829176721175829 0.341646557648343 0.170823278824171 30 0.800638397415137 0.398723205169726 0.199361602584863 31 0.749094322652359 0.501811354695282 0.250905677347641 32 0.798705143893434 0.402589712213133 0.201294856106566 33 0.851383210936844 0.297233578126312 0.148616789063156 34 0.848554319786691 0.302891360426618 0.151445680213309 35 0.81748049306207 0.365039013875861 0.182519506937930 36 0.870446795434613 0.259106409130774 0.129553204565387 37 0.834233046923523 0.331533906152955 0.165766953076477 38 0.796711980925371 0.406576038149257 0.203288019074629 39 0.844804329439024 0.310391341121953 0.155195670560976 40 0.80158637711153 0.396827245776941 0.198413622888471 41 0.825477581694982 0.349044836610037 0.174522418305019 42 0.791816539098327 0.416366921803347 0.208183460901673 43 0.73792869925791 0.524142601484181 0.262071300742090 44 0.706759756884982 0.586480486230035 0.293240243115018 45 0.842786097486259 0.314427805027482 0.157213902513741 46 0.834920305004231 0.330159389991538 0.165079694995769 47 0.784838665778188 0.430322668443623 0.215161334221812 48 0.787642924901685 0.42471415019663 0.212357075098315 49 0.738174297681172 0.523651404637657 0.261825702318828 50 0.684184245398645 0.63163150920271 0.315815754601355 51 0.656551571181495 0.68689685763701 0.343448428818505 52 0.594250858183723 0.811498283632554 0.405749141816277 53 0.621024691651342 0.757950616697316 0.378975308348658 54 0.543020937630334 0.913958124739332 0.456979062369666 55 0.487621651752868 0.975243303505736 0.512378348247132 56 0.497965279983 0.995930559966 0.502034720017 57 0.486085462530791 0.972170925061582 0.513914537469209 58 0.40046359536768 0.80092719073536 0.59953640463232 59 0.315351806039726 0.630703612079452 0.684648193960274 60 0.428746119335819 0.857492238671637 0.571253880664181 61 0.336492634022713 0.672985268045426 0.663507365977287 62 0.264726832576032 0.529453665152064 0.735273167423968 63 0.384666772107881 0.769333544215762 0.615333227892119 64 0.302867255806089 0.605734511612179 0.69713274419391 65 0.202543932238644 0.405087864477287 0.797456067761356 66 0.171259444426702 0.342518888853403 0.828740555573299 67 0.102576586546251 0.205153173092501 0.89742341345375 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 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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