PAPER - maandinvloed

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R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Sun, 19 Dec 2010 15:48:17 +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/19/t1292773672c4hig5prfqe5b5c.htm/, Retrieved Sun, 19 Dec 2010 16:47:55 +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/19/t1292773672c4hig5prfqe5b5c.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}, }

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Dataseries X:

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104,37 167.16 101,56 100,93 1 104,89 179.84 102,13 101,18 2 105,15 174.44 102,39 101,11 3 105,72 180.35 102,42 102,42 4 106,38 193.17 103,87 102,37 5 106,40 195.16 104,44 101,95 6 106,47 202.43 104,97 102,20 7 106,59 189.91 105,17 103,35 8 106,76 195.98 105,35 103,65 9 107,35 212.09 104,65 102,06 10 107,81 205.81 106,62 102,66 11 108,03 204.31 107,05 102,32 12 109,08 196.07 112,30 102,21 1 109,86 199.98 114,70 102,33 2 110,29 199.1 115,40 104,41 3 110,34 198.31 115,64 104,33 4 110,59 195.72 115,66 105,27 5 110,64 223.04 114,50 105,34 6 110,83 238.41 115,14 104,88 7 111,51 259.73 115,41 105,49 8 113,32 326.54 119,32 105,90 9 115,89 335.15 124,77 105,39 10 116,51 321.81 130,96 104,40 11 117,44 368.62 141,02 106,19 12 118,25 369.59 150,60 106,54 1 118,65 425 151,10 108,26 2 118,52 439.72 157,19 106,95 3 119,07 362.23 157,28 108,32 4 119,12 328.76 156,54 108,35 5 119,28 348.55 159,62 109,29 6 119,30 328.18 163,77 109,46 7 119,44 329.34 165,08 109,50 8 119,57 295.55 164,75 109,84 9 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 6 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation Brood[t] = + 26.9368149549099 + 0.00691507030535941Tarwe[t] + 0.14533634271945Meel[t] + 0.617258582045496Water[t] + 0.0919681490672806Maand[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) 26.9368149549099 10.936337 2.4631 0.017123 0.008562 Tarwe 0.00691507030535941 0.002812 2.4589 0.017301 0.00865 Meel 0.14533634271945 0.020765 6.999 0 0 Water 0.617258582045496 0.123112 5.0138 7e-06 3e-06 Maand 0.0919681490672806 0.04176 2.2023 0.0321 0.01605 Multiple Linear Regression - Regression Statistics Multiple R 0.983371743070837 R-squared 0.967019985070176 Adjusted R-squared 0.964483060844805 F-TEST (value) 381.178111430868 F-TEST (DF numerator) 4 F-TEST (DF denominator) 52 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.06188809433039 Sum Squared Residuals 58.6355288937926 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.37 105.24497390866 -0.874973908660293 2 104.89 105.661781510061 -0.771781510060987 3 105.15 105.710987627843 -0.560987627843191 4 105.72 106.656792675176 -0.936792675176336 5 106.38 107.017286793399 -0.637286793399259 6 106.4 106.946609043265 -0.54660904326517 7 106.47 107.320192660605 -0.850192660605103 8 106.59 108.064498767345 -1.47449876734548 9 106.76 108.409779509469 -1.64977950946945 10 107.35 107.5299728558 -0.179972855800128 11 107.81 108.235182107734 -0.425182107734355 12 108.03 108.169404360817 -0.13940436081749 13 109.08 107.795891897013 1.28410810298664 14 109.86 108.337776223347 1.52222377665327 15 110.29 109.809292401104 0.480707598896462 16 110.34 109.881297680319 0.458702319681384 17 110.59 110.538485591272 0.0515144087278311 18 110.64 110.693991404271 -0.0539914042704987 19 110.83 110.701320495531 0.128679504469329 20 111.51 111.35648649109 0.153513508909789 21 113.32 112.73179160593 0.588208394069724 22 115.89 113.360579701304 2.52942029869551 23 116.51 113.648846777707 2.86115322229336 24 117.44 116.631485837387 0.808514162613097 25 118.25 117.234906482811 1.01509351718873 26 118.65 118.844391609976 -0.194391609976491 27 118.52 119.114639178621 -0.594639178620524 28 119.07 119.529483057973 -0.459483057972582 29 119.12 119.300972667768 -0.180972667768443 30 119.28 120.557649060877 -1.27764906087747 31 119.3 121.216837009058 -1.91683700905803 32 119.44 121.531907591924 -2.09190759192383 33 119.57 121.552122440171 -1.98212244017107 34 119.93 120.437508122475 -0.507508122475135 35 120.03 119.924819339298 0.10518066070232 36 119.66 119.731424107737 -0.0714241077371322 37 119.46 120.054501426214 -0.594501426213957 38 119.48 119.424315868105 0.0556841318953103 39 119.56 119.380415688488 0.179584311512184 40 119.43 118.739285269569 0.690714730430552 41 119.57 118.679978516861 0.890021483139059 42 119.59 119.229529877343 0.36047012265742 43 119.5 118.772874568734 0.727125431266112 44 119.54 118.916882274833 0.623117725166798 45 119.56 119.502892654527 0.0571073454729357 46 119.61 118.858021127093 0.751978872907436 47 119.64 119.003987803479 0.636012196521126 48 119.6 117.781330995047 1.8186690049528 49 119.71 117.798238861161 1.91176113883943 50 119.72 119.009238478778 0.710761521222345 51 119.66 119.303744212736 0.356255787264052 52 119.76 119.551445835026 0.208554164974476 53 119.8 119.655193085424 0.144806914575532 54 119.88 120.419492482171 -0.539492482170778 55 119.78 120.455532536769 -0.675532536769455 56 120.08 120.983294195006 -0.90329419500576 57 120.22 121.238435647497 -1.01843564749659 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.0179510353437288 0.0359020706874577 0.982048964656271 9 0.00786290964127806 0.0157258192825561 0.992137090358722 10 0.00182285617448373 0.00364571234896747 0.998177143825516 11 0.00132415441248646 0.00264830882497293 0.998675845587514 12 0.000526344579975682 0.00105268915995136 0.999473655420024 13 0.00046636516578076 0.000932730331561519 0.99953363483422 14 0.000129006009256283 0.000258012018512566 0.999870993990744 15 3.6300086366172e-05 7.2600172732344e-05 0.999963699913634 16 1.09999878616509e-05 2.19999757233018e-05 0.999989000012138 17 6.10061922761496e-06 1.22012384552299e-05 0.999993899380772 18 4.33893330486185e-06 8.6778666097237e-06 0.999995661066695 19 2.44999786395372e-05 4.89999572790744e-05 0.99997550002136 20 0.000838897325757385 0.00167779465151477 0.999161102674243 21 0.121003365074157 0.242006730148313 0.878996634925843 22 0.175925483504095 0.351850967008191 0.824074516495905 23 0.904156302542942 0.191687394914116 0.095843697457058 24 0.999999999715778 5.68444904657157e-10 2.84222452328579e-10 25 0.99999999999866 2.67929001295145e-12 1.33964500647573e-12 26 0.999999999999643 7.14245123591491e-13 3.57122561795746e-13 27 0.999999999999931 1.38188460959554e-13 6.90942304797768e-14 28 0.99999999999986 2.7888188213317e-13 1.39440941066585e-13 29 0.999999999999447 1.10689154527527e-12 5.53445772637635e-13 30 0.99999999999877 2.45961707708046e-12 1.22980853854023e-12 31 0.999999999998586 2.827602372973e-12 1.4138011864865e-12 32 0.99999999999796 4.07872844219966e-12 2.03936422109983e-12 33 0.99999999999812 3.75861781349372e-12 1.87930890674686e-12 34 0.999999999996754 6.49278539575786e-12 3.24639269787893e-12 35 0.999999999999505 9.89360755214046e-13 4.94680377607023e-13 36 0.9999999999979 4.19903913382688e-12 2.09951956691344e-12 37 0.999999999994474 1.10522288376817e-11 5.52611441884083e-12 38 0.999999999977245 4.55101375128955e-11 2.27550687564477e-11 39 0.999999999850218 2.99563913888552e-10 1.49781956944276e-10 40 0.999999999465894 1.06821283858483e-09 5.34106419292417e-10 41 0.999999996436699 7.12660268616598e-09 3.56330134308299e-09 42 0.999999990544126 1.89117485489977e-08 9.45587427449883e-09 43 0.999999980089708 3.9820583670797e-08 1.99102918353985e-08 44 0.999999953719719 9.25605625314703e-08 4.62802812657352e-08 45 0.999999838322902 3.2335419512058e-07 1.6167709756029e-07 46 0.999998530556565 2.93888686940062e-06 1.46944343470031e-06 47 0.999986880602227 2.62387955452412e-05 1.31193977726206e-05 48 0.999874095896826 0.000251808206347456 0.000125904103173728 49 0.999429799221052 0.00114040155789652 0.00057020077894826 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 37 0.880952380952381 NOK 5% type I error level 39 0.928571428571429 NOK 10% type I error level 39 0.928571428571429 NOK

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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