bbb

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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 16:21:48 +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/t1292775622ufnr5bj0mr3msr9.htm/, Retrieved Sun, 19 Dec 2010 17:20:22 +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/t1292775622ufnr5bj0mr3msr9.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?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

104,37 1 1 167.16 101,56 100,93 104,89 2 2 179.84 102,13 101,18 105,15 3 3 174.44 102,39 101,11 105,72 4 4 180.35 102,42 102,42 106,38 5 5 193.17 103,87 102,37 106,40 6 6 195.16 104,44 101,95 106,47 7 7 202.43 104,97 102,20 106,59 8 8 189.91 105,17 103,35 106,76 9 9 195.98 105,35 103,65 107,35 10 10 212.09 104,65 102,06 107,81 11 11 205.81 106,62 102,66 108,03 12 12 204.31 107,05 102,32 109,08 1 13 196.07 112,30 102,21 109,86 2 14 199.98 114,70 102,33 110,29 3 15 199.1 115,40 104,41 110,34 4 16 198.31 115,64 104,33 110,59 5 17 195.72 115,66 105,27 110,64 6 18 223.04 114,50 105,34 110,83 7 19 238.41 115,14 104,88 111,51 8 20 259.73 115,41 105,49 113,32 9 21 326.54 119,32 105,90 115,89 10 22 335.15 124,77 105,39 116,51 11 23 321.81 130,96 104,40 117,44 12 24 368.62 141,02 106,19 118,25 1 25 369.59 150,60 106,54 118,65 2 26 425 151,10 108,26 118,52 3 27 439.72 157,19 106,95 119,07 4 28 362.23 157,28 108,32 119,12 5 29 328.76 156,54 108,35 119,28 6 30 348.55 159,62 109,29 119,30 7 31 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Brood[t] = + 86.2737357314676 + 0.0469329787978492Maand[t] + 0.140300419345309Trend[t] + 0.0119520172881480Tarwe[t] + 0.136581920664192Meel[t] + 0.0278949529470116Water[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) 86.2737357314676 13.330912 6.4717 0 0 Maand 0.0469329787978492 0.033617 1.3961 0.168728 0.084364 Trend 0.140300419345309 0.024151 5.8093 0 0 Tarwe 0.0119520172881480 0.002367 5.0487 6e-06 3e-06 Meel 0.136581920664192 0.016335 8.3611 0 0 Water 0.0278949529470116 0.139972 0.1993 0.842828 0.421414 Multiple Linear Regression - Regression Statistics Multiple R 0.990026897365883 R-squared 0.980153257507916 Adjusted R-squared 0.978207498440064 F-TEST (value) 503.738244730502 F-TEST (DF numerator) 5 F-TEST (DF denominator) 51 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.831791597301993 Sum Squared Residuals 35.2857403284523 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 104.37 105.145565803095 -0.775565803094795 2 104.89 105.569176213467 -0.679176213466997 3 105.15 105.725427370921 -0.575427370920542 4 105.72 106.023937037217 -0.303937037217179 5 106.38 106.561044334310 -0.181044334310126 6 106.4 106.838198061398 -0.438198061397531 7 106.47 107.191684781414 -0.721684781414306 8 106.59 107.288674503132 -0.698674503131749 9 106.76 107.581409877818 -0.82140987781762 10 107.35 107.821229954822 -0.471229954822171 11 107.81 108.219208039872 -0.409208039872416 12 108.03 108.437759353967 -0.407759353966970 13 109.08 108.677299022744 0.402700977255563 14 109.86 109.242408812432 0.617591187568045 15 110.29 109.572753281956 0.717246718043745 16 110.34 109.781092651165 0.558907348834577 17 110.59 109.966323218716 0.623676781284248 18 110.64 110.323603347907 0.316396652093056 19 110.83 110.769120002638 0.0608799973616042 20 111.51 111.265063449242 0.244936550758131 21 113.32 112.796283362911 0.523716637088532 22 115.89 113.816568671522 2.07343132847756 23 116.51 114.662188244536 1.84781175546449 24 117.44 116.832841659594 0.6071583404062 25 118.25 117.786690802427 0.463309197573323 26 118.65 118.752455757907 -0.102455757907064 27 118.52 119.910864359016 -1.39086435901611 28 119.07 119.222444395898 -0.152444395897871 29 119.12 118.909410002704 0.210589997296388 30 119.28 119.780067394395 -0.500067394395126 31 119.3 120.295395313136 -0.995395313136102 32 119.44 120.676531165521 -1.23653116552148 33 119.57 120.424318149681 -0.854318149680924 34 119.93 119.773342129457 0.156657870543317 35 120.03 118.975996574307 1.05400342569291 36 119.66 118.532674987929 1.12732501207087 37 119.46 118.891890974311 0.568109025688831 38 119.48 118.635211602429 0.84478839757137 39 119.56 118.894717980257 0.665282019743291 40 119.43 118.859380413315 0.570619586685042 41 119.57 119.290661257077 0.279338742922919 42 119.59 119.409574178347 0.180425821652910 43 119.5 119.262856169685 0.237143830315206 44 119.54 119.281437074797 0.258562925203140 45 119.56 119.187278753438 0.372721246562096 46 119.61 119.370429208077 0.239570791923080 47 119.64 119.492666139166 0.147333860834233 48 119.6 119.373615682524 0.226384317475989 49 119.71 119.047646323778 0.66235367622155 50 119.72 119.122860238803 0.597139761196748 51 119.66 119.504576605493 0.155423394507061 52 119.76 119.632573259386 0.127426740613803 53 119.8 120.111823314196 -0.311823314196292 54 119.88 120.342021731695 -0.462021731695 55 119.78 121.122715611642 -1.34271561164224 56 120.08 121.904962255848 -1.82496225584834 57 120.22 122.302049136561 -2.08204913656087 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.0550575586782799 0.110115117356560 0.94494244132172 10 0.0169701677790844 0.0339403355581687 0.983029832220916 11 0.0125536731703830 0.0251073463407661 0.987446326829617 12 0.00625798421548152 0.0125159684309630 0.993742015784518 13 0.0020334853641235 0.004066970728247 0.997966514635876 14 0.000755968930355649 0.00151193786071130 0.999244031069644 15 0.000284385173187904 0.000568770346375807 0.999715614826812 16 9.8821501049854e-05 0.000197643002099708 0.99990117849895 17 3.78605267089099e-05 7.57210534178198e-05 0.999962139473291 18 3.25076415995319e-05 6.50152831990637e-05 0.9999674923584 19 0.000182038534042769 0.000364077068085537 0.999817961465957 20 0.00390034974431261 0.00780069948862521 0.996099650255687 21 0.183193624662647 0.366387249325294 0.816806375337353 22 0.39187059460027 0.78374118920054 0.60812940539973 23 0.86036129998349 0.279277400033021 0.139638700016511 24 0.999988421601017 2.31567979667903e-05 1.15783989833952e-05 25 0.999999756588795 4.86822409450413e-07 2.43411204725206e-07 26 0.999999823014463 3.53971074895282e-07 1.76985537447641e-07 27 0.999999999182296 1.63540728488650e-09 8.17703642443248e-10 28 0.999999996708831 6.58233727334197e-09 3.29116863667099e-09 29 0.99999998873639 2.25272199547836e-08 1.12636099773918e-08 30 0.999999964430545 7.11389105865679e-08 3.55694552932840e-08 31 0.99999996419112 7.16177603627023e-08 3.58088801813511e-08 32 0.999999974426828 5.11463434041318e-08 2.55731717020659e-08 33 0.999999984582514 3.08349728975206e-08 1.54174864487603e-08 34 0.99999996766251 6.46749810209135e-08 3.23374905104567e-08 35 0.999999999988272 2.34553392907448e-11 1.17276696453724e-11 36 0.999999999998836 2.32867266970921e-12 1.16433633485460e-12 37 0.99999999998986 2.02790167012056e-11 1.01395083506028e-11 38 0.999999999915955 1.68089901524581e-10 8.40449507622904e-11 39 0.999999999802853 3.94294645621236e-10 1.97147322810618e-10 40 0.999999998946143 2.10771356126984e-09 1.05385678063492e-09 41 0.999999994702195 1.05956107182679e-08 5.29780535913394e-09 42 0.999999963598168 7.28036631610388e-08 3.64018315805194e-08 43 0.999999769829284 4.60341432793175e-07 2.30170716396587e-07 44 0.99999817330792 3.65338415838868e-06 1.82669207919434e-06 45 0.999984197639338 3.16047213247703e-05 1.58023606623851e-05 46 0.999877167920207 0.000245664159586575 0.000122832079793288 47 0.999113176950657 0.00177364609868612 0.000886823049343058 48 0.993649568149025 0.0127008637019498 0.00635043185097492 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 32 0.8 NOK 5% type I error level 36 0.9 NOK 10% type I error level 36 0.9 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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