Paper - Multiple Regression zonder noten

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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: Tue, 21 Dec 2010 11:18:37 +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/21/t1292930451snjguzuk6go2isj.htm/, Retrieved Tue, 21 Dec 2010 12:20:54 +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/21/t1292930451snjguzuk6go2isj.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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105.31 1576.23 29.29 105.63 1546.37 28.99 106.02 1545.05 28.91 105.85 1552.34 29.29 106.57 1594.3 30.96 106.48 1605.78 30.57 106.60 1673.21 30.59 106.75 1612.94 31.39 106.69 1566.34 31.28 106.69 1530.17 31.1 106.93 1582.54 31.7 107.21 1702.16 32.57 107.88 1701.93 32.49 108.84 1811.15 32.46 108.96 1924.2 32.3 109.52 2034.25 32.97 108.45 2011.13 32.9 108.67 2013.04 32.93 108.96 2151.67 33.72 108.76 1902.09 33.33 107.85 1944.01 33.44 108.78 1916.67 33.89 107.51 1967.31 34.34 108.83 2119.88 33.56 111.54 2216.38 32.67 111.74 2522.83 32.57 112.04 2647.64 33.23 111.74 2631.23 32.85 111.81 2693.41 32.61 111.86 3021.76 32.57 114.23 2953.67 32.98 114.80 2796.8 31.33 115.17 2672.05 29.8 115.11 2251.23 28.06 114.43 2046.08 25.47 114.66 2420.04 24.65 115.11 2608.89 23.94 117.74 2660.47 23.89 118.18 2493.98 23.54 118.56 2541.7 24.28 117.63 2554.6 25.51 117.71 2699.61 27.03 117.46 2805.48 27.09 117.37 2956.66 27.3 117.34 3149.51 27.11 117.09 3372.5 26.39 116.65 3379.33 27.54 11 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 PC&S[t] = + 119.883087082453 + 0.00593299378877386PCacao[t] -0.714042903039172PSuiker[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) 119.883087082453 4.442558 26.9851 0 0 PCacao 0.00593299378877386 0.000632 9.3822 0 0 PSuiker -0.714042903039172 0.116204 -6.1447 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.912982305798785 R-squared 0.833536690701666 Adjusted R-squared 0.827371382949876 F-TEST (value) 135.197904834457 F-TEST (DF numerator) 2 F-TEST (DF denominator) 54 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.47941809058175 Sum Squared Residuals 331.965759666818 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.31 108.320533252115 -3.01053325211469 2 105.63 108.357586928494 -2.72758692849363 3 106.02 108.406878808936 -2.38687880893557 4 105.85 108.178794030501 -2.32879403050085 5 106.57 107.235290801802 -0.665290801802381 6 106.48 107.581878302683 -1.10187830268277 7 106.6 107.967659215799 -1.36765921579902 8 106.75 107.038843357718 -0.288843357718276 9 106.69 106.840910566496 -0.150910566495724 10 106.69 106.754841903703 -0.064841903702825 11 106.93 106.637127046597 0.292872953402599 12 107.21 106.725614437966 0.484385562033536 13 107.88 106.781373281638 1.09862671836182 14 108.84 107.450796150339 1.38920384966077 15 108.96 108.235767962646 0.72423203735361 16 109.52 108.410285184065 1.1097148159353 17 108.45 108.323097370881 0.126902629119011 18 108.67 108.313008101926 0.356991898073628 19 108.96 108.571405137463 0.388594862536845 20 108.76 107.369125279846 1.39087472015376 21 107.85 107.539291660137 0.310708339862657 22 108.78 107.055764303585 1.72423569641537 23 107.51 107.034891802681 0.475108197319495 24 108.83 108.497042129404 0.332957870595705 25 111.54 109.705074213726 1.83492578627417 26 111.74 111.5946444506 0.145355549400494 27 112.04 111.863873089371 0.176126910629491 28 111.74 112.037848964452 -0.297848964451624 29 111.81 112.578132814967 -0.768132814966977 30 111.86 114.554793041632 -2.69479304163245 31 114.23 113.858057904309 0.37194209569123 32 114.8 114.105519958678 0.694480041321547 33 115.17 114.457864625179 0.712135374821159 34 115.11 113.203576830275 1.90642316972481 35 114.43 113.83579427338 0.594205726620325 36 114.66 116.640011811122 -1.98001181112168 37 115.11 118.267428149289 -3.15742814928943 38 117.74 118.609154114066 -0.869154114066347 39 118.18 117.871284994237 0.308715005762913 40 118.56 117.626015709588 0.933984290411609 41 117.63 116.824278558725 0.8057214412746 42 117.71 116.599276775416 1.11072322458404 43 117.46 117.184560253651 0.275439746348901 44 117.37 117.931561245 -0.561561244999693 45 117.34 119.211407248742 -1.87140724874218 46 117.09 121.048516423889 -3.95851642388906 47 116.65 120.267889432971 -3.61788943297134 48 116.71 121.580578107615 -4.87057810761481 49 116.82 121.660142733836 -4.84014273383597 50 117.33 120.855884494333 -3.52588449433278 51 117.95 120.39145048208 -2.44145048208039 52 123.53 120.867012407967 2.66298759203315 53 124.91 121.257155523107 3.6528444768933 54 125.99 121.402793202941 4.58720679705946 55 126.29 120.885816818764 5.40418318123645 56 125.68 119.514024228041 6.16597577195886 57 125.52 118.52077010063 6.99922989936984 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 6 0.00262944060191681 0.00525888120383363 0.997370559398083 7 0.000671995370219654 0.00134399074043931 0.99932800462978 8 7.84089128754805e-05 0.000156817825750961 0.999921591087125 9 8.31006631406678e-06 1.66201326281336e-05 0.999991689933686 10 8.59777244138035e-07 1.71955448827607e-06 0.999999140222756 11 7.91459703656312e-08 1.58291940731262e-07 0.99999992085403 12 7.65550100895781e-09 1.53110020179156e-08 0.999999992344499 13 5.74599545370543e-09 1.14919909074109e-08 0.999999994254005 14 2.04884649190072e-08 4.09769298380144e-08 0.999999979511535 15 2.70382098527279e-09 5.40764197054558e-09 0.99999999729618 16 3.60204764253826e-10 7.20409528507652e-10 0.999999999639795 17 6.9958447967448e-10 1.39916895934896e-09 0.999999999300415 18 1.78482463203316e-10 3.56964926406631e-10 0.999999999821518 19 1.49947438319745e-10 2.99894876639489e-10 0.999999999850053 20 2.2134667581953e-11 4.4269335163906e-11 0.999999999977865 21 3.1543537573233e-11 6.3087075146466e-11 0.999999999968456 22 4.92081117318807e-12 9.84162234637614e-12 0.99999999999508 23 6.21649106976868e-11 1.24329821395374e-10 0.999999999937835 24 1.3090986113522e-11 2.6181972227044e-11 0.99999999998691 25 3.20242502681842e-10 6.40485005363685e-10 0.999999999679758 26 6.93344004448647e-11 1.38668800889729e-10 0.999999999930666 27 1.52502490800022e-11 3.05004981600044e-11 0.99999999998475 28 3.31783880273398e-12 6.63567760546795e-12 0.999999999996682 29 7.58919810928779e-13 1.51783962185756e-12 0.999999999999241 30 2.05398409090948e-12 4.10796818181896e-12 0.999999999997946 31 1.56492061223863e-12 3.12984122447726e-12 0.999999999998435 32 2.52783075877829e-11 5.05566151755658e-11 0.999999999974722 33 5.0297472905076e-10 1.00594945810152e-09 0.999999999497025 34 5.10769701107677e-08 1.02153940221535e-07 0.99999994892303 35 8.81892639576383e-08 1.76378527915277e-07 0.999999911810736 36 5.29516759194689e-08 1.05903351838938e-07 0.999999947048324 37 1.26615890504022e-07 2.53231781008044e-07 0.99999987338411 38 1.66227228287562e-07 3.32454456575125e-07 0.999999833772772 39 9.80993800405661e-07 1.96198760081132e-06 0.9999990190062 40 9.18005680279354e-06 1.83601136055871e-05 0.999990819943197 41 6.3925942436551e-05 0.000127851884873102 0.999936074057563 42 4.80205792414452e-05 9.60411584828905e-05 0.999951979420759 43 3.29770690296893e-05 6.59541380593786e-05 0.99996702293097 44 2.02683431865625e-05 4.0536686373125e-05 0.999979731656813 45 1.84107114880467e-05 3.68214229760933e-05 0.999981589288512 46 5.25028542541051e-05 0.00010500570850821 0.999947497145746 47 5.01782394262971e-05 0.000100356478852594 0.999949821760574 48 6.46030177335705e-05 0.000129206035467141 0.999935396982266 49 5.82346797494907e-05 0.000116469359498981 0.99994176532025 50 0.00226771103711088 0.00453542207422177 0.997732288962889 51 0.571679149399627 0.856641701200747 0.428320850600373 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 45 0.978260869565217 NOK 5% type I error level 45 0.978260869565217 NOK 10% type I error level 45 0.978260869565217 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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