Paper - Multiple Regression trend 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 11:34:09 +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/t12929312081i5wtw148c0jzpd.htm/, Retrieved Tue, 21 Dec 2010 12:33:31 +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/2010/Dec/21/t12929312081i5wtw148c0jzpd.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 5 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation PC&S[t] = + 114.487750507981 -0.00127274618908405PCacao[t] -0.283150866571514PSuiker[t] + 0.346451616630639t + 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) 114.487750507981 3.093671 37.0071 0 0 PCacao -0.00127274618908405 0.000999 -1.2747 0.207992 0.103996 PSuiker -0.283150866571514 0.095611 -2.9615 0.004573 0.002287 t 0.346451616630639 0.043334 7.9949 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.961530688149687 R-squared 0.92454126425361 Adjusted R-squared 0.920270015060419 F-TEST (value) 216.456877703899 F-TEST (DF numerator) 3 F-TEST (DF denominator) 53 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1.68501670582991 Sum Squared Residuals 150.481908843071 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.31 104.534572517112 0.775427482887872 2 105.63 105.00397359492 0.626026405079763 3 106.02 105.374757305846 0.645242694153813 4 105.85 105.604333273461 0.245666726538768 5 106.57 105.424518512823 1.14548148717652 6 106.48 105.866787841166 0.613212158833689 7 106.6 106.121755164936 0.478244835064408 8 106.75 106.318394501125 0.43160549887489 9 106.69 106.75530268549 -0.0653026854899347 10 106.69 107.198756687763 -0.508756687762616 11 106.93 107.308664066528 -0.378664066528007 12 107.21 107.256528530103 -0.0465285301032079 13 107.88 107.625924947683 0.254075052316945 14 108.84 107.841861751539 0.998138248460927 15 108.96 108.089733550145 0.870266449854787 16 109.52 108.106408368064 1.41359163193576 17 108.45 108.502106437246 -0.052106437246497 18 108.67 108.837632582659 -0.167632582658841 19 108.96 108.783954210505 0.176045789494729 20 108.76 109.55848665897 -0.798486658970387 21 107.85 109.820438160032 -1.97043816003177 22 108.78 110.074268767515 -1.29426876751478 23 107.51 110.228850627173 -2.71885062717301 24 108.83 110.601977033661 -1.77197703366089 25 111.54 111.077612914294 0.462387085706446 26 111.74 111.062346547937 0.677653452063451 27 112.04 111.06306714077 0.976932859229601 28 111.74 111.538001851661 0.201998148338908 29 111.81 111.873270318232 -0.0632703182316416 30 111.86 111.813141758339 0.0468582416606035 31 114.23 112.13016280769 2.09983719230956 32 114.8 113.143469048846 1.6565309511543 33 115.17 114.081916578419 1.08808342158101 34 115.11 115.456647754174 -0.346647754174414 35 114.43 116.797563995916 -2.36756399591586 36 114.66 116.900243158265 -2.24024315826528 37 115.11 117.207373772353 -2.09737377235317 38 117.74 117.502334683879 0.237665316120569 39 118.18 118.159788616831 0.0202113831693081 40 118.56 118.235973144055 0.324026855944677 41 117.63 118.217730768964 -0.587730768963824 42 117.71 117.949232143527 -0.239232143526685 43 117.46 118.143949069125 -0.683949069124706 44 117.37 118.23852523491 -0.86852523490959 45 117.34 118.393326413624 -1.05332641362396 46 117.09 118.659836981482 -1.56983698148224 47 116.65 118.671972245084 -2.02197224508419 48 116.71 119.037891708856 -2.32789170885588 49 116.82 119.380364938831 -2.56036493883064 50 117.33 120.300767284155 -2.97076728415469 51 117.95 121.156997063415 -3.20699706341512 52 123.53 121.209447053525 2.32055294647468 53 124.91 121.917259086837 2.9927409131633 54 125.99 122.079753911741 3.91024608825893 55 126.29 122.231678158258 4.0583218417419 56 125.68 122.606247094918 3.07375290508243 57 125.52 123.362118974621 2.15788102537924 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.0019036663403363 0.00380733268067261 0.998096333659664 8 0.000396652723299419 0.000793305446598838 0.9996033472767 9 9.13287013048175e-05 0.000182657402609635 0.999908671298695 10 1.24427501362221e-05 2.48855002724441e-05 0.999987557249864 11 1.51689736132479e-06 3.03379472264957e-06 0.999998483102639 12 2.32744667210869e-07 4.65489334421739e-07 0.999999767255333 13 1.09995647289447e-07 2.19991294578893e-07 0.999999890004353 14 1.52479238185335e-07 3.0495847637067e-07 0.999999847520762 15 2.92920931337806e-08 5.85841862675612e-08 0.999999970707907 16 5.48597397505826e-09 1.09719479501165e-08 0.999999994514026 17 1.30876446225399e-07 2.61752892450798e-07 0.999999869123554 18 9.15791236022793e-08 1.83158247204559e-07 0.999999908420876 19 8.28414053050987e-08 1.65682810610197e-07 0.999999917158595 20 2.04351593364731e-08 4.08703186729463e-08 0.99999997956484 21 1.08068077297339e-07 2.16136154594677e-07 0.999999891931923 22 2.88735320803835e-08 5.7747064160767e-08 0.999999971126468 23 9.25209962446574e-07 1.85041992489315e-06 0.999999074790038 24 6.12273696198485e-07 1.22454739239697e-06 0.999999387726304 25 7.06309413645766e-06 1.41261882729153e-05 0.999992936905864 26 2.47565033706057e-06 4.95130067412115e-06 0.999997524349663 27 8.58346317336744e-07 1.71669263467349e-06 0.999999141653683 28 3.19236656982403e-07 6.38473313964805e-07 0.999999680763343 29 1.32577040988132e-07 2.65154081976263e-07 0.99999986742296 30 2.45824305781393e-07 4.91648611562786e-07 0.999999754175694 31 6.25617062709716e-07 1.25123412541943e-06 0.999999374382937 32 4.73806487255322e-06 9.47612974510643e-06 0.999995261935127 33 3.54599817573111e-05 7.09199635146222e-05 0.999964540018243 34 3.56053807494438e-05 7.12107614988876e-05 0.99996439461925 35 4.51164821847274e-05 9.02329643694548e-05 0.999954883517815 36 7.88488496893838e-05 0.000157697699378768 0.99992115115031 37 0.000102675783658726 0.000205351567317453 0.999897324216341 38 8.85772654964112e-05 0.000177154530992822 0.999911422734504 39 7.55729293468e-05 0.0001511458586936 0.999924427070653 40 6.8519524420848e-05 0.000137039048841696 0.99993148047558 41 3.10564128709167e-05 6.21128257418333e-05 0.99996894358713 42 1.61871922930673e-05 3.23743845861347e-05 0.999983812807707 43 7.68566442976524e-06 1.53713288595305e-05 0.99999231433557 44 8.40310086553699e-06 1.6806201731074e-05 0.999991596899134 45 0.00015479216296231 0.000309584325924621 0.999845207837038 46 0.00224598988688579 0.00449197977377158 0.997754010113114 47 0.209627426674064 0.419254853348128 0.790372573325936 48 0.294256866654595 0.588513733309189 0.705743133345405 49 0.238380640365474 0.476761280730947 0.761619359634526 50 0.206025755602722 0.412051511205443 0.793974244397278 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 40 0.909090909090909 NOK 5% type I error level 40 0.909090909090909 NOK 10% type I error level 40 0.909090909090909 NOK

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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