Model 4, kijken naar het verleden

*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: Wed, 16 Dec 2009 08:04:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/16/t12609764702h7sc6lvhuu5dfn.htm/, Retrieved Wed, 16 Dec 2009 16:14:42 +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/2009/Dec/16/t12609764702h7sc6lvhuu5dfn.htm/}, year = {2009}, } @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 = {2009}, 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:

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97.4 114 102.9 112.7 97 95.1 111.4 116 97.4 102.9 112.7 97 87.4 153 111.4 97.4 102.9 112.7 96.8 162 87.4 111.4 97.4 102.9 114.1 161 96.8 87.4 111.4 97.4 110.3 149 114.1 96.8 87.4 111.4 103.9 139 110.3 114.1 96.8 87.4 101.6 135 103.9 110.3 114.1 96.8 94.6 130 101.6 103.9 110.3 114.1 95.9 127 94.6 101.6 103.9 110.3 104.7 122 95.9 94.6 101.6 103.9 102.8 117 104.7 95.9 94.6 101.6 98.1 112 102.8 104.7 95.9 94.6 113.9 113 98.1 102.8 104.7 95.9 80.9 149 113.9 98.1 102.8 104.7 95.7 157 80.9 113.9 98.1 102.8 113.2 157 95.7 80.9 113.9 98.1 105.9 147 113.2 95.7 80.9 113.9 108.8 137 105.9 113.2 95.7 80.9 102.3 132 108.8 105.9 113.2 95.7 99 125 102.3 108.8 105.9 113.2 100.7 123 99 102.3 108.8 105.9 115.5 117 100.7 99 102.3 108.8 100.7 114 115.5 100.7 99 102.3 109.9 111 100.7 115.5 100.7 99 114.6 112 109.9 100.7 115.5 100.7 85.4 144 114.6 109.9 100.7 115.5 100.5 150 85.4 114.6 109.9 100.7 114.8 149 100.5 85.4 114.6 109.9 116.5 134 114.8 100.5 85.4 114.6 112.9 123 116.5 114.8 100.5 85.4 102 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = -38.0009327756717 + 0.0702381579760955X[t] + 0.121123120132540Y1[t] + 0.452742857897186Y2[t] + 0.733822466637121Y3[t] + 0.0310925954506842Y4[t] -4.98250336335315M1[t] + 0.511931555884507M2[t] -24.2147514902035M3[t] -13.8700341648047M4[t] + 4.55421564347214M5[t] + 17.3762426394411M6[t] -2.40026840685621M7[t] -20.1709936068584M8[t] -16.2763932431094M9[t] -7.26353676755452M10[t] + 7.27102447826702M11[t] -0.056984051960174t + 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) -38.0009327756717 47.006737 -0.8084 0.423756 0.211878 X 0.0702381579760955 0.147125 0.4774 0.635739 0.317869 Y1 0.121123120132540 0.164451 0.7365 0.465815 0.232908 Y2 0.452742857897186 0.154436 2.9316 0.005616 0.002808 Y3 0.733822466637121 0.185307 3.96 0.000309 0.000154 Y4 0.0310925954506842 0.205663 0.1512 0.880611 0.440306 M1 -4.98250336335315 3.398698 -1.466 0.150664 0.075332 M2 0.511931555884507 3.916573 0.1307 0.896677 0.448339 M3 -24.2147514902035 6.27432 -3.8593 0.000416 0.000208 M4 -13.8700341648047 8.073987 -1.7179 0.093752 0.046876 M5 4.55421564347214 6.980102 0.6525 0.517934 0.258967 M6 17.3762426394411 5.258601 3.3043 0.002048 0.001024 M7 -2.40026840685621 4.933543 -0.4865 0.629321 0.314661 M8 -20.1709936068584 4.983499 -4.0476 0.000237 0.000119 M9 -16.2763932431094 6.51345 -2.4989 0.016779 0.008389 M10 -7.26353676755452 5.493703 -1.3222 0.193818 0.096909 M11 7.27102447826702 4.006508 1.8148 0.077251 0.038625 t -0.056984051960174 0.107224 -0.5314 0.598123 0.299062 Multiple Linear Regression - Regression Statistics Multiple R 0.92390862741869 R-squared 0.853607151818689 Adjusted R-squared 0.789794884662732 F-TEST (value) 13.3768504060902 F-TEST (DF numerator) 17 F-TEST (DF denominator) 39 p-value 2.49332776647293e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 4.22248137423918 Sum Squared Residuals 695.344609276074 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 97.4 102.592104056102 -5.19210405610183 2 111.4 114.647062728769 -3.24706272876941 3 87.4 84.9645390147898 2.43546098521025 4 96.8 94.975129835472 1.82487016452801 5 114.1 113.647391431467 0.45260856853307 6 110.3 114.744346459308 -4.44434645930778 7 103.9 107.732362261979 -3.83236226197947 8 101.6 100.115488619314 1.48451138068626 9 94.6 98.1751532024511 -3.57515320245115 10 95.9 100.216525088836 -4.31652508883601 11 104.7 109.444387259559 -4.74438725955913 12 102.8 98.2113668758878 4.58863312411224 13 98.1 97.3110129304108 0.788987069589157 14 113.9 107.887269941529 6.01273005847063 15 80.9 84.2973825499535 -3.39738254995349 16 95.7 94.7952537530518 0.904746246948233 17 113.2 111.462887150971 1.73711284902876 18 105.9 108.620919023513 -2.72091902351273 19 108.8 104.958360438084 3.84163956191573 20 102.3 97.127758160796 5.17224183920394 21 99 96.1865777877286 2.8134222122714 22 100.7 103.560548229060 -2.86054822905963 23 115.5 111.648876841895 3.85112315810527 24 100.7 104.048722863794 -3.34872286379412 25 109.9 104.851385721765 5.04861427823489 26 114.6 115.686243073855 -1.08624307385528 27 85.4 87.4843078947599 -2.08430789475992 28 100.5 103.075562720693 -2.57556272069307 29 114.8 113.716475453778 1.08352454622203 30 116.5 112.714942973102 3.78505702689751 31 112.9 108.961775768324 3.93822423167648 32 102 101.939178500693 0.0608214993073078 33 106 104.589038980811 1.41096101918897 34 105.3 106.084174318372 -0.784174318372481 35 118.8 113.755909581906 5.04409041809384 36 106.1 110.131809275148 -4.03180927514797 37 109.3 108.785114365087 0.514885634912531 38 117.2 118.604687088328 -1.40468708832829 39 92.5 89.50425739415 2.99574260585008 40 104.2 102.751703056574 1.44829694342579 41 112.5 116.8286255724 -4.32862557240002 42 122.4 117.384155007245 5.01584499275535 43 113.3 109.693136849083 3.60686315091651 44 100 101.629633178982 -1.62963317898212 45 110.7 107.259262948092 3.44073705190798 46 112.8 104.838752363732 7.96124763626811 47 109.8 113.95082631664 -4.15082631663997 48 117.3 114.508100985170 2.79189901482985 49 109.1 110.260382926635 -1.16038292663474 50 115.9 116.174737167518 -0.274737167517643 51 96 95.949513146347 0.0504868536530736 52 99.8 101.402350634209 -1.60235063420896 53 116.8 115.744620391384 1.05537960861616 54 115.7 117.335636536832 -1.63563653683234 55 99.4 106.954364682529 -7.55436468252923 56 94.3 99.3879415402154 -5.08794154021538 57 91 95.0899670809172 -4.0899670809172 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.64706550254988 0.705868994900239 0.352934497450120 22 0.628010871146624 0.743978257706752 0.371989128853376 23 0.531717741698212 0.936564516603575 0.468282258301788 24 0.625776461342083 0.748447077315834 0.374223538657917 25 0.559425704967485 0.88114859006503 0.440574295032515 26 0.439845004034697 0.879690008069394 0.560154995965303 27 0.432664097214060 0.865328194428119 0.56733590278594 28 0.340267138540383 0.680534277080765 0.659732861459617 29 0.245235547546132 0.490471095092263 0.754764452453868 30 0.29218705964853 0.58437411929706 0.70781294035147 31 0.414777800044649 0.829555600089297 0.585222199955351 32 0.393943039723842 0.787886079447683 0.606056960276158 33 0.419715160409991 0.839430320819981 0.580284839590009 34 0.496584289689892 0.993168579379785 0.503415710310108 35 0.697338152570744 0.605323694858512 0.302661847429256 36 0.524833090136734 0.950333819726532 0.475166909863266 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 = Include Monthly Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly 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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