Model 4

*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: Sun, 20 Dec 2009 04:10:48 -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/20/t12613076061whrt61i4saljbh.htm/, Retrieved Sun, 20 Dec 2009 12:13:37 +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/20/t12613076061whrt61i4saljbh.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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86,0 88,4 90,7 95,3 100,0 94,7 86,0 86,0 88,4 90,7 95,3 110,6 95,3 86,0 86,0 88,4 90,7 71,3 95,3 95,3 86,0 86,0 88,4 104,1 88,4 95,3 95,3 86,0 86,0 112,3 86,0 88,4 95,3 95,3 86,0 110,2 81,4 86,0 88,4 95,3 95,3 112,9 83,7 81,4 86,0 88,4 95,3 95,1 95,3 83,7 81,4 86,0 88,4 103,1 88,4 95,3 83,7 81,4 86,0 101,9 86,0 88,4 95,3 83,7 81,4 100,4 83,7 86,0 88,4 95,3 83,7 106,9 76,7 83,7 86,0 88,4 95,3 100,7 79,1 76,7 83,7 86,0 88,4 114,3 86,0 79,1 76,7 83,7 86,0 73,3 86,0 86,0 79,1 76,7 83,7 105,9 79,1 86,0 86,0 79,1 76,7 113,9 76,7 79,1 86,0 86,0 79,1 112,1 69,8 76,7 79,1 86,0 86,0 117,5 69,8 69,8 76,7 79,1 86,0 97,5 76,7 69,8 69,8 76,7 79,1 112,3 69,8 76,7 69,8 69,8 76,7 106,9 67,4 69,8 76,7 69,8 69,8 120,9 65,1 67,4 69,8 76,7 69,8 92,7 58,1 65,1 67,4 69,8 76,7 110,9 60,5 58,1 65,1 67,4 69,8 116,5 65,1 60,5 58,1 65,1 67,4 77,1 62,8 65,1 60,5 58,1 65,1 113,1 55,8 62,8 65,1 60,5 58,1 115,9 51,2 55,8 62,8 65,1 60,5 123,5 48,8 51,2 55,8 62,8 65,1 123,6 48,8 48,8 51,2 55,8 62,8 101,5 53,5 4 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 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheid(Y(t))[t] = + 2.85103732321234 + 0.976127794666543`Y(t-1)`[t] + 0.236365899150279`Y(t-2)`[t] + 0.134593358559729`Y(t-3)`[t] -0.341976205796012`Y(t-4)`[t] -0.0864265177172897Productie[t] + 2.5704281506859M1[t] + 8.0452757771165M2[t] + 10.6852562679373M3[t] + 5.13454323216124M4[t] -2.36138688814796M5[t] + 0.840375791480767M6[t] + 3.94041195459863M7[t] + 7.0899908939364M8[t] + 13.9240510104693M9[t] + 0.826377650593013M10[t] + 1.18103914539342M11[t] + 0.0648222506919648t + 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) 2.85103732321234 10.306593 0.2766 0.783569 0.391784 `Y(t-1)` 0.976127794666543 0.151884 6.4268 0 0 `Y(t-2)` 0.236365899150279 0.217164 1.0884 0.283264 0.141632 `Y(t-3)` 0.134593358559729 0.216229 0.6225 0.537359 0.268679 `Y(t-4)` -0.341976205796012 0.173163 -1.9749 0.05558 0.02779 Productie -0.0864265177172897 0.055892 -1.5463 0.130315 0.065158 M1 2.5704281506859 2.406703 1.068 0.292246 0.146123 M2 8.0452757771165 2.084308 3.8599 0.000427 0.000213 M3 10.6852562679373 2.782161 3.8406 0.000452 0.000226 M4 5.13454323216124 2.873556 1.7868 0.081945 0.040973 M5 -2.36138688814796 2.513384 -0.9395 0.353395 0.176698 M6 0.840375791480767 1.792159 0.4689 0.641807 0.320904 M7 3.94041195459863 2.04567 1.9262 0.061582 0.030791 M8 7.0899908939364 2.597087 2.73 0.009546 0.004773 M9 13.9240510104693 2.239463 6.2176 0 0 M10 0.826377650593013 2.851568 0.2898 0.773547 0.386773 M11 1.18103914539342 2.563276 0.4608 0.647601 0.323801 t 0.0648222506919648 0.095957 0.6755 0.503428 0.251714 Multiple Linear Regression - Regression Statistics Multiple R 0.99638054568302 R-squared 0.992774191815591 Adjusted R-squared 0.989541593417303 F-TEST (value) 307.113371194316 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.03448320450095 Sum Squared Residuals 157.286632557065 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 86 83.6589070893564 2.34109291064364 2 86 85.9262057773954 0.0737942226046428 3 95.3 92.7238183292111 2.57618167078890 4 95.3 93.9446474661863 1.35535253381374 5 88.4 88.8237879072953 -0.423787907295282 6 86 86.7883049762286 -0.788304976228623 7 81.4 82.5658016669622 -1.16580166696223 8 83.7 81.3324346848708 2.36756531512918 9 95.3 90.7343274614483 4.56567253855169 10 88.4 89.8735256042379 -1.47352560423791 11 86 88.3118670445993 -2.31186704459934 12 83.7 83.4349840593609 0.265015940639098 13 76.7 78.8980886235964 -2.19808862359638 14 79.1 77.9224334885015 1.17756651149850 15 86 85.3700470387939 0.629952961206113 16 86 84.2136034806987 1.78639651930127 17 79.1 80.4388656745955 -1.33886567459555 18 76.7 77.2336878337599 -0.533687833759903 19 69.8 73.5985758205673 -3.79857582056726 20 69.8 70.3102532497208 -0.510253249720842 21 76.7 76.3357102100421 0.364289789957942 22 69.8 70.3968927995785 -0.596892799578531 23 67.4 66.8616840379591 0.538315962040915 24 65.1 65.1377577056107 -0.0377577056107264 25 58.1 60.0993434047856 -1.99934340478557 26 60.5 59.815100411429 0.684899588570984 27 65.1 67.1244315333738 -2.02443153337376 28 62.8 63.4290438873068 -0.629043887306756 29 55.8 57.3149884775548 -1.51498847755478 30 51.2 52.346582297977 -1.14658229797695 31 48.8 47.475393639148 1.32460636085203 32 48.8 49.0142227908515 -0.214222790851544 33 53.5 55.435213895826 -1.93521389582595 34 48.8 49.0007832636048 -0.200783263604812 35 46.5 45.5714430495826 0.928556950417436 36 44.2 43.8233230151309 0.376676984869109 37 39.5 40.0384940330097 -0.538494033009721 38 41.9 41.3728111235234 0.52718887647657 39 48.8 49.2002288447059 -0.400228844705945 40 46.5 47.9039321191682 -1.40393211916824 41 41.9 41.8062525572829 0.0937474427170518 42 39.5 38.9456307479733 0.554369252026719 43 37.2 36.529857880116 0.670142119884006 44 37.2 39.493317349177 -2.29331734917701 45 41.9 44.8947484326837 -2.99474843268369 46 39.5 37.2287983325787 2.27120166742125 47 39.5 38.655005867859 0.844994132140992 48 34.9 35.5039352198975 -0.603935219897477 49 34.9 32.5051668492520 2.39483315074803 50 34.9 37.3634491991507 -2.46344919915070 51 41.9 42.6814742539153 -0.781474253915302 52 41.9 43.00877304664 -1.10877304664000 53 39.5 36.3161053832714 3.18389461672855 54 39.5 37.5857941440612 1.91420585593875 55 41.9 38.9303709932065 2.96962900679346 56 46.5 45.8497719253798 0.650228074620219 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.511403350885411 0.977193298229179 0.488596649114589 22 0.344657621482333 0.689315242964666 0.655342378517667 23 0.841910465743089 0.316179068513823 0.158089534256911 24 0.749249662393189 0.501500675213622 0.250750337606811 25 0.707882230510599 0.584235538978803 0.292117769489401 26 0.645280988208059 0.709438023583883 0.354719011791941 27 0.579009633017837 0.841980733964325 0.420990366982163 28 0.495760638547543 0.991521277095086 0.504239361452457 29 0.432083966257842 0.864167932515684 0.567916033742158 30 0.492270091696039 0.984540183392078 0.507729908303961 31 0.582569273483456 0.834861453033089 0.417430726516544 32 0.447762107908364 0.895524215816728 0.552237892091636 33 0.401742253161213 0.803484506322425 0.598257746838787 34 0.410191879457695 0.82038375891539 0.589808120542305 35 0.303597315841075 0.60719463168215 0.696402684158925 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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