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: Thu, 19 Nov 2009 14:22:17 -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/Nov/19/t1258665827hr1xta6gr7zhaav.htm/, Retrieved Thu, 19 Nov 2009 22:23:58 +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/Nov/19/t1258665827hr1xta6gr7zhaav.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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3,7 91,1 88 109,9 96,8 96,2 3,7 106,4 91,1 88 109,9 96,8 4,1 68,6 106,4 91,1 88 109,9 4,1 100,1 68,6 106,4 91,1 88 3,8 108 100,1 68,6 106,4 91,1 3,7 106 108 100,1 68,6 106,4 3,5 108,6 106 108 100,1 68,6 3,6 91,5 108,6 106 108 100,1 4,1 99,2 91,5 108,6 106 108 3,8 98 99,2 91,5 108,6 106 3,7 96,6 98 99,2 91,5 108,6 3,6 102,8 96,6 98 99,2 91,5 3,3 96,9 102,8 96,6 98 99,2 3,4 110 96,9 102,8 96,6 98 3,7 70,5 110 96,9 102,8 96,6 3,7 101,9 70,5 110 96,9 102,8 3,4 109,6 101,9 70,5 110 96,9 3,3 107,8 109,6 101,9 70,5 110 3 113 107,8 109,6 101,9 70,5 3 93,8 113 107,8 109,6 101,9 3,3 108 93,8 113 107,8 109,6 3 102,8 108 93,8 113 107,8 2,9 116,3 102,8 108 93,8 113 2,8 89,2 116,3 102,8 108 93,8 2,5 106,7 89,2 116,3 102,8 108 2,6 112,1 106,7 89,2 116,3 102,8 2,8 74,2 112,1 106,7 89,2 116,3 2,7 108,8 74,2 112,1 106,7 89,2 2,4 111,5 108,8 74,2 112,1 106,7 2,2 118,8 111,5 108,8 74,2 112,1 2,1 118,9 118,8 111,5 108,8 74,2 2,1 97,6 118,9 118,8 111,5 108,8 2,3 116,4 97,6 118,9 118,8 111,5 2,1 107 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 unempl[t] = + 11.788943645127 -0.0216975031746144proman[t] -0.0215687859575112`Y(t-1)`[t] -0.0199890687288202`Y(t-2)`[t] -0.0135066127680023`Y(t-3)`[t] -0.00627148987336246`Y(t-4)`[t] -0.104253154848955M1[t] + 0.117848899752461M2[t] -0.204196193128170M3[t] -0.162831247286175M4[t] -0.175727991703866M5[t] + 0.157906470768276M6[t] + 0.425400895722570M7[t] + 0.384400491946936M8[t] + 0.573141529469105M9[t] + 0.232224239562924M10[t] + 0.172740476997167M11[t] -0.0167897060162920t + 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) 11.788943645127 2.859838 4.1222 0.000196 9.8e-05 proman -0.0216975031746144 0.007946 -2.7306 0.009531 0.004766 `Y(t-1)` -0.0215687859575112 0.009729 -2.217 0.032679 0.01634 `Y(t-2)` -0.0199890687288202 0.009947 -2.0096 0.051609 0.025805 `Y(t-3)` -0.0135066127680023 0.009366 -1.4421 0.157472 0.078736 `Y(t-4)` -0.00627148987336246 0.007982 -0.7857 0.436897 0.218449 M1 -0.104253154848955 0.20647 -0.5049 0.616523 0.308261 M2 0.117848899752461 0.203158 0.5801 0.565281 0.282641 M3 -0.204196193128170 0.270803 -0.754 0.455472 0.227736 M4 -0.162831247286175 0.320756 -0.5076 0.614634 0.307317 M5 -0.175727991703866 0.321887 -0.5459 0.588305 0.294152 M6 0.157906470768276 0.3462 0.4561 0.650904 0.325452 M7 0.425400895722570 0.29807 1.4272 0.161694 0.080847 M8 0.384400491946936 0.259912 1.479 0.147392 0.073696 M9 0.573141529469105 0.284491 2.0146 0.051061 0.02553 M10 0.232224239562924 0.255656 0.9083 0.369419 0.18471 M11 0.172740476997167 0.237766 0.7265 0.471975 0.235987 t -0.0167897060162920 0.012274 -1.3679 0.179365 0.089682 Multiple Linear Regression - Regression Statistics Multiple R 0.971181360953543 R-squared 0.943193235863577 Adjusted R-squared 0.917779683486755 F-TEST (value) 37.1137895984914 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.245413358624484 Sum Squared Residuals 2.28865323047128 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3.7 3.68564898573593 0.0143510142640743 2 3.7 3.74918738325750 -0.0491873832575032 3 4.1 4.05218796842994 0.0478120315700565 4 4.1 3.9982343445441 0.101765655455901 5 3.8 3.6472148653606 0.152785134639397 6 3.7 3.62200172171155 0.0779982782884519 7 3.5 3.51312087637392 -0.0131208763739243 8 3.6 3.50600319295788 0.0939968070421203 9 4.1 3.80520686673418 0.294793133265823 10 3.8 3.62669608456115 0.173303915438851 11 3.7 3.66742303902276 0.0325769609772449 12 3.6 3.40079307766267 0.199206922337333 13 3.3 3.26994117210814 0.0300588278918644 14 3.4 3.22077488585968 0.179225114140319 15 3.7 3.49941495847776 0.200585041522239 16 3.7 3.47360462171109 0.226395378288912 17 3.4 3.24922089554712 0.150779104452875 18 3.3 3.26273943475453 0.0372605652454654 19 3 3.10914133177869 -0.109141331778691 20 3 3.09084021933498 -0.0908402193349808 21 3.3 3.2408859697132 0.0591140302868022 22 3 3.01457364467385 -0.0145736446738475 23 2.9 2.70041201206848 0.199587987931524 24 2.8 2.84026741631346 -0.0402674163134567 25 2.5 2.63535915169381 -0.135359151693805 26 2.6 2.73802746640404 -0.138027466404044 27 2.8 3.03661198362256 -0.236611983622564 28 2.7 2.95356128238874 -0.253561282388737 29 2.4 2.69391050234463 -0.293910502344634 30 2.2 2.58054056411447 -0.380540564114472 31 2.1 2.38801357410492 -0.288013574104923 32 2.1 2.3908417975242 -0.290841797524198 33 2.3 2.49676500750494 -0.196765007504937 34 2.1 2.296628239137 -0.196628239136998 35 2 2.02638186984072 -0.0263818698407166 36 1.9 2.10510415602002 -0.205104156020022 37 1.7 1.88135029357376 -0.181350293573761 38 1.8 2.00063196197474 -0.20063196197474 39 2.1 2.31717607957364 -0.217176079573639 40 2 2.22656494803053 -0.22656494803053 41 1.8 2.02391981300625 -0.223919813006249 42 1.7 1.81563961697356 -0.115639616973563 43 1.6 1.65519250794873 -0.0551925079487312 44 1.6 1.80684766033947 -0.206847660339466 45 1.8 1.95714215604769 -0.157142156047688 46 1.7 1.66210203162801 0.0378979683719942 47 1.7 1.90578307906805 -0.205783079068052 48 1.5 1.45383535000385 0.0461646499961458 49 1.5 1.22770039688837 0.272299603111628 50 1.5 1.29137830250403 0.208621697495968 51 1.8 1.59460900989609 0.205390990103907 52 1.8 1.64803480332555 0.151965196674454 53 1.7 1.48573392374139 0.214266076258611 54 1.7 1.31907866244588 0.380921337554117 55 1.8 1.33453170979373 0.46546829020627 56 2 1.50546712984347 0.494532870156525 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.078695102605272 0.157390205210544 0.921304897394728 22 0.128019546563223 0.256039093126446 0.871980453436777 23 0.248644513675192 0.497289027350384 0.751355486324808 24 0.328870739328796 0.657741478657593 0.671129260671204 25 0.305273999480638 0.610547998961276 0.694726000519362 26 0.230622052063212 0.461244104126424 0.769377947936788 27 0.269930729890083 0.539861459780166 0.730069270109917 28 0.345651711422728 0.691303422845456 0.654348288577272 29 0.362275012132952 0.724550024265904 0.637724987867048 30 0.340769326470546 0.681538652941092 0.659230673529454 31 0.22885043625766 0.45770087251532 0.77114956374234 32 0.143605773282727 0.287211546565454 0.856394226717273 33 0.147357394365420 0.294714788730840 0.85264260563458 34 0.100677901838679 0.201355803677359 0.89932209816132 35 0.908923040947025 0.182153918105951 0.0910769590529753 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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