Multiple Regression analysis (2 time lags)

*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: Tue, 15 Dec 2009 12:28:15 -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/15/t12609053793ifp3hrr6dz43jz.htm/, Retrieved Tue, 15 Dec 2009 20:29:54 +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/2009/Dec/15/t12609053793ifp3hrr6dz43jz.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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105.67 96.90 96.33 123.61 95.10 96.33 113.08 97.00 95.05 106.46 112.70 96.84 123.38 102.90 96.92 109.87 97.40 97.44 95.74 111.40 97.78 123.06 87.40 97.69 123.39 96.80 96.67 120.28 114.10 98.29 115.33 110.30 98.20 110.40 103.90 98.71 114.49 101.60 98.54 132.03 94.60 98.20 123.16 95.90 100.80 118.82 104.70 101.33 128.32 102.80 101.88 112.24 98.10 101.85 104.53 113.90 102.04 132.57 80.90 102.22 122.52 95.70 102.63 131.80 113.20 102.65 124.55 105.90 102.54 120.96 108.80 102.37 122.60 102.30 102.68 145.52 99.00 102.76 118.57 100.70 102.82 134.25 115.50 103.31 136.70 100.70 103.23 121.37 109.90 103.60 111.63 114.60 103.95 134.42 85.40 103.93 137.65 100.50 104.25 137.86 114.80 104.38 119.77 116.50 104.36 130.69 112.90 104.32 128.28 102.00 104.58 147.45 106.00 104.68 128.42 105.30 104.92 136.90 118.80 105.46 143.95 106.10 105.23 135.64 109.30 105.58 122.48 117.20 105.34 136.83 92.50 105.28 153.04 104.20 105.70 142.71 112.50 105.67 123.46 122.40 105.71 144.37 113.30 106.1 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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Uitvoer[t] = -41.7635583530285 + 1.39214975483713TIP[t] + 0.0611793827341157cons[t] + 11.0612384622747M1[t] + 25.6224237457095M2[t] + 13.0495707174011M3[t] -1.25943975198516M4[t] + 19.2286263713111M5[t] + 9.50320871169308M6[t] -19.6451676889559M7[t] + 41.2540745646001M8[t] + 27.0430471556376M9[t] -0.91340532957285M10[t] -12.9295824939500M11[t] + 0.246133906068330t + 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) -41.7635583530285 140.650485 -0.2969 0.767725 0.383862 TIP 1.39214975483713 0.221449 6.2866 0 0 cons 0.0611793827341157 1.393556 0.0439 0.965154 0.482577 M1 11.0612384622747 5.893395 1.8769 0.06626 0.03313 M2 25.6224237457095 5.920731 4.3276 7e-05 3.5e-05 M3 13.0495707174011 5.816838 2.2434 0.029242 0.014621 M4 -1.25943975198516 5.719368 -0.2202 0.82659 0.413295 M5 19.2286263713111 5.677039 3.3871 0.001368 0.000684 M6 9.50320871169308 5.726045 1.6596 0.103123 0.051562 M7 -19.6451676889559 6.162256 -3.188 0.002448 0.001224 M8 41.2540745646001 7.184715 5.7419 1e-06 0 M9 27.0430471556376 6.127812 4.4132 5.3e-05 2.6e-05 M10 -0.91340532957285 6.087566 -0.15 0.881321 0.440661 M11 -12.9295824939500 6.049551 -2.1373 0.037392 0.018696 t 0.246133906068330 0.34175 0.7202 0.47468 0.23734 Multiple Linear Regression - Regression Statistics Multiple R 0.834961366215876 R-squared 0.697160483073082 Adjusted R-squared 0.614028066661771 F-TEST (value) 8.38614481772993 F-TEST (DF numerator) 14 F-TEST (DF denominator) 51 p-value 6.12966200019827e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.2784167987223 Sum Squared Residuals 4390.53993283141 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 105.67 110.336535197810 -4.66653519780981 2 123.61 122.637984828606 0.972015171393703 3 113.08 112.878040630657 0.201959369342846 4 106.46 120.781426313376 -14.3214263133763 5 123.38 127.877453095956 -4.49745309595576 6 109.87 110.773158969824 -0.903158969823521 7 95.74 101.381814033092 -5.64181403309236 8 123.06 129.110089932179 -6.05008993217936 9 123.39 128.169001154365 -4.77900115436542 10 120.28 124.641983933935 -4.36198393393502 11 115.33 107.576265462799 7.75373453720092 12 110.4 111.873424917054 -1.47342491705413 13 114.49 119.968452354207 -5.4784523542069 14 132.03 125.009922269720 7.02007773027952 15 123.16 114.652064223877 8.50793577612254 16 118.82 112.872530575975 5.94746942402463 17 128.32 130.995294731653 -2.6752947316532 18 112.24 114.971071748887 -2.73107174888694 19 104.53 108.076419463452 -3.54641946345249 20 132.57 123.291866002344 9.27813399765648 21 122.52 129.95587241796 -7.43587241795991 22 131.8 126.609398136122 5.19060186387768 23 124.55 104.669931935402 19.8800680645983 24 120.96 121.872482129383 -0.912482129382903 25 122.6 124.149846699932 -1.5498466999321 26 145.52 134.367966049091 11.1520339509086 27 118.57 124.411572273039 -5.84157227303858 28 134.25 130.98248997885 3.26751002115008 29 136.7 131.107979286006 5.59202071399375 30 121.37 134.459109648570 -13.0891096485698 31 111.63 112.121383785681 -0.491383785680599 32 134.42 132.614763516406 1.80523648359408 33 137.65 139.690908714027 -2.04090871402737 34 137.86 131.896284948812 5.9637150511883 35 119.77 122.491672686071 -2.72167268607139 36 130.69 130.653202793367 0.0367972066333527 37 128.28 126.802049473496 1.47795052650425 38 147.45 147.184085620621 0.265914379379180 39 128.42 133.897544721851 -5.477544721851 40 136.9 138.661726715511 -1.76172671551075 41 143.95 141.701553600415 2.24844639958504 42 135.64 136.698561846301 -1.05856184630102 43 122.48 118.779619363078 3.70038063692247 44 136.83 145.535225815261 -8.70522581526054 45 153.04 147.884179784709 5.15582021529079 46 142.71 131.726868789233 10.9831312107667 47 123.46 133.741555279122 -10.2815552791215 48 144.37 134.278075013834 10.0919249861658 49 146.15 127.115128386067 19.0348716139334 50 147.61 156.849651437521 -9.23965143752145 51 158.51 147.471530347360 11.0384696526396 52 147.4 129.284818788682 18.1151812113176 53 165.05 160.497461402793 4.55253859720668 54 154.64 139.612950154644 15.0270498453561 55 126.2 120.220763354697 5.97923664530297 56 157.36 153.688054733811 3.67194526618934 57 154.15 145.050037928938 9.0999620710619 58 123.21 140.985464191898 -17.7754641918977 59 113.07 127.700574636606 -14.6305746366063 60 110.45 118.192815146362 -7.74281514636206 61 113.57 122.387987888489 -8.81798788848885 62 122.44 132.610389794440 -10.1703897944395 63 114.93 123.359247803215 -8.42924780321539 64 111.85 123.097007627605 -11.2470076276053 65 126.04 131.260257883177 -5.22025788317651 66 121.34 118.585147631775 2.75485236822519 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.0231035201070465 0.046207040214093 0.976896479892953 19 0.00649708027916446 0.0129941605583289 0.993502919720836 20 0.00137811347691789 0.00275622695383579 0.998621886523082 21 0.00172206761044630 0.00344413522089259 0.998277932389554 22 0.0007394619044245 0.001478923808849 0.999260538095575 23 0.000401306010754884 0.000802612021509767 0.999598693989245 24 0.000188633106930085 0.000377266213860171 0.99981136689307 25 4.96477799116417e-05 9.92955598232834e-05 0.999950352220088 26 7.41820691158854e-05 0.000148364138231771 0.999925817930884 27 0.000973132655090395 0.00194626531018079 0.99902686734491 28 0.00151578478485105 0.00303156956970209 0.998484215215149 29 0.000842507452460654 0.00168501490492131 0.99915749254754 30 0.000822945100525795 0.00164589020105159 0.999177054899474 31 0.000358265750031302 0.000716531500062605 0.999641734249969 32 0.000262015736496177 0.000524031472992353 0.999737984263504 33 0.00014370373967548 0.00028740747935096 0.999856296260325 34 6.23364720439406e-05 0.000124672944087881 0.999937663527956 35 0.000227575668450101 0.000455151336900202 0.99977242433155 36 0.000113196119325458 0.000226392238650916 0.999886803880675 37 4.7452268751705e-05 9.490453750341e-05 0.999952547731248 38 2.0611163373137e-05 4.1222326746274e-05 0.999979388836627 39 1.14866714176032e-05 2.29733428352064e-05 0.999988513328582 40 8.78317949079055e-06 1.75663589815811e-05 0.99999121682051 41 2.88829158308810e-06 5.77658316617621e-06 0.999997111708417 42 5.17837094290594e-05 0.000103567418858119 0.99994821629057 43 4.46360310082033e-05 8.92720620164066e-05 0.999955363968992 44 0.0054576670601954 0.0109153341203908 0.994542332939805 45 0.086046097603231 0.172092195206462 0.913953902396769 46 0.0506000156542782 0.101200031308556 0.949399984345722 47 0.363051784466097 0.726103568932194 0.636948215533903 48 0.256832317681012 0.513664635362024 0.743167682318988 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.774193548387097 NOK 5% type I error level 27 0.870967741935484 NOK 10% type I error level 27 0.870967741935484 NOK

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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