*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 11:57:25 -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/15/t12609035010ac0u9a6yx4de5q.htm/, Retrieved Tue, 15 Dec 2009 19:58:36 +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/t12609035010ac0u9a6yx4de5q.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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139 0 149 135 0 139 130 0 135 127 0 130 122 0 127 117 0 122 112 0 117 113 0 112 149 0 113 157 0 149 157 0 157 147 0 157 137 0 147 132 0 137 125 0 132 123 0 125 117 0 123 114 0 117 111 0 114 112 0 111 144 0 112 150 0 144 149 0 150 134 0 149 123 0 134 116 0 123 117 0 116 111 0 117 105 0 111 102 0 105 95 0 102 93 0 95 124 0 93 130 0 124 124 0 130 115 0 124 106 0 115 105 0 106 105 0 105 101 0 105 95 0 101 93 0 95 84 0 93 87 0 84 116 0 87 120 0 116 117 1 120 109 1 117 105 1 109 107 1 105 109 1 107 109 1 109 108 1 109 107 1 108 99 1 107 103 1 99 131 1 103 137 1 131 135 1 137

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 WLH[t] = + 9.04393654328443 + 4.53773313169803X[t] + 0.875770345031125`Y(t-1)`[t] + 0.572726124650886M1[t] + 5.40250397789863M2[t] + 6.35281382996584M3[t] + 5.05219926799572M4[t] + 3.00250912006294M5[t] + 4.52920559318618M6[t] + 0.704361376247183M7[t] + 7.83229040142024M8[t] + 37.9292107353505M9[t] + 16.7281747873532M10[t] + 8.2890049078007M11[t] -0.122998816973845t + 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) 9.04393654328443 8.295615 1.0902 0.281557 0.140778 X 4.53773313169803 1.302917 3.4828 0.001134 0.000567 `Y(t-1)` 0.875770345031125 0.051729 16.9299 0 0 M1 0.572726124650886 1.665996 0.3438 0.732654 0.366327 M2 5.40250397789863 1.828325 2.9549 0.005009 0.002504 M3 6.35281382996584 1.885266 3.3697 0.001574 0.000787 M4 5.05219926799572 1.912227 2.6421 0.011368 0.005684 M5 3.00250912006294 1.976694 1.519 0.135927 0.067964 M6 4.52920559318618 2.105413 2.1512 0.036989 0.018495 M7 0.704361376247183 2.174117 0.324 0.747491 0.373746 M8 7.83229040142024 2.380574 3.2901 0.001977 0.000989 M9 37.9292107353505 2.297326 16.5102 0 0 M10 16.7281747873532 1.597106 10.4741 0 0 M11 8.2890049078007 1.60831 5.1539 6e-06 3e-06 t -0.122998816973845 0.050641 -2.4288 0.019302 0.009651 Multiple Linear Regression - Regression Statistics Multiple R 0.992953343119385 R-squared 0.985956341611964 Adjusted R-squared 0.981487904852134 F-TEST (value) 220.649053484545 F-TEST (DF numerator) 14 F-TEST (DF denominator) 44 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 2.37014623783598 Sum Squared Residuals 247.174100304034 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 139 139.983445260599 -0.983445260599118 2 135 135.932520846562 -0.93252084656179 3 130 133.256750501531 -3.25675050153071 4 127 127.454285397431 -0.454285397431072 5 122 122.654285397431 -0.654285397431074 6 117 119.679131328425 -2.67913132842486 7 112 111.352436569356 0.647563430643625 8 113 113.9785150524 -0.978515052399952 9 149 144.828206914387 4.17179308561251 10 157 155.031904570537 1.9680954294631 11 157 153.475898634260 3.52410136574045 12 147 145.063894909485 1.93610509051501 13 137 136.755918766851 0.244081233149242 14 132 132.704994352813 -0.704994352813419 15 125 129.153453662751 -4.15345366275116 16 123 121.599447868589 1.40055213141069 17 117 117.675218213620 -0.675218213620437 18 114 113.824293799583 0.175706200416914 19 111 107.249139730577 3.75086026942314 20 112 111.626758903683 0.373241096317314 21 144 142.476450765670 1.52354923432977 22 150 149.177067041695 0.822932958304861 23 149 145.869520415356 3.13047958464447 24 134 136.581746345550 -2.58174634554986 25 123 123.89491847776 -0.894918477760012 26 116 118.968223718692 -2.96822371869152 27 117 113.665142338567 3.33485766143299 28 111 113.117299304654 -2.11729930465417 29 105 105.689988269561 -0.689988269560793 30 102 101.839063855523 0.160936144476559 31 95 95.2639097865172 -0.263909786517211 32 93 96.1384475794985 -3.13844757949854 33 124 124.360828406393 -0.360828406392718 34 130 130.185674337386 -0.185674337386484 35 124 126.878127711047 -2.87812771104688 36 115 113.211501916086 1.78849808391442 37 106 105.779296118482 0.220703881517516 38 105 102.604142049476 2.39585795052375 39 105 102.555682739538 2.44431726046151 40 101 101.132069360595 -0.132069360594526 41 95 95.4562990155634 -0.456299015563395 42 93 91.605374601526 1.39462539847396 43 84 85.905990877551 -1.90599087755094 44 87 85.02898798047 1.97101201952998 45 116 117.630220532520 -1.63022053251982 46 120 121.703525773451 -1.70352577345134 47 117 121.182171588748 -4.18217158874752 48 109 110.142856828880 -1.14285682887959 49 105 103.586421376308 1.41357862369237 50 107 104.790119032457 2.20988096754298 51 109 107.368970757613 1.63102924238736 52 109 107.696898068731 1.30310193126908 53 108 105.524209103824 2.47579089617570 54 107 106.052136414943 0.947863585057428 55 99 101.228523035999 -2.22852303599861 56 103 101.227290483949 1.77270951605119 57 131 134.704293381030 -3.70429338102974 58 137 137.901828276930 -0.90182827693013 59 135 134.594281650591 0.405718349409481 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.110959151241921 0.221918302483842 0.889040848758079 19 0.136760804843620 0.273521609687240 0.86323919515638 20 0.0711040777759339 0.142208155551868 0.928895922224066 21 0.109139950039461 0.218279900078922 0.890860049960539 22 0.132874972275792 0.265749944551584 0.867125027724208 23 0.256221116978536 0.512442233957071 0.743778883021464 24 0.430223969880825 0.86044793976165 0.569776030119175 25 0.338880329851945 0.67776065970389 0.661119670148055 26 0.383741852293647 0.767483704587294 0.616258147706353 27 0.858813804741692 0.282372390516616 0.141186195258308 28 0.864751706065631 0.270496587868738 0.135248293934369 29 0.809143750225587 0.381712499548825 0.190856249774413 30 0.731917225779401 0.536165548441198 0.268082774220599 31 0.760385488832535 0.47922902233493 0.239614511167465 32 0.911537856755153 0.176924286489694 0.0884621432448469 33 0.940433569775867 0.119132860448265 0.0595664302241325 34 0.969888604370989 0.0602227912580224 0.0301113956290112 35 0.964631151664008 0.070737696671983 0.0353688483359915 36 0.99006505702362 0.0198698859527617 0.00993494297638086 37 0.977217217251874 0.0455655654962523 0.0227827827481262 38 0.968492629857846 0.0630147402843084 0.0315073701421542 39 0.985588094490518 0.028823811018965 0.0144119055094825 40 0.985855279560222 0.0282894408795567 0.0141447204397784 41 0.950218270540348 0.0995634589193043 0.0497817294596522 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 4 0.166666666666667 NOK 10% type I error level 8 0.333333333333333 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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