W6Q3 (2)

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 06:15:57 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t1227792212c47e5hs3x3dtkt9.htm/, Retrieved Thu, 27 Nov 2008 13:23:43 +0000

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/2008/Nov/27/t1227792212c47e5hs3x3dtkt9.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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115.6 0 120.3 0 121.9 0 121.7 0 118.9 0 113.4 0 114 0 117.5 0 120.9 0 125.1 0 124.7 0 128.2 0 149.7 0 163.6 0 173.9 0 164.5 0 154.2 0 147.9 0 159.3 0 170.3 0 170 0 174.2 0 190.8 0 179.9 0 240.8 0 241.9 0 241.1 0 239.6 0 220.8 0 209.3 0 209.9 0 228.3 0 242.1 0 226.4 0 231.5 0 229.7 0 257.6 0 260 0 264.4 0 268.8 0 271.4 0 273.8 0 277.4 0 268.2 0 264.6 0 266.6 0 266 0 267.4 0 289.8 0 294 0 310.3 0 311.7 0 302.1 0 298.2 0 299.2 0 296.2 0 299 0 300 0 299.4 0 300.2 0 470.2 0 472.1 0 484.8 0 513.4 1 547.2 1 548.1 1 544.7 1 521.1 1 459 1 413.2 1

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] = + 63.837894736842 + 133.843609022556D[t] + 54.7091812865496M1[t] + 55.0413450292399M2[t] + 58.0901754385965M3[t] + 35.2984043441938M4[t] + 30.0805680868839M5[t] + 21.7293984962406M6[t] + 19.6615622389307M7[t] + 14.8103926482874M8[t] + 2.77588972431076M9[t] -9.94194653299918M10[t] + 5.76783625730993M11[t] + 4.36783625730994t + 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) 63.837894736842 15.749137 4.0534 0.000157 7.9e-05 D 133.843609022556 14.869626 9.0011 0 0 M1 54.7091812865496 18.621068 2.938 0.004789 0.002394 M2 55.0413450292399 18.609965 2.9576 0.004534 0.002267 M3 58.0901754385965 18.601324 3.1229 0.002833 0.001417 M4 35.2984043441938 18.788928 1.8787 0.065497 0.032748 M5 30.0805680868839 18.770584 1.6025 0.114663 0.057332 M6 21.7293984962406 18.754671 1.1586 0.251531 0.125766 M7 19.6615622389307 18.741196 1.0491 0.298635 0.149317 M8 14.8103926482874 18.730164 0.7907 0.432441 0.216221 M9 2.77588972431076 18.721579 0.1483 0.882661 0.44133 M10 -9.94194653299918 18.715444 -0.5312 0.59737 0.298685 M11 5.76783625730993 19.418023 0.297 0.767539 0.383769 t 4.36783625730994 0.214319 20.3801 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.97198092869887 R-squared 0.944746925754318 Adjusted R-squared 0.931920319232999 F-TEST (value) 73.6552512298603 F-TEST (DF numerator) 13 F-TEST (DF denominator) 56 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 30.7007198242396 Sum Squared Residuals 52781.9150726817 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 115.6 122.914912280702 -7.3149122807023 2 120.3 127.614912280702 -7.31491228070157 3 121.9 135.031578947368 -13.1315789473684 4 121.7 116.607644110276 5.09235588972419 5 118.9 115.757644110276 3.14235588972434 6 113.4 111.774310776942 1.62568922305774 7 114 114.074310776942 -0.0743107769423977 8 117.5 113.590977443609 3.90902255639095 9 120.9 105.924310776942 14.9756892230576 10 125.1 97.5743107769423 27.5256892230577 11 124.7 117.651929824561 7.04807017543864 12 128.2 116.251929824561 11.9480701754386 13 149.7 175.328947368421 -25.628947368421 14 163.6 180.028947368421 -16.428947368421 15 173.9 187.445614035088 -13.5456140350877 16 164.5 169.021679197995 -4.52167919799496 17 154.2 168.171679197995 -13.9716791979950 18 147.9 164.188345864662 -16.2883458646617 19 159.3 166.488345864662 -7.18834586466163 20 170.3 166.005012531328 4.2949874686717 21 170 158.338345864662 11.6616541353384 22 174.2 149.988345864662 24.2116541353383 23 190.8 170.065964912281 20.7340350877193 24 179.9 168.665964912281 11.2340350877193 25 240.8 227.74298245614 13.0570175438598 26 241.9 232.442982456140 9.4570175438596 27 241.1 239.859649122807 1.24035087719295 28 239.6 221.435714285714 18.1642857142857 29 220.8 220.585714285714 0.214285714285712 30 209.3 216.602380952381 -7.30238095238096 31 209.9 218.902380952381 -9.00238095238093 32 228.3 218.419047619048 9.8809523809524 33 242.1 210.752380952381 31.3476190476191 34 226.4 202.402380952381 23.9976190476191 35 231.5 222.48 9.01999999999997 36 229.7 221.08 8.62 37 257.6 280.157017543860 -22.5570175438595 38 260 284.85701754386 -24.8570175438597 39 264.4 292.273684210526 -27.8736842105264 40 268.8 273.849749373434 -5.04974937343354 41 271.4 272.999749373434 -1.59974937343361 42 273.8 269.0164160401 4.78358395989974 43 277.4 271.3164160401 6.08358395989974 44 268.2 270.833082706767 -2.63308270676692 45 264.6 263.166416040100 1.43358395989976 46 266.6 254.8164160401 11.7835839598998 47 266 274.894035087719 -8.8940350877193 48 267.4 273.494035087719 -6.0940350877193 49 289.8 332.571052631579 -42.7710526315788 50 294 337.271052631579 -43.271052631579 51 310.3 344.687719298246 -34.3877192982456 52 311.7 326.263784461153 -14.5637844611529 53 302.1 325.413784461153 -23.3137844611529 54 298.2 321.430451127820 -23.2304511278196 55 299.2 323.730451127820 -24.5304511278196 56 296.2 323.247117794486 -27.0471177944862 57 299 315.580451127820 -16.5804511278196 58 300 307.230451127820 -7.2304511278196 59 299.4 327.308070175439 -27.9080701754387 60 300.2 325.908070175439 -25.7080701754386 61 470.2 384.985087719298 85.2149122807018 62 472.1 389.685087719298 82.4149122807017 63 484.8 397.101754385965 87.698245614035 64 513.4 512.521428571429 0.87857142857141 65 547.2 511.671428571429 35.5285714285714 66 548.1 507.688095238095 40.4119047619048 67 544.7 509.988095238095 34.7119047619048 68 521.1 509.504761904762 11.5952380952381 69 459 501.838095238095 -42.8380952380953 70 413.2 493.488095238095 -80.2880952380952 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.00631004684316712 0.0126200936863342 0.993689953156833 18 0.00120858136972457 0.00241716273944915 0.998791418630275 19 0.000193290587761962 0.000386581175523924 0.999806709412238 20 7.07521739968231e-05 0.000141504347993646 0.999929247826003 21 1.34286962969354e-05 2.68573925938708e-05 0.999986571303703 22 2.52463853339033e-06 5.04927706678066e-06 0.999997475361467 23 6.88001675690013e-06 1.37600335138003e-05 0.999993119983243 24 1.43127513325214e-06 2.86255026650429e-06 0.999998568724867 25 4.04284829785219e-05 8.08569659570439e-05 0.999959571517022 26 3.14033838812095e-05 6.2806767762419e-05 0.99996859661612 27 1.13786544257290e-05 2.27573088514581e-05 0.999988621345574 28 4.8523842593926e-06 9.7047685187852e-06 0.99999514761574 29 1.23811624296263e-06 2.47623248592526e-06 0.999998761883757 30 3.29539136680130e-07 6.59078273360261e-07 0.999999670460863 31 1.04055441845221e-07 2.08110883690442e-07 0.999999895944558 32 2.52367006212459e-08 5.04734012424918e-08 0.9999999747633 33 1.61755756509510e-08 3.23511513019019e-08 0.999999983824424 34 9.02708554182095e-09 1.80541710836419e-08 0.999999990972914 35 4.0655935225616e-09 8.1311870451232e-09 0.999999995934406 36 1.79451216468308e-09 3.58902432936615e-09 0.999999998205488 37 1.56119140644418e-09 3.12238281288837e-09 0.999999998438809 38 1.56355317520187e-09 3.12710635040374e-09 0.999999998436447 39 1.1686962723879e-09 2.3373925447758e-09 0.999999998831304 40 3.67696615505176e-10 7.35393231010352e-10 0.999999999632303 41 8.5688111102323e-11 1.71376222204646e-10 0.999999999914312 42 3.20942619589646e-11 6.41885239179291e-11 0.999999999967906 43 1.12658185304108e-11 2.25316370608217e-11 0.999999999988734 44 3.55253306702863e-12 7.10506613405725e-12 0.999999999996448 45 5.90117063298988e-12 1.18023412659798e-11 0.9999999999941 46 2.04146826871416e-10 4.08293653742832e-10 0.999999999795853 47 2.9668244823087e-09 5.9336489646174e-09 0.999999997033175 48 3.08929610370999e-06 6.17859220741997e-06 0.999996910703896 49 3.55988329512363e-06 7.11976659024726e-06 0.999996440116705 50 3.19264338186226e-06 6.38528676372452e-06 0.999996807356618 51 1.09279495923175e-06 2.18558991846350e-06 0.99999890720504 52 2.96585682510153e-07 5.93171365020307e-07 0.999999703414318 53 2.66726696200074e-07 5.33453392400147e-07 0.999999733273304 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 36 0.972972972972973 NOK 5% type I error level 37 1 NOK 10% type I error level 37 1 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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