Q3

*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: Mon, 24 Nov 2008 10:25:36 -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/24/t1227547709a2we7tychqn3xy9.htm/, Retrieved Mon, 24 Nov 2008 17:28:29 +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/24/t1227547709a2we7tychqn3xy9.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}, }

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Original text written by user:

IsPrivate?

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User-defined keywords:

Dataseries X:

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98,6 0 98 0 106,8 0 96,7 0 100,2 0 107,7 0 92 0 98,4 0 107,4 0 117,7 0 105,7 0 97,5 0 99,9 0 98,2 0 104,5 0 100,8 0 101,5 0 103,9 0 99,6 0 98,4 0 112,7 0 118,4 0 108,1 0 105,4 0 114,6 0 106,9 0 115,9 0 109,8 0 101,8 0 114,2 0 110,8 0 108,4 0 127,5 1 128,6 1 116,6 1 127,4 1 105 1 108,3 1 125 1 111,6 1 106,5 1 130,3 1 115 1 116,1 1 134 1 126,5 1 125,8 1 136,4 1 114,9 1 110,9 1 125,5 1 116,8 1 116,8 1 125,5 1 104,2 1 115,1 1 132,8 1 123,3 1 124,8 1 122 1 117,4 1 117,9 1 137,4 1 114,6 1 124,7 1 129,6 1 109,4 1 120,9 1 134,9 1 136,3 1 133,2 1 127,2 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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 103.842307692308 + 5.36153846153846D[t] -6.90641025641023M1[t] -8.8897435897436M2[t] + 3.31025641025641M3[t] -7.77307692307693M4[t] -7.85641025641026M5[t] + 1.81025641025641M6[t] -11.8397435897436M7[t] -7.73974358974359M8[t] + 6.41666666666667M9[t] + 6.38333333333333M10[t] -6.2461389791266e-15M11[t] + 0.283333333333333t + 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) 103.842307692308 2.46422 42.14 0 0 D 5.36153846153846 2.413054 2.2219 0.030206 0.015103 M1 -6.90641025641023 2.962447 -2.3313 0.023233 0.011616 M2 -8.8897435897436 2.957373 -3.006 0.003908 0.001954 M3 3.31025641025641 2.95342 1.1208 0.266983 0.133492 M4 -7.77307692307693 2.950593 -2.6344 0.01079 0.005395 M5 -7.85641025641026 2.948896 -2.6642 0.009976 0.004988 M6 1.81025641025641 2.94833 0.614 0.54162 0.27081 M7 -11.8397435897436 2.948896 -4.015 0.000173 8.6e-05 M8 -7.73974358974359 2.950593 -2.6231 0.011114 0.005557 M9 6.41666666666667 2.94637 2.1778 0.033499 0.01675 M10 6.38333333333333 2.943537 2.1686 0.034228 0.017114 M11 -6.2461389791266e-15 2.941836 0 1 0.5 t 0.283333333333333 0.057772 4.9043 8e-06 4e-06 Multiple Linear Regression - Regression Statistics Multiple R 0.920304038737113 R-squared 0.846959523715841 Adjusted R-squared 0.812657347996978 F-TEST (value) 24.6911312756785 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.09442622902778 Sum Squared Residuals 1505.28435897436 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.6 97.2192307692306 1.38076923076939 2 98 95.5192307692308 2.48076923076922 3 106.8 108.002564102564 -1.20256410256411 4 96.7 97.202564102564 -0.502564102564097 5 100.2 97.4025641025641 2.79743589743590 6 107.7 107.352564102564 0.347435897435890 7 92 93.9858974358974 -1.98589743589744 8 98.4 98.3692307692308 0.0307692307692309 9 107.4 112.808974358974 -5.40897435897437 10 117.7 113.058974358974 4.64102564102563 11 105.7 106.958974358974 -1.25897435897436 12 97.5 107.242307692308 -9.7423076923077 13 99.9 100.619230769231 -0.719230769230802 14 98.2 98.9192307692308 -0.719230769230773 15 104.5 111.402564102564 -6.90256410256411 16 100.8 100.602564102564 0.197435897435894 17 101.5 100.802564102564 0.697435897435894 18 103.9 110.752564102564 -6.8525641025641 19 99.6 97.3858974358974 2.21410256410256 20 98.4 101.769230769231 -3.36923076923077 21 112.7 116.208974358974 -3.50897435897436 22 118.4 116.458974358974 1.94102564102564 23 108.1 110.358974358974 -2.25897435897436 24 105.4 110.642307692308 -5.24230769230769 25 114.6 104.019230769231 10.5807692307692 26 106.9 102.319230769231 4.58076923076923 27 115.9 114.802564102564 1.09743589743590 28 109.8 104.002564102564 5.7974358974359 29 101.8 104.202564102564 -2.40256410256411 30 114.2 114.152564102564 0.0474358974358975 31 110.8 100.785897435897 10.0141025641026 32 108.4 105.169230769231 3.23076923076923 33 127.5 124.970512820513 2.52948717948717 34 128.6 125.220512820513 3.37948717948717 35 116.6 119.120512820513 -2.52051282051283 36 127.4 119.403846153846 7.99615384615385 37 105 112.780769230769 -7.78076923076927 38 108.3 111.080769230769 -2.78076923076924 39 125 123.564102564103 1.43589743589743 40 111.6 112.764102564103 -1.16410256410257 41 106.5 112.964102564103 -6.46410256410257 42 130.3 122.914102564103 7.38589743589745 43 115 109.547435897436 5.4525641025641 44 116.1 113.930769230769 2.16923076923076 45 134 128.370512820513 5.62948717948718 46 126.5 128.620512820513 -2.12051282051282 47 125.8 122.520512820513 3.27948717948718 48 136.4 122.803846153846 13.5961538461538 49 114.9 116.180769230769 -1.28076923076926 50 110.9 114.480769230769 -3.58076923076923 51 125.5 126.964102564103 -1.46410256410256 52 116.8 116.164102564103 0.635897435897439 53 116.8 116.364102564103 0.435897435897437 54 125.5 126.314102564103 -0.814102564102563 55 104.2 112.947435897436 -8.74743589743589 56 115.1 117.330769230769 -2.23076923076923 57 132.8 131.770512820513 1.02948717948719 58 123.3 132.020512820513 -8.72051282051282 59 124.8 125.920512820513 -1.12051282051281 60 122 126.203846153846 -4.20384615384615 61 117.4 119.580769230769 -2.18076923076925 62 117.9 117.880769230769 0.0192307692307785 63 137.4 130.364102564103 7.03589743589745 64 114.6 119.564102564103 -4.96410256410256 65 124.7 119.764102564103 4.93589743589745 66 129.6 129.714102564103 -0.114102564102566 67 109.4 116.347435897436 -6.94743589743589 68 120.9 120.730769230769 0.169230769230778 69 134.9 135.170512820513 -0.270512820512813 70 136.3 135.420512820513 0.879487179487195 71 133.2 129.320512820513 3.87948717948718 72 127.2 129.603846153846 -2.40384615384615 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0518418829843924 0.103683765968785 0.948158117015608 18 0.0499600139064959 0.0999200278129919 0.950039986093504 19 0.0901064302907905 0.180212860581581 0.90989356970921 20 0.0451965049190051 0.0903930098380102 0.954803495080995 21 0.0356102925637833 0.0712205851275666 0.964389707436217 22 0.0161065514467586 0.0322131028935172 0.983893448553241 23 0.00776099299342394 0.0155219859868479 0.992239007006576 24 0.0182147380816481 0.0364294761632961 0.981785261918352 25 0.160694084511473 0.321388169022946 0.839305915488527 26 0.121856006307856 0.243712012615712 0.878143993692144 27 0.102846675531672 0.205693351063345 0.897153324468328 28 0.0869043679811956 0.173808735962391 0.913095632018804 29 0.098666584206045 0.19733316841209 0.901333415793955 30 0.0886690556783131 0.177338111356626 0.911330944321687 31 0.143190991507237 0.286381983014474 0.856809008492763 32 0.103900383113795 0.20780076622759 0.896099616886205 33 0.0693844582779265 0.138768916555853 0.930615541722074 34 0.0666064131674257 0.133212826334851 0.933393586832574 35 0.0605586363157947 0.121117272631589 0.939441363684205 36 0.138627878042919 0.277255756085838 0.861372121957081 37 0.419289154945452 0.838578309890903 0.580710845054548 38 0.393365403144101 0.786730806288202 0.606634596855899 39 0.330834049748853 0.661668099497707 0.669165950251147 40 0.272834628612247 0.545669257224494 0.727165371387753 41 0.404644426996183 0.809288853992365 0.595355573003817 42 0.431963661189752 0.863927322379503 0.568036338810248 43 0.533890738335598 0.932218523328804 0.466109261664402 44 0.44784061853858 0.89568123707716 0.55215938146142 45 0.41577800405548 0.83155600811096 0.58422199594452 46 0.36824438605085 0.7364887721017 0.63175561394915 47 0.291963063091222 0.583926126182444 0.708036936908778 48 0.955960569024254 0.0880788619514912 0.0440394309757456 49 0.93941333283456 0.121173334330879 0.0605866671654396 50 0.904566930311925 0.19086613937615 0.095433069688075 51 0.904706678955922 0.190586642088156 0.095293321044078 52 0.957903701520733 0.084192596958535 0.0420962984792675 53 0.913454951697151 0.173090096605697 0.0865450483028486 54 0.844649577836496 0.310700844327008 0.155350422163504 55 0.757554656535953 0.484890686928094 0.242445343464047 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 3 0.076923076923077 NOK 10% type I error level 8 0.205128205128205 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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