Multiple Regression Season Dummies WS7

*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: Sun, 22 Nov 2009 09:22:51 -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/22/t12589070650g9mld7n11flcjk.htm/, Retrieved Sun, 22 Nov 2009 17:24:37 +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/22/t12589070650g9mld7n11flcjk.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:

KVN WS7

Dataseries X:

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9487 1169 8700 2154 9627 2249 8947 2687 9283 4359 8829 5382 9947 4459 9628 6398 9318 4596 9605 3024 8640 1887 9214 2070 9567 1351 8547 2218 9185 2461 9470 3028 9123 4784 9278 4975 10170 4607 9434 6249 9655 4809 9429 3157 8739 1910 9552 2228 9687 1594 9019 2467 9672 2222 9206 3607 9069 4685 9788 4962 10312 5770 10105 5480 9863 5000 9656 3228 9295 1993 9946 2288 9701 1580 9049 2111 10190 2192 9706 3601 9765 4665 9893 4876 9994 5813 10433 5589 10073 5331 10112 3075 9266 2002 9820 2306 10097 1507 9115 1992 10411 2487 9678 3490 10408 4647 10153 5594 10368 5611 10581 5788 10597 6204 10680 3013 9738 1931 9556 2549

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 Y[t] = + 9128.86904445696 + 0.213587516625750X[t] + 271.322214098642M1[t] -710.28396584075M2[t] + 192.138024434725M3[t] -428.591426532646M4[t] -587.75207140093M5[t] -642.310737709253M6[t] -92.4306817753984M7[t] -353.006262562185M8[t] -335.761080711350M9[t] + 105.537806513191M10[t] -408.611329287392M11[t] + 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) 9128.86904445696 442.168472 20.6457 0 0 X 0.213587516625750 0.175243 1.2188 0.229 0.1145 M1 271.322214098642 302.525411 0.8969 0.374366 0.187183 M2 -710.28396584075 264.090333 -2.6895 0.009872 0.004936 M3 192.138024434725 263.57794 0.729 0.469643 0.234821 M4 -428.591426532646 315.919282 -1.3566 0.181374 0.090687 M5 -587.75207140093 487.407022 -1.2059 0.233901 0.116951 M6 -642.310737709253 567.73567 -1.1314 0.263645 0.131823 M7 -92.4306817753984 582.408115 -0.1587 0.874582 0.437291 M8 -353.006262562185 685.734879 -0.5148 0.609116 0.304558 M9 -335.761080711350 572.428687 -0.5866 0.560309 0.280155 M10 105.537806513191 299.410264 0.3525 0.72605 0.363025 M11 -408.611329287392 270.302608 -1.5117 0.13731 0.068655 Multiple Linear Regression - Regression Statistics Multiple R 0.697057008729458 R-squared 0.48588847341886 Adjusted R-squared 0.354625955993888 F-TEST (value) 3.70165438657374 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0.000596500404973055 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 416.646822002174 Sum Squared Residuals 8158944.99137204 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9487 9649.87506549107 -162.875065491074 2 8700 8878.65258942807 -178.652589428074 3 9627 9801.365393783 -174.365393782995 4 8947 9274.1872750977 -327.187275097703 5 9283 9472.14495802767 -189.144958027674 6 8829 9636.0863212275 -807.086321227493 7 9947 9988.82509931578 -41.8250993157801 8 9628 10142.3957132663 -514.395713266323 9 9318 9774.75619015756 -456.756190157556 10 9605 9880.29550124642 -275.295501246418 11 8640 9123.29735904236 -483.297359042357 12 9214 9570.99520387226 -356.995203872261 13 9567 9688.7479935170 -121.747993516989 14 8547 8892.32219049212 -345.322190492122 15 9185 9846.64594730765 -661.645947307654 16 9470 9347.02061826708 122.979381732916 17 9123 9562.91965259362 -439.919652593617 18 9278 9549.15620196081 -271.156201960813 19 10170 10020.4360517764 149.563948223609 20 9434 10110.5711732891 -676.571173289086 21 9655 9820.25033119884 -165.250331198841 22 9429 9908.70264095764 -479.702640957643 23 8739 9128.20987192475 -389.209871924749 24 9552 9604.74203149913 -52.7420314991297 25 9687 9740.64976005705 -53.6497600570461 26 9019 8945.50548213193 73.4945178680658 27 9672 9795.5985308341 -123.598530834100 28 9206 9470.6877903934 -264.687790393394 29 9069 9541.77448844767 -472.774488447668 30 9788 9546.37956424468 241.620435755322 31 10312 10268.8383336121 43.1616663878614 32 10105 9946.32237300388 158.677626996116 33 9863 9861.04554687436 1.95445312564103 34 9656 9923.86735463807 -267.867354638071 35 9295 9145.93763580469 149.062364195314 36 9946 9617.55728249667 328.442717503325 37 9701 9737.65953482429 -36.6595348242857 38 9049 8869.46832621317 179.531673786833 39 10190 9789.19090533533 400.809094664673 40 9706 9469.40626529364 236.593734706361 41 9765 9537.50273811515 227.497261884847 42 9893 9528.01103781486 364.988962185137 43 9994 10278.0225968270 -284.022596827046 44 10433 9969.6034123161 463.396587683909 45 10073 9931.74301487748 141.256985122518 46 10112 9891.18846459433 220.811535405668 47 9266 9147.85992345432 118.140076545682 48 9820 9621.40185779594 198.598142204062 49 10097 9722.0676461106 374.932353889394 50 9115 8844.0514117347 270.948588265297 51 10411 9852.19922273992 558.800777260076 52 9678 9445.69805094818 232.301949051819 53 10408 9533.6581628159 874.34183718411 54 10153 9681.36687475215 471.633125247848 55 10368 10234.8779184686 133.122081531356 56 10581 10012.1073281246 568.892671875385 57 10597 10118.2049168918 478.795083108238 58 10680 9877.94603856354 802.053961436465 59 9738 9132.69520977389 605.30479022611 60 9556 9673.303624336 -117.303624335996 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.297866954263022 0.595733908526043 0.702133045736978 17 0.206405991838846 0.412811983677692 0.793594008161154 18 0.190242652887006 0.380485305774012 0.809757347112994 19 0.126845161254860 0.253690322509721 0.87315483874514 20 0.13726200146111 0.27452400292222 0.86273799853889 21 0.117361863893614 0.234723727787228 0.882638136106386 22 0.103562497899591 0.207124995799181 0.89643750210041 23 0.0880303104802777 0.176060620960555 0.911969689519722 24 0.0752818391624606 0.150563678324921 0.92471816083754 25 0.0491912430752624 0.0983824861505248 0.950808756924738 26 0.0474824705389019 0.0949649410778038 0.952517529461098 27 0.0538254956110305 0.107650991222061 0.94617450438897 28 0.0438750746339446 0.0877501492678892 0.956124925366055 29 0.122753338494420 0.245506676988839 0.87724666150558 30 0.284787974060412 0.569575948120823 0.715212025939588 31 0.224754429159455 0.449508858318911 0.775245570840545 32 0.303017358585395 0.60603471717079 0.696982641414605 33 0.297482324022435 0.59496464804487 0.702517675977565 34 0.494497240554337 0.988994481108673 0.505502759445663 35 0.540136075962006 0.919727848075988 0.459863924037994 36 0.577373847681587 0.845252304636826 0.422626152318413 37 0.558945010059005 0.88210997988199 0.441054989940996 38 0.477153181118847 0.954306362237693 0.522846818881153 39 0.48554012989518 0.97108025979036 0.51445987010482 40 0.414512044111328 0.829024088222656 0.585487955888672 41 0.573208547410865 0.85358290517827 0.426791452589135 42 0.486670822421124 0.973341644842248 0.513329177578876 43 0.458796564482613 0.917593128965226 0.541203435517387 44 0.346891288375522 0.693782576751044 0.653108711624478 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 3 0.103448275862069 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Include Monthly Dummies ; par3 = No 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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