Q3 Monthly Dummies

*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, 01 Dec 2008 11:56:26 -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/Dec/01/t1228157847jmw5zoc5039zynd.htm/, Retrieved Mon, 01 Dec 2008 18:57:27 +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/Dec/01/t1228157847jmw5zoc5039zynd.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)

Feedback Forum:

2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc]  [reply]  test Post a new message

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

12192.5 0 11268.8 0 9097.4 0 12639.8 0 13040.1 0 11687.3 0 11191.7 0 11391.9 0 11793.1 0 13933.2 0 12778.1 0 11810.3 0 13698.4 0 11956.6 0 10723.8 0 13938.9 0 13979.8 0 13807.4 0 12973.9 0 12509.8 0 12934.1 0 14908.3 0 13772.1 0 13012.6 0 14049.9 0 11816.5 0 11593.2 0 14466.2 0 13615.9 0 14733.9 0 13880.7 0 13527.5 0 13584 0 16170.2 0 13260.6 0 14741.9 0 15486.5 0 13154.5 0 12621.2 0 15031.6 0 15452.4 0 15428 0 13105.9 0 14716.8 1 14180 1 16202.2 1 14392.4 1 15140.6 1 15960.1 1 14351.3 1 13230.2 1 15202.1 1 17157.3 1 16159.1 1 13405.7 1 17224.7 1 17338.4 1 17370.6 1 18817.8 1 16593.2 1 17979.5 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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation y[t] = + 13249.3123076923 + 2526.01923076923x[t] + 803.164615384617M1[t] -1244.97615384615M2[t] -2301.35615384615M3[t] + 501.203846153846M4[t] + 894.583846153845M5[t] + 608.623846153846M6[t] -842.936153846154M7[t] -385.580000000001M8[t] -293.8M9[t] + 1457.18M10[t] + 344.48M11[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) 13249.3123076923 570.611062 23.2195 0 0 x 2526.01923076923 354.788842 7.1198 0 0 M1 803.164615384617 748.70814 1.0727 0.288754 0.144377 M2 -1244.97615384615 784.824142 -1.5863 0.119235 0.059618 M3 -2301.35615384615 784.824142 -2.9323 0.005142 0.002571 M4 501.203846153846 784.824142 0.6386 0.526106 0.263053 M5 894.583846153845 784.824142 1.1399 0.260004 0.130002 M6 608.623846153846 784.824142 0.7755 0.441854 0.220927 M7 -842.936153846154 784.824142 -1.074 0.288172 0.144086 M8 -385.580000000001 781.609831 -0.4933 0.624039 0.31202 M9 -293.8 781.609831 -0.3759 0.708654 0.354327 M10 1457.18 781.609831 1.8643 0.068397 0.034198 M11 344.48 781.609831 0.4407 0.661386 0.330693 Multiple Linear Regression - Regression Statistics Multiple R 0.821100104405425 R-squared 0.6742053814546 Adjusted R-squared 0.592756726818249 F-TEST (value) 8.27767363948213 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 3.73530576469605e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1235.83365422433 Sum Squared Residuals 73309671.4038461 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 12192.5 14052.4769230769 -1859.97692307691 2 11268.8 12004.3361538462 -735.536153846155 3 9097.4 10947.9561538462 -1850.55615384615 4 12639.8 13750.5161538462 -1110.71615384616 5 13040.1 14143.8961538462 -1103.79615384615 6 11687.3 13857.9361538462 -2170.63615384615 7 11191.7 12406.3761538462 -1214.67615384615 8 11391.9 12863.7323076923 -1471.83230769231 9 11793.1 12955.5123076923 -1162.41230769231 10 13933.2 14706.4923076923 -773.292307692307 11 12778.1 13593.7923076923 -815.692307692308 12 11810.3 13249.3123076923 -1439.01230769231 13 13698.4 14052.4769230769 -354.076923076925 14 11956.6 12004.3361538462 -47.7361538461534 15 10723.8 10947.9561538462 -224.156153846155 16 13938.9 13750.5161538462 188.383846153846 17 13979.8 14143.8961538462 -164.096153846154 18 13807.4 13857.9361538462 -50.5361538461538 19 12973.9 12406.3761538462 567.523846153845 20 12509.8 12863.7323076923 -353.932307692308 21 12934.1 12955.5123076923 -21.4123076923074 22 14908.3 14706.4923076923 201.807692307692 23 13772.1 13593.7923076923 178.307692307693 24 13012.6 13249.3123076923 -236.712307692308 25 14049.9 14052.4769230769 -2.57692307692543 26 11816.5 12004.3361538462 -187.836153846154 27 11593.2 10947.9561538462 645.243846153846 28 14466.2 13750.5161538462 715.683846153847 29 13615.9 14143.8961538462 -527.996153846154 30 14733.9 13857.9361538462 875.963846153846 31 13880.7 12406.3761538462 1474.32384615385 32 13527.5 12863.7323076923 663.767692307693 33 13584 12955.5123076923 628.487692307692 34 16170.2 14706.4923076923 1463.70769230769 35 13260.6 13593.7923076923 -333.192307692307 36 14741.9 13249.3123076923 1492.58769230769 37 15486.5 14052.4769230769 1434.02307692308 38 13154.5 12004.3361538462 1150.16384615385 39 12621.2 10947.9561538462 1673.24384615385 40 15031.6 13750.5161538462 1281.08384615385 41 15452.4 14143.8961538462 1308.50384615385 42 15428 13857.9361538462 1570.06384615385 43 13105.9 12406.3761538462 699.523846153846 44 14716.8 15389.7515384615 -672.951538461539 45 14180 15481.5315384615 -1301.53153846154 46 16202.2 17232.5115384615 -1030.31153846154 47 14392.4 16119.8115384615 -1727.41153846154 48 15140.6 15775.3315384615 -634.731538461538 49 15960.1 16578.4961538462 -618.396153846156 50 14351.3 14530.3553846154 -179.055384615384 51 13230.2 13473.9753846154 -243.775384615384 52 15202.1 16276.5353846154 -1074.43538461538 53 17157.3 16669.9153846154 487.384615384615 54 16159.1 16383.9553846154 -224.855384615384 55 13405.7 14932.3953846154 -1526.69538461538 56 17224.7 15389.7515384615 1834.94846153846 57 17338.4 15481.5315384615 1856.86846153846 58 17370.6 17232.5115384615 138.088461538460 59 18817.8 16119.8115384615 2697.98846153846 60 16593.2 15775.3315384615 817.868461538462 61 17979.5 16578.4961538462 1401.00384615384 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.573436956242077 0.853126087515846 0.426563043757923 17 0.458563382972723 0.917126765945446 0.541436617027277 18 0.550728466150623 0.898543067698754 0.449271533849377 19 0.546928642964014 0.906142714071972 0.453071357035986 20 0.492018855546516 0.984037711093032 0.507981144453484 21 0.430125928794166 0.860251857588332 0.569874071205834 22 0.354013920073652 0.708027840147304 0.645986079926348 23 0.288034491150248 0.576068982300496 0.711965508849752 24 0.261782857058673 0.523565714117345 0.738217142941327 25 0.243953000364905 0.487906000729811 0.756046999635095 26 0.184841492260500 0.369682984520999 0.8151585077395 27 0.197166482848731 0.394332965697462 0.802833517151269 28 0.16460356446793 0.32920712893586 0.83539643553207 29 0.146144486641189 0.292288973282379 0.85385551335881 30 0.169097983732316 0.338195967464631 0.830902016267684 31 0.189630796133017 0.379261592266034 0.810369203866983 32 0.185412749935631 0.370825499871262 0.814587250064369 33 0.158642674945210 0.317285349890421 0.84135732505479 34 0.148325951516728 0.296651903033455 0.851674048483272 35 0.155578201317322 0.311156402634644 0.844421798682678 36 0.164840021739473 0.329680043478947 0.835159978260526 37 0.167711088337852 0.335422176675704 0.832288911662148 38 0.132731424495865 0.265462848991729 0.867268575504135 39 0.118471002386599 0.236942004773197 0.881528997613401 40 0.0856399428537066 0.171279885707413 0.914360057146293 41 0.0695869807627261 0.139173961525452 0.930413019237274 42 0.0508950568894209 0.101790113778842 0.94910494311058 43 0.0260797934632079 0.0521595869264158 0.973920206536792 44 0.0227842676497799 0.0455685352995599 0.97721573235022 45 0.0323610287857641 0.0647220575715282 0.967638971214236 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 1 0.0333333333333333 OK 10% type I error level 3 0.1 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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