Workshop 7: model 2

*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: Fri, 20 Nov 2009 03:54:01 -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/20/t1258714824jiiapobrrziscq8.htm/, Retrieved Fri, 20 Nov 2009 12:00:36 +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/Nov/20/t1258714824jiiapobrrziscq8.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:

ws7m2mldg

Dataseries X:

» Textbox « » Textfile « » CSV «

267413 21.4 267366 26.4 264777 26.4 258863 29.4 254844 34.4 254868 24.4 277267 26.4 285351 25.4 286602 31.4 283042 27.4 276687 27.4 277915 29.4 277128 32.4 277103 26.4 275037 22.4 270150 19.4 267140 21.4 264993 23.4 287259 23.4 291186 25.4 292300 28.4 288186 27.4 281477 21.4 282656 17.4 280190 24.4 280408 26.4 276836 22.4 275216 14.4 274352 18.4 271311 25.4 289802 29.4 290726 26.4 292300 26.4 278506 20.4 269826 26.4 265861 29.4 269034 33.4 264176 32.4 255198 35.4 253353 34.4 246057 36.4 235372 32.4 258556 34.4 260993 31.4 254663 27.4 250643 27.4 243422 30.4 247105 32.4 248541 32.4 245039 27.4 237080 31.4 237085 29.4 225554 27.4 226839 25.4 247934 26.4 248333 23.4 246969 18.4 245098 22.4 246263 17.4 255765 17.4 264319 11.4 268347 9.4 273046 6.4 273963 0 267430 7.8 271993 7.9 292710 12 295881 16.9 293299 12.3

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] = + 284296.210684253 -731.579789057658X[t] + 2422.53918567349M1[t] + 871.362765106428M2[t] -3027.19042759867M3[t] -7372.77181586589M4[t] -10622.6551434852M5[t] -13130.8052342349M6[t] + 9825.14397187436M7[t] + 12604.1610808612M8[t] + 10987.1165759170M9[t] + 3088.28404218847M10[t] -2764.34787343459M11[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) 284296.210684253 9679.166192 29.372 0 0 X -731.579789057658 257.065011 -2.8459 0.006177 0.003088 M1 2422.53918567349 9739.338985 0.2487 0.804474 0.402237 M2 871.362765106428 9738.415413 0.0895 0.929022 0.464511 M3 -3027.19042759867 9742.033806 -0.3107 0.757156 0.378578 M4 -7372.77181586589 9792.719622 -0.7529 0.454674 0.227337 M5 -10622.6551434852 9740.424541 -1.0906 0.280131 0.140065 M6 -13130.8052342349 9751.925699 -1.3465 0.183572 0.091786 M7 9825.14397187436 9737.736815 1.009 0.317326 0.158663 M8 12604.1610808612 9738.175081 1.2943 0.200872 0.100436 M9 10987.1165759170 9742.162874 1.1278 0.264217 0.132109 M10 3088.28404218847 10170.801336 0.3036 0.762526 0.381263 M11 -2764.34787343459 10171.840845 -0.2718 0.786802 0.393401 Multiple Linear Regression - Regression Statistics Multiple R 0.544664723571685 R-squared 0.296659661103420 Adjusted R-squared 0.145943874197011 F-TEST (value) 1.96833833530417 F-TEST (DF numerator) 12 F-TEST (DF denominator) 56 p-value 0.0450649302679921 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16081.2434620038 Sum Squared Residuals 14481957911.9175 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 267413 271062.942384094 -3649.94238409385 2 267366 265853.867018237 1512.13298176276 3 264777 261955.313825532 2821.68617446786 4 258863 255414.993070092 3448.00692990804 5 254844 248507.210797184 6336.78920281566 6 254868 253314.858597011 1553.14140298873 7 277267 274807.648225005 2459.35177499484 8 285351 278318.245123050 7032.75487695027 9 286602 272311.721883760 14290.2781162404 10 283042 267339.208506262 15702.7914937384 11 276687 261486.576590639 15200.4234093614 12 277915 262787.764885958 15127.2351140422 13 277128 263015.564704458 14112.4352955416 14 277103 265853.867018237 11249.1329817628 15 275037 264881.632981763 10155.3670182372 16 270150 262730.790960669 7419.20903933147 17 267140 258017.748054934 9122.25194506612 18 264993 254046.438386069 10946.5616139311 19 287259 277002.387592178 10256.6124078219 20 291186 278318.245123050 12867.7548769503 21 292300 274506.461250933 17793.5387490675 22 288186 267339.208506262 20846.7914937384 23 281477 265876.055324984 15600.9446750155 24 282656 271566.72235465 11089.2776453503 25 280190 268868.203016920 11321.7969830804 26 280408 265853.867018237 14554.1329817628 27 276836 264881.632981763 11954.3670182372 28 275216 266388.689905957 8827.31009404318 29 274352 260212.487422107 14139.5125778932 30 271311 252583.278807954 18727.7211920464 31 289802 272612.908857832 17189.0911421678 32 290726 277586.665333992 13139.3346660080 33 292300 275969.620829048 16330.3791709522 34 278506 272460.267029665 6045.73297033477 35 269826 262218.156379696 7607.84362030378 36 265861 262787.764885958 3073.23511404216 37 269034 262283.984915401 6750.0150845993 38 264176 261464.388283891 2711.61171610871 39 255198 255371.095724013 -173.095724013213 40 253353 251757.094124804 1595.90587519633 41 246057 247044.051219069 -987.051219069012 42 235372 247462.22028455 -12090.22028455 43 258556 268955.009912544 -10399.0099125439 44 260993 273928.766388704 -12935.7663887037 45 254663 275238.04103999 -20575.0410399902 46 250643 267339.208506262 -16696.2085062616 47 243422 259291.837223466 -15869.8372234656 48 247105 260593.025518785 -13488.0255187849 49 248541 263015.564704458 -14474.5647044583 50 245039 265122.287229180 -20083.2872291796 51 237080 258297.414880244 -21217.4148802438 52 237085 255414.993070092 -18329.9930700920 53 225554 253628.269320588 -28074.2693205879 54 226839 252583.278807954 -25744.2788079536 55 247934 274807.648225005 -26873.6482250052 56 248333 279781.404701165 -31448.404701165 57 246969 281822.259141509 -34853.2591415091 58 245098 270997.10745155 -25899.1074515499 59 246263 268802.374481215 -22539.3744812151 60 255765 271566.72235465 -15801.7223546497 61 264319 278378.740274669 -14059.7402746692 62 268347 278290.723432217 -9943.7234322174 63 273046 276586.909606685 -3540.90960668529 64 273963 276923.438868387 -2960.43886838708 65 267430 267967.233186118 -537.233186118014 66 271993 265385.925116463 6607.07488353739 67 292710 285342.397187435 7367.60281256456 68 295881 284536.67333004 11344.3266699602 69 293299 286284.895854761 7014.10414523919 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.118224212245494 0.236448424490988 0.881775787754506 17 0.0549234048119934 0.109846809623987 0.945076595188007 18 0.0294786596751302 0.0589573193502604 0.97052134032487 19 0.0144941280975493 0.0289882561950986 0.98550587190245 20 0.00628762596977568 0.0125752519395514 0.993712374030224 21 0.00270969245523458 0.00541938491046915 0.997290307544765 22 0.00139502983406424 0.00279005966812847 0.998604970165936 23 0.000553327570660461 0.00110665514132092 0.99944667242934 24 0.000202094877113869 0.000404189754227738 0.999797905122886 25 0.000102946012597557 0.000205892025195115 0.999897053987402 26 7.5301022346048e-05 0.000150602044692096 0.999924698977654 27 3.79703356015315e-05 7.5940671203063e-05 0.999962029664399 28 1.48953887144259e-05 2.97907774288518e-05 0.999985104611286 29 8.8401208702266e-06 1.76802417404532e-05 0.99999115987913 30 2.00818648204844e-05 4.01637296409687e-05 0.99997991813518 31 3.04426377056152e-05 6.08852754112304e-05 0.999969557362294 32 1.90051988191343e-05 3.80103976382685e-05 0.99998099480118 33 2.08031806036161e-05 4.16063612072321e-05 0.999979196819396 34 4.08259290902648e-05 8.16518581805296e-05 0.99995917407091 35 5.57416449967083e-05 0.000111483289993417 0.999944258355003 36 6.83363907838866e-05 0.000136672781567773 0.999931663609216 37 6.0402449525086e-05 0.000120804899050172 0.999939597550475 38 6.99575465209093e-05 0.000139915093041819 0.99993004245348 39 7.72882511476298e-05 0.000154576502295260 0.999922711748852 40 8.35434253109684e-05 0.000167086850621937 0.999916456574689 41 0.000204174427723525 0.000408348855447051 0.999795825572277 42 0.0008548517611612 0.0017097035223224 0.99914514823884 43 0.00160808927911828 0.00321617855823657 0.998391910720882 44 0.00337404544143199 0.00674809088286398 0.996625954558568 45 0.0266709865084713 0.0533419730169426 0.973329013491529 46 0.0497882923625857 0.0995765847251714 0.950211707637414 47 0.0703496912295551 0.140699382459110 0.929650308770445 48 0.0700947750120264 0.140189550024053 0.929905224987974 49 0.0842590229833847 0.168518045966769 0.915740977016615 50 0.087679490148068 0.175358980296136 0.912320509851932 51 0.0812485455750862 0.162497091150172 0.918751454424914 52 0.200853957317887 0.401707914635773 0.799146042682113 53 0.237352828469072 0.474705656938144 0.762647171530928 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.631578947368421 NOK 5% type I error level 26 0.68421052631579 NOK 10% type I error level 29 0.763157894736842 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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