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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 13:43:15 -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/t122816439807cgs5s99vod1tk.htm/, Retrieved Mon, 01 Dec 2008 20:46:48 +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/t122816439807cgs5s99vod1tk.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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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:

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1202455 1 1201423 0 1505916 0 1513378 0 1977605 0 1873830 0 1424049 0 1322740 0 1584826 0 1680460 0 1648574 0 3095469 1 1307983 0 1367589 0 1572718 0 1611603 0 1641196 0 1845262 0 1464238 0 1402386 0 2077100 0 1691130 0 1729013 0 3347792 1 1365088 0 1545460 0 1844355 0 1775550 0 1721779 0 2128726 0 1664320 0 1769471 0 1904578 0 1872042 0 1802181 0 3222199 1 1491414 0 1658519 0 2079207 0 1748767 0 2084447 0 2067182 0 1718123 0 1782337 0 1958118 0 2028681 0 2076128 0 3383873 1 1870369 0 1654853 0 2074338 0 1888654 0 1991138 0 2168238 0 1867424 0 1842360 0 1927476 0 2065555 0 2455609 0 3336171 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 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation y[t] = + 2979354.60869565 -31710.9130434736x[t] -1754340.28188406M1[t] -1731727.05072463M2[t] -1411140.63695652M3[t] -1528008.62318840M4[t] -1361517.60942029M5[t] -1237254.59565217M6[t] -1635422.98188406M7[t] -1648346.56811594M8[t] -1390937.35434782M9[t] -1422934.94057971M10[t] -1357359.12681159M11[t] + 9151.58623188407t + 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) 2979354.60869565 161109.641781 18.4927 0 0 x -31710.9130434736 140583.401935 -0.2256 0.822538 0.411269 M1 -1754340.28188406 138936.874338 -12.6269 0 0 M2 -1731727.05072463 162680.81869 -10.6449 0 0 M3 -1411140.63695652 162458.502064 -8.6862 0 0 M4 -1528008.62318840 162241.520541 -9.4181 0 0 M5 -1361517.60942029 162029.895556 -8.4029 0 0 M6 -1237254.59565217 161823.648123 -7.6457 0 0 M7 -1635422.98188406 161622.798829 -10.1188 0 0 M8 -1648346.56811594 161427.367823 -10.2111 0 0 M9 -1390937.35434782 161237.374808 -8.6266 0 0 M10 -1422934.94057971 161052.839028 -8.8352 0 0 M11 -1357359.12681159 160873.779264 -8.4374 0 0 t 9151.58623188407 956.548892 9.5673 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.97577386236217 R-squared 0.952134630469186 Adjusted R-squared 0.938607460819174 F-TEST (value) 70.3868329520288 F-TEST (DF numerator) 13 F-TEST (DF denominator) 46 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 123094.128845674 Sum Squared Residuals 696999569588.663 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1202455 1202455 -3.67435859516263e-10 2 1201423 1265930.73043479 -64507.730434786 3 1505916 1595668.73043478 -89752.7304347819 4 1513378 1487952.33043479 25425.6695652131 5 1977605 1663594.93043478 314010.06956522 6 1873830 1797009.53043478 76820.4695652184 7 1424049 1407992.73043478 16056.2695652168 8 1322740 1404220.73043478 -81480.730434783 9 1584826 1670781.53043478 -85955.53043478 10 1680460 1647935.53043478 32524.4695652169 11 1648574 1722662.93043478 -74088.9304347816 12 3095469 3057462.73043478 38006.2695652177 13 1307983 1343984.94782609 -36001.9478260867 14 1367589 1375749.76521739 -8160.76521739052 15 1572718 1705487.76521739 -132769.765217392 16 1611603 1597771.36521739 13831.6347826099 17 1641196 1773413.96521739 -132217.965217392 18 1845262 1906828.56521739 -61566.5652173915 19 1464238 1517811.76521739 -53573.7652173909 20 1402386 1514039.76521739 -111653.765217391 21 2077100 1780600.56521739 296499.434782608 22 1691130 1757754.56521739 -66624.565217391 23 1729013 1832481.96521739 -103468.965217391 24 3347792 3167281.76521739 180510.234782609 25 1365088 1453803.98260870 -88715.9826086955 26 1545460 1485568.8 59891.2000000009 27 1844355 1815306.8 29048.1999999997 28 1775550 1707590.4 67959.6000000012 29 1721779 1883233 -161454.000000001 30 2128726 2016647.6 112078.400000000 31 1664320 1627630.8 36689.2000000002 32 1769471 1623858.8 145612.2 33 1904578 1890419.6 14158.3999999994 34 1872042 1867573.6 4468.40000000019 35 1802181 1942301 -140120.000000000 36 3222199 3277100.8 -54901.7999999999 37 1491414 1563623.01739130 -72209.0173913043 38 1658519 1595387.83478261 63131.1652173922 39 2079207 1925125.83478261 154081.165217391 40 1748767 1817409.43478261 -68642.4347826076 41 2084447 1993052.03478261 91394.9652173906 42 2067182 2126466.63478261 -59284.634782609 43 1718123 1737449.83478261 -19326.8347826085 44 1782337 1733677.83478261 48659.1652173914 45 1958118 2000238.63478261 -42120.6347826095 46 2028681 1977392.63478261 51288.3652173914 47 2076128 2052120.03478261 24007.9652173911 48 3383873 3386919.83478261 -3046.83478260870 49 1870369 1673442.05217391 196926.947826087 50 1654853 1705206.86956522 -50353.8695652166 51 2074338 2034944.86956522 39393.1304347823 52 1888654 1927228.46956522 -38574.4695652164 53 1991138 2102871.06956522 -111733.069565218 54 2168238 2236285.66956522 -68047.6695652178 55 1867424 1847268.86956522 20155.1304347827 56 1842360 1843496.86956522 -1136.86956521749 57 1927476 2110057.66956522 -182581.669565218 58 2065555 2087211.66956522 -21656.6695652173 59 2455609 2161939.06956522 293669.930434782 60 3336171 3496738.86956522 -160567.869565217 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.777817268473271 0.444365463053458 0.222182731526729 18 0.64051805490899 0.71896389018202 0.35948194509101 19 0.50302413232454 0.99395173535092 0.49697586767546 20 0.419510414508979 0.839020829017958 0.580489585491021 21 0.876746290974283 0.246507418051433 0.123253709025717 22 0.819358726670731 0.361282546658537 0.180641273329269 23 0.781258675676125 0.437482648647749 0.218741324323875 24 0.816920112716389 0.366159774567223 0.183079887283611 25 0.777268209982035 0.445463580035931 0.222731790017965 26 0.726412722473332 0.547174555053336 0.273587277526668 27 0.69054530824285 0.618909383514299 0.309454691757149 28 0.618553776953446 0.762892446093109 0.381446223046554 29 0.706667191419088 0.586665617161824 0.293332808580912 30 0.688893344007038 0.622213311985924 0.311106655992962 31 0.600269431849415 0.79946113630117 0.399730568150585 32 0.622952373515953 0.754095252968095 0.377047626484047 33 0.589857000469205 0.82028599906159 0.410142999530795 34 0.485748258502089 0.971496517004178 0.514251741497911 35 0.661132099817581 0.677735800364838 0.338867900182419 36 0.594820091823827 0.810359816352347 0.405179908176173 37 0.755155512515312 0.489688974969376 0.244844487484688 38 0.673431768372003 0.653136463255995 0.326568231627997 39 0.627787826833605 0.74442434633279 0.372212173166395 40 0.532856073361024 0.934287853277952 0.467143926638976 41 0.519942870625039 0.960114258749922 0.480057129374961 42 0.382329695705308 0.764659391410615 0.617670304294692 43 0.248965103894767 0.497930207789535 0.751034896105233 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 0 0 OK

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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