*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 07:22:29 -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/t1258727015i5afb97vf8x4t59.htm/, Retrieved Fri, 20 Nov 2009 15:23:47 +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/t1258727015i5afb97vf8x4t59.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:

shwws7

Dataseries X:

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7024 2735 6981 6962 6699 6539 6940 2659 7024 6981 6962 6699 6774 2654 6940 7024 6981 6962 6671 2670 6774 6940 7024 6981 6965 2785 6671 6774 6940 7024 6969 2845 6965 6671 6774 6940 6822 2723 6969 6965 6671 6774 6878 2746 6822 6969 6965 6671 6691 2767 6878 6822 6969 6965 6837 2940 6691 6878 6822 6969 7018 2977 6837 6691 6878 6822 7167 2993 7018 6837 6691 6878 7076 2892 7167 7018 6837 6691 7171 2824 7076 7167 7018 6837 7093 2771 7171 7076 7167 7018 6971 2686 7093 7171 7076 7167 7142 2738 6971 7093 7171 7076 7047 2723 7142 6971 7093 7171 6999 2731 7047 7142 6971 7093 6650 2632 6999 7047 7142 6971 6475 2606 6650 6999 7047 7142 6437 2605 6475 6650 6999 7047 6639 2646 6437 6475 6650 6999 6422 2627 6639 6437 6475 6650 6272 2535 6422 6639 6437 6475 6232 2456 6272 6422 6639 6437 6003 2404 6232 6272 6422 6639 5673 2319 6003 6232 6272 6422 6050 2519 5673 6003 6232 6272 5977 2504 6050 5673 6003 6232 5796 2382 5977 6050 5673 6003 5752 2394 5796 5977 6050 5673 5609 2381 5752 5796 5977 6050 5 etc...

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] = -620.645522131992 + 1.12559599862179X[t] + 0.588250430193732`Y-1`[t] + 0.202239932456929`Y-2`[t] -0.119445465275896`Y-3`[t] -0.0445844438979129`Y-4`[t] -3.14891715732790M1[t] + 121.751080764899M2[t] + 45.263293361877M3[t] + 74.9696221902687M4[t] + 280.845825566085M5[t] + 64.0656486594804M6[t] -16.3205169905858M7[t] + 35.6389122153682M8[t] -1.96193224239403M9[t] + 75.2337682511196M10[t] + 193.584054612444M11[t] + 0.18436507248157t + 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) -620.645522131992 275.31328 -2.2543 0.030022 0.015011 X 1.12559599862179 0.188956 5.9569 1e-06 0 `Y-1` 0.588250430193732 0.137351 4.2828 0.000121 6e-05 `Y-2` 0.202239932456929 0.16725 1.2092 0.234054 0.117027 `Y-3` -0.119445465275896 0.166839 -0.7159 0.47841 0.239205 `Y-4` -0.0445844438979129 0.12344 -0.3612 0.719963 0.359982 M1 -3.14891715732790 77.242578 -0.0408 0.967695 0.483848 M2 121.751080764899 89.33078 1.3629 0.180929 0.090464 M3 45.263293361877 75.025065 0.6033 0.549888 0.274944 M4 74.9696221902687 78.713692 0.9524 0.346896 0.173448 M5 280.845825566085 78.656329 3.5705 0.000986 0.000493 M6 64.0656486594804 62.499966 1.0251 0.31182 0.15591 M7 -16.3205169905858 73.532638 -0.2219 0.825542 0.412771 M8 35.6389122153682 94.442939 0.3774 0.708006 0.354003 M9 -1.96193224239403 76.091243 -0.0258 0.979565 0.489782 M10 75.2337682511196 78.190287 0.9622 0.342038 0.171019 M11 193.584054612444 69.290445 2.7938 0.008116 0.004058 t 0.18436507248157 0.998013 0.1847 0.854421 0.427211 Multiple Linear Regression - Regression Statistics Multiple R 0.99121820663942 R-squared 0.98251353317347 Adjusted R-squared 0.974690640119495 F-TEST (value) 125.594652310160 F-TEST (DF numerator) 17 F-TEST (DF denominator) 38 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 82.3882273668344 Sum Squared Residuals 257937.16032867 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 7024 6877.76279442965 146.237205570348 2 6940 6907.8915203529 32.1084796471026 3 6774 6771.24822640323 2.75177359677171 4 6671 6698.52747110258 -27.5274711025852 5 6965 6947.98624429015 17.0137557098505 6 6969 6974.61414633045 -5.61414633045086 7 6822 6838.60507639459 -16.6050763945905 8 6878 6800.44895606305 77.5510439369518 9 6691 6776.29713830142 -85.2971383014155 10 6837 6967.1080630203 -130.108063020306 11 7018 7175.2204290395 -157.2204290395 12 7167 7155.67020662957 11.3297933704273 13 7076 7154.17345363612 -78.1734536361246 14 7171 7151.19129148897 19.8087085110280 15 7093 7026.84407957467 66.1559204253303 16 6971 6938.6148288203 32.3851711796947 17 7142 7108.37498717516 33.6250128248395 18 7047 6955.89401128631 91.1059887136883 19 6999 6881.44614966713 117.553850332872 20 6650 6759.72125344267 -109.721253442666 21 6475 6481.75574049234 -6.75574049234104 22 6437 6394.45355285189 42.5464471481121 23 6639 6545.21865639025 93.7813436097497 24 6422 6478.0370396859 -56.037039685898 25 6272 6297.06098409473 -25.0609840947254 26 6232 6178.66585820849 53.3341417915107 27 6003 6006.87904517082 -3.87904517081784 28 5673 5825.88677749343 -152.886777493429 29 6050 6028.09644436524 21.9035556347609 30 5977 5978.78431632814 -1.78431632813645 31 5796 5844.18881824448 -48.1888182444806 32 5752 5758.28484764926 -6.28484764925505 33 5609 5635.65835719429 -26.6583571942899 34 5839 5779.96586766858 59.0341323314237 35 6069 6053.09666848054 15.9033315194631 36 6006 6041.41704743962 -35.4170474396174 37 5809 5930.00976530013 -121.009765300131 38 5797 5843.71695874704 -46.7169587470405 39 5502 5573.70761895243 -71.7076189524322 40 5568 5466.35868936643 101.641310633569 41 5864 5849.77401893376 14.2259810662402 42 5764 5782.13025965327 -18.1302596532649 43 5615 5656.45803036863 -41.4580303686308 44 5615 5604.07713823259 10.9228617674137 45 5681 5562.28876401195 118.711235988046 46 5915 5886.47251645923 28.5274835407697 47 6334 6286.46424608971 47.5357539102873 48 6494 6413.87570624491 80.1242937550881 49 6620 6541.99300253937 78.0069974606331 50 6578 6636.5343712026 -58.5343712026009 51 6495 6488.32102989885 6.678970101148 52 6538 6491.61223321725 46.3877667827503 53 6737 6823.76830523569 -86.7683052356914 54 6651 6716.57726640184 -65.5772664018361 55 6530 6541.30192532517 -11.3019253251700 56 6563 6535.46780461244 27.5321953875558 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 21 0.936606761384888 0.126786477230224 0.063393238615112 22 0.950322061126077 0.0993558777478457 0.0496779388739229 23 0.96902215359003 0.0619556928199387 0.0309778464099693 24 0.972947918289392 0.0541041634212155 0.0270520817106078 25 0.959119147625496 0.0817617047490081 0.0408808523745041 26 0.989853432222732 0.0202931355545368 0.0101465677772684 27 0.984411031073958 0.0311779378520843 0.0155889689260422 28 0.976625259154368 0.0467494816912650 0.0233747408456325 29 0.964235441310298 0.0715291173794042 0.0357645586897021 30 0.941026925605586 0.117946148788827 0.0589730743944137 31 0.92762244691465 0.144755106170699 0.0723775530853494 32 0.873984181385375 0.25203163722925 0.126015818614625 33 0.949458131786104 0.101083736427792 0.050541868213896 34 0.907950496457666 0.184099007084667 0.0920495035423337 35 0.9182035947995 0.163592810401002 0.0817964052005011 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 0.2 NOK 10% type I error level 8 0.533333333333333 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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