*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, 20 Dec 2009 08:09:56 -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/Dec/20/t1261323491xeifv8ovdyvnq6w.htm/, Retrieved Sun, 20 Dec 2009 16:38:23 +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/Dec/20/t1261323491xeifv8ovdyvnq6w.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:

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Dataseries X:

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2849,27 10872 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 2408,64 2440,25 2350,44 2196,72 2174,56 2921,44 10625 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 2408,64 2440,25 2350,44 2196,72 2981,85 10407 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 2408,64 2440,25 2350,44 3080,58 10463 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 2408,64 2440,25 3106,22 10556 3080,58 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 2408,64 3119,31 10646 3106,22 3080,58 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 2472,81 3061,26 10702 3119,31 3106,22 3080,58 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 2407,6 3097,31 11353 3061,26 3119,31 3106,22 3080,58 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 2454,62 3161,69 11346 3097,31 3061,26 3119,31 3106,22 3080,58 2981,85 2921,44 2849,27 2756,76 2645,64 2497,84 2448,05 3257,16 11451 3161,69 3097,31 30 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 263.734200766228 + 0.000253339919810202X[t] + 1.23877863761127Y1[t] -0.317282826192632Y2[t] + 0.169813272838906Y3[t] -0.0593898141762464Y4[t] + 0.230078665812567Y5[t] -0.455301377384477Y6[t] + 0.133074244597905Y7[t] + 0.144344462501845Y8[t] + 0.0194396382456085Y9[t] -0.264854112662661Y10[t] + 0.55307300684554Y11[t] -0.525001084215331Y12[t] + 47.9017286725281M1[t] + 94.2651699586358M2[t] + 60.4857327806912M3[t] + 121.951904260527M4[t] + 40.5584718885717M5[t] + 228.392489428843M6[t] + 66.902963518707M7[t] -25.7832520296353M8[t] + 39.6934894694768M9[t] + 58.4457634559164M10[t] + 78.4448469281772M11[t] + 3.98110966935865t + 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) 263.734200766228 318.672045 0.8276 0.413666 0.206833 X 0.000253339919810202 0.026648 0.0095 0.99247 0.496235 Y1 1.23877863761127 0.15515 7.9844 0 0 Y2 -0.317282826192632 0.242012 -1.311 0.198636 0.099318 Y3 0.169813272838906 0.244708 0.6939 0.492432 0.246216 Y4 -0.0593898141762464 0.246685 -0.2408 0.811194 0.405597 Y5 0.230078665812567 0.243412 0.9452 0.351214 0.175607 Y6 -0.455301377384477 0.245696 -1.8531 0.072562 0.036281 Y7 0.133074244597905 0.247521 0.5376 0.594336 0.297168 Y8 0.144344462501845 0.242146 0.5961 0.555053 0.277527 Y9 0.0194396382456085 0.246411 0.0789 0.937582 0.468791 Y10 -0.264854112662661 0.244295 -1.0842 0.285924 0.142962 Y11 0.55307300684554 0.248093 2.2293 0.032507 0.016254 Y12 -0.525001084215331 0.191239 -2.7453 0.00959 0.004795 M1 47.9017286725281 118.261871 0.405 0.68798 0.34399 M2 94.2651699586358 121.023341 0.7789 0.441426 0.220713 M3 60.4857327806912 123.436782 0.49 0.627271 0.313636 M4 121.951904260527 123.801433 0.9851 0.331553 0.165776 M5 40.5584718885717 122.992699 0.3298 0.743602 0.371801 M6 228.392489428843 125.422446 1.821 0.077419 0.03871 M7 66.902963518707 120.687384 0.5543 0.582968 0.291484 M8 -25.7832520296353 113.91537 -0.2263 0.822295 0.411147 M9 39.6934894694768 117.451843 0.338 0.737475 0.368737 M10 58.4457634559164 121.293747 0.4819 0.632998 0.316499 M11 78.4448469281772 115.395537 0.6798 0.501239 0.25062 t 3.98110966935865 6.649876 0.5987 0.553358 0.276679 Multiple Linear Regression - Regression Statistics Multiple R 0.988781225067778 R-squared 0.977688311046536 Adjusted R-squared 0.961282657404283 F-TEST (value) 59.5945966168931 F-TEST (DF numerator) 25 F-TEST (DF denominator) 34 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 167.808885383951 Sum Squared Residuals 957433.948469338 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 2849.27 2816.27508428207 32.9949157179337 2 2921.44 2994.6896361064 -73.2496361063972 3 2981.85 3024.85793243141 -43.0079324314072 4 3080.58 3085.71836399457 -5.13836399457217 5 3106.22 3152.44982234285 -46.2298223428475 6 3119.31 3265.90736121444 -146.597361214440 7 3061.26 3203.22651156427 -141.966511564271 8 3097.31 3007.86951229216 89.4404877078393 9 3161.69 3153.27157074454 8.41842925545732 10 3257.16 3241.08683008212 16.0731699178766 11 3277.01 3346.56555055549 -69.5555505554946 12 3295.32 3248.58037234679 46.7396276532099 13 3363.99 3346.7858985894 17.2041014106021 14 3494.17 3436.72119326856 57.4488067314444 15 3667.03 3553.93972106815 113.090278931848 16 3813.06 3735.51249197224 77.5475080277635 17 3917.96 3829.19687812337 88.7631218766249 18 3895.51 4103.14352127401 -207.633521274014 19 3801.06 3938.5486635358 -137.488663535800 20 3570.12 3732.68652617856 -162.566526178561 21 3701.61 3532.4409747153 169.169025284701 22 3862.27 3733.35929508236 128.910704917641 23 3970.1 3856.36344203787 113.736557962129 24 4138.52 3921.27749320525 217.242506794749 25 4199.75 4162.25804757055 37.4919524294548 26 4290.89 4353.91182206719 -63.021822067185 27 4443.91 4334.37922231134 109.530777688664 28 4502.64 4482.3423429824 20.2976570176018 29 4356.98 4423.91805323185 -66.9380532318512 30 4591.27 4435.50795617548 155.762043824521 31 4696.96 4536.49989715262 160.460102847375 32 4621.4 4655.78653367334 -34.3865336733385 33 4562.84 4605.86279664817 -43.0227966481657 34 4202.52 4489.22308052641 -286.703080526411 35 4296.49 4238.72967804291 57.7603219570854 36 4435.23 4220.70906782703 214.520932172969 37 4105.18 4280.62612881557 -175.446128815567 38 4116.68 4002.66949525508 114.010504744920 39 3844.49 4054.47376382167 -209.983763821667 40 3720.98 3710.57670651112 10.4032934888799 41 3674.4 3697.39253654014 -22.9925365401388 42 3857.62 3599.11699593431 258.503004065688 43 3801.06 3774.68478380079 26.3752161992075 44 3504.37 3569.97868720109 -65.6086872010924 45 3032.6 3182.59820690516 -149.998206905158 46 3047.03 2903.21761383401 143.812386165994 47 2962.34 3170.51292384835 -208.172923848345 48 2197.82 2540.18267213309 -342.362672133095 49 2014.45 1926.69484074242 87.7551592575769 50 1862.83 1898.01785330278 -35.1878533027819 51 1905.41 1875.03936036744 30.3706396325610 52 1810.99 1914.10009453967 -103.110094539673 53 1670.07 1622.67270976179 47.3972902382125 54 1864.44 1924.47416540175 -60.0341654017546 55 2052.02 1959.40014394651 92.6198560534883 56 2029.6 1856.47874065485 173.121259345153 57 2070.83 2055.39645098683 15.4335490131661 58 2293.41 2295.5031804751 -2.09318047510133 59 2443.27 2337.03840551537 106.231594484625 60 2513.17 2649.31039448783 -136.140394487834 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 29 0.0241374538447278 0.0482749076894557 0.975862546155272 30 0.00440780505639465 0.0088156101127893 0.995592194943605 31 0.00122077032687833 0.00244154065375667 0.998779229673122 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 2 0.666666666666667 NOK 5% type I error level 3 1 NOK 10% type I error level 3 1 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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