*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, 22 Nov 2009 09:56:15 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Nov/22/t1258909036yp5al6jbxsy57j9.htm/, Retrieved Sun, 22 Nov 2009 17:57:28 +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/22/t1258909036yp5al6jbxsy57j9.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:

Dataseries X:

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99.9 98.8 98.6 100.5 107.2 110.4 95.7 96.4 93.7 101.9 106.7 106.2 86.7 81 95.3 94.7 99.3 101 101.8 109.4 96 102.3 91.7 90.7 95.3 96.2 96.6 96.1 107.2 106 108 103.1 98.4 102 103.1 104.7 81.1 86 96.6 92.1 103.7 106.9 106.6 112.6 97.6 101.7 87.6 92 99.4 97.4 98.5 97 105.2 105.4 104.6 102.7 97.5 98.1 108.9 104.5 86.8 87.4 88.9 89.9 110.3 109.8 114.8 111.7 94.6 98.6 92 96.9 93.8 95.1 93.8 97 107.6 112.7 101 102.9 95.4 97.4 96.5 111.4 89.2 87.4 87.1 96.8 110.5 114.1 110.8 110.3 104.2 103.9 88.9 101.6 89.8 94.6 90 95.9 93.9 104.7 91.3 102.8 87.8 98.1 99.7 113.9 73.5 80.9 79.2 95.7 96.9 113.2 95.2 105.9 95.6 108.8 89.7 102.3

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation TotProd[t] = + 57.9679669988610 + 0.331044808698439ProdMetal[t] + 5.75269254643562M1[t] + 5.32137311478093M2[t] + 10.5521608310994M3[t] + 8.52450133355162M4[t] + 3.65307453564437M5[t] + 9.21284738848986M6[t] -2.49449512622698M7[t] + 0.386788152877537M8[t] + 10.0881488530092M9[t] + 11.4637249404847M10[t] + 5.51455501667793M11[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) 57.9679669988610 21.660842 2.6762 0.010219 0.00511 ProdMetal 0.331044808698439 0.222609 1.4871 0.143663 0.071831 M1 5.75269254643562 3.409913 1.687 0.098221 0.049111 M2 5.32137311478093 3.411959 1.5596 0.125558 0.062779 M3 10.5521608310994 4.215844 2.503 0.015849 0.007925 M4 8.52450133355162 3.578231 2.3823 0.021302 0.010651 M5 3.65307453564437 3.465852 1.054 0.297263 0.148631 M6 9.21284738848986 4.255469 2.1649 0.035503 0.017751 M7 -2.49449512622698 4.353281 -0.573 0.569366 0.284683 M8 0.386788152877537 3.468279 0.1115 0.911678 0.455839 M9 10.0881488530092 4.372728 2.3071 0.025505 0.012753 M10 11.4637249404847 4.512539 2.5404 0.014435 0.007218 M11 5.51455501667793 3.691624 1.4938 0.141911 0.070956 Multiple Linear Regression - Regression Statistics Multiple R 0.814925846393735 R-squared 0.664104135120545 Adjusted R-squared 0.578343488768344 F-TEST (value) 7.74369321323916 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.14025975106458e-07 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 5.39064515829913 Sum Squared Residuals 1365.77559546661 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 99.9 96.427886644702 3.47211335529794 2 98.6 96.559343387835 2.040656612165 3 107.2 105.067474710268 2.13252528973200 4 95.7 98.405187890942 -2.70518789094208 5 93.7 95.3545075408763 -1.65450754087626 6 106.7 102.337773071125 4.36222692887497 7 86.7 82.2881013772075 4.41189862279248 8 95.3 89.7046985354807 5.59530146451934 9 99.3 101.491641530412 -2.19164153041248 10 101.8 105.647994010955 -3.84799401095491 11 96 97.3484059453892 -1.34840594538917 12 91.7 87.9937311478094 3.70626885219064 13 95.3 95.5671701420864 -0.267170142086404 14 96.6 95.1027462295619 1.49725377043812 15 107.2 103.610877551995 3.58912244800513 16 108 100.623188109222 7.37681189077837 17 98.4 95.387612021746 3.01238797825391 18 103.1 101.841205858077 1.25879414192263 19 81.1 83.9433254206997 -2.84332542069973 20 96.6 88.8439820328647 7.75601796713528 21 103.7 103.444805901733 0.255194098266718 22 106.6 106.70733739879 -0.107337398789911 23 97.6 97.1497790601701 0.450220939829870 24 87.6 88.4240893991173 -0.824089399117342 25 99.4 95.9644239125245 3.43557608747548 26 98.5 95.4006865573905 3.09931344260953 27 105.2 103.412250666776 1.78774933322419 28 104.6 100.490770185742 4.10922981425774 29 97.5 94.0965372678222 3.40346273217782 30 108.9 101.774996896338 7.12500310366232 31 86.8 84.4067881528775 2.39321184712246 32 88.9 88.1156834537282 0.784316546271857 33 110.3 104.404835846959 5.89516415304124 34 114.8 106.409397070961 8.39060292903869 35 94.6 96.123540153205 -1.52354015320497 36 92 90.0462089617397 1.95379103826031 37 93.8 95.203020852518 -1.40302085251812 38 93.8 95.4006865573905 -1.60068655739047 39 107.6 105.828877770274 1.77112222972558 40 101 100.556979147482 0.443020852518057 41 95.4 93.8648059017333 1.53519409826673 42 96.5 104.059206076357 -7.55920607635692 43 89.2 84.4067881528775 4.79321184712246 44 87.1 90.3998926337474 -3.29989263374738 45 110.5 105.828328524362 4.67167147563796 46 110.8 105.945934338784 4.8540656612165 47 104.2 97.8780776393067 6.32192236069331 48 88.9 91.6021195626223 -2.70211956262234 49 89.8 95.0374984481689 -5.2374984481689 50 90 95.0365372678222 -5.03653726782219 51 93.9 103.180519300687 -9.2805193006869 52 91.3 100.523874666612 -9.2238746666121 53 87.8 94.0965372678222 -6.29653726782219 54 99.7 104.886818098103 -5.18681809810301 55 73.5 82.2549968963377 -8.75499689633769 56 79.2 90.035743344179 -10.8357433441791 57 96.9 105.530388196533 -8.63038819653344 58 95.2 104.489337180510 -9.28933718051036 59 95.6 99.500197201929 -3.90019720192905 60 89.7 91.8338509287113 -2.13385092871126 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.15609546910124 0.31219093820248 0.84390453089876 17 0.106456257338005 0.212912514676009 0.893543742661995 18 0.0494150740094112 0.0988301480188225 0.950584925990589 19 0.128252646062678 0.256505292125356 0.871747353937322 20 0.098748157408818 0.197496314817636 0.901251842591182 21 0.0522515161125840 0.104503032225168 0.947748483887416 22 0.0289718211230598 0.0579436422461196 0.97102817887694 23 0.0146315789409702 0.0292631578819404 0.98536842105903 24 0.0103341942833584 0.0206683885667168 0.989665805716642 25 0.00571565077629259 0.0114313015525852 0.994284349223707 26 0.00305642005271608 0.00611284010543216 0.996943579947284 27 0.00142995129332808 0.00285990258665617 0.998570048706672 28 0.000789388223759572 0.00157877644751914 0.99921061177624 29 0.000563992542502653 0.00112798508500531 0.999436007457497 30 0.00151942601831112 0.00303885203662225 0.99848057398169 31 0.000682124722288089 0.00136424944457618 0.999317875277712 32 0.00137110759247551 0.00274221518495101 0.998628892407525 33 0.00260142809641477 0.00520285619282953 0.997398571903585 34 0.0123969842241173 0.0247939684482345 0.987603015775883 35 0.0071927815034362 0.0143855630068724 0.992807218496564 36 0.00972323927551902 0.0194464785510380 0.99027676072448 37 0.00576374291054047 0.0115274858210809 0.99423625708946 38 0.00338812135556609 0.00677624271113218 0.996611878644434 39 0.00175895543549514 0.00351791087099028 0.998241044564505 40 0.0020873968911785 0.004174793782357 0.997912603108821 41 0.00193296708975173 0.00386593417950346 0.998067032910248 42 0.00722712213065592 0.0144542442613118 0.992772877869344 43 0.0047447629831715 0.009489525966343 0.995255237016828 44 0.00501408706213681 0.0100281741242736 0.994985912937863 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 13 0.448275862068966 NOK 5% type I error level 22 0.758620689655172 NOK 10% type I error level 24 0.827586206896552 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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