*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: Tue, 17 Nov 2009 11:05:01 -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/17/t1258481426jhm8vra37iyq6nj.htm/, Retrieved Tue, 17 Nov 2009 19:10:38 +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/17/t1258481426jhm8vra37iyq6nj.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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16643 16196.7 18252.1 17570.4 89.1 17729 16643 16196.7 18252.1 82.6 16446.1 17729 16643 16196.7 102.7 15993.8 16446.1 17729 16643 91.8 16373.5 15993.8 16446.1 17729 94.1 17842.2 16373.5 15993.8 16446.1 103.1 22321.5 17842.2 16373.5 15993.8 93.2 22786.7 22321.5 17842.2 16373.5 91 18274.1 22786.7 22321.5 17842.2 94.3 22392.9 18274.1 22786.7 22321.5 99.4 23899.3 22392.9 18274.1 22786.7 115.7 21343.5 23899.3 22392.9 18274.1 116.8 22952.3 21343.5 23899.3 22392.9 99.8 21374.4 22952.3 21343.5 23899.3 96 21164.1 21374.4 22952.3 21343.5 115.9 20906.5 21164.1 21374.4 22952.3 109.1 17877.4 20906.5 21164.1 21374.4 117.3 20664.3 17877.4 20906.5 21164.1 109.8 22160 20664.3 17877.4 20906.5 112.8 19813.6 22160 20664.3 17877.4 110.7 17735.4 19813.6 22160 20664.3 100 19640.2 17735.4 19813.6 22160 113.3 20844.4 19640.2 17735.4 19813.6 122.4 19823.1 20844.4 19640.2 17735.4 112.5 18594.6 19823.1 20844.4 19640.2 104.2 21350.6 18594.6 19823.1 20844.4 92.5 18574.1 21350.6 18594.6 19823.1 117.2 18924.2 1857 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 uitvoer[t] = + 9486.87770849843 + 0.318535135680348uitvoer1[t] + 0.315810646656787uitvoer2[t] + 0.347323160619945uitvoer3[t] -70.0796722770106indproc[t] -2475.72420865457M1[t] -1731.61352082471M2[t] -1874.84363157971M3[t] -2511.57931145036M4[t] -2856.95818219675M5[t] + 289.214687944714M6[t] + 420.325783557970M7[t] -504.489001948494M8[t] -4938.92262906067M9[t] -1376.62966118202M10[t] + 1409.51340847633M11[t] -15.8575218202351t + 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) 9486.87770849843 2815.240549 3.3698 0.001705 0.000853 uitvoer1 0.318535135680348 0.145496 2.1893 0.034625 0.017312 uitvoer2 0.315810646656787 0.136508 2.3135 0.026056 0.013028 uitvoer3 0.347323160619945 0.136001 2.5538 0.014676 0.007338 indproc -70.0796722770106 32.509416 -2.1557 0.037339 0.018669 M1 -2475.72420865457 993.900594 -2.4909 0.017106 0.008553 M2 -1731.61352082471 1280.493891 -1.3523 0.184069 0.092034 M3 -1874.84363157971 788.041807 -2.3791 0.022344 0.011172 M4 -2511.57931145036 949.378819 -2.6455 0.011698 0.005849 M5 -2856.95818219675 1048.276869 -2.7254 0.009567 0.004784 M6 289.214687944714 909.429069 0.318 0.752168 0.376084 M7 420.325783557970 871.204114 0.4825 0.632172 0.316086 M8 -504.489001948494 851.274346 -0.5926 0.556851 0.278425 M9 -4938.92262906067 995.42483 -4.9616 1.4e-05 7e-06 M10 -1376.62966118202 1177.147116 -1.1695 0.249315 0.124658 M11 1409.51340847633 1043.009628 1.3514 0.184358 0.092179 t -15.8575218202351 10.67918 -1.4849 0.145609 0.072804 Multiple Linear Regression - Regression Statistics Multiple R 0.901321613188379 R-squared 0.8123806504005 Adjusted R-squared 0.735408609539168 F-TEST (value) 10.5542303583197 F-TEST (DF numerator) 16 F-TEST (DF denominator) 39 p-value 1.30710486878627e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1064.52415988787 Sum Squared Residuals 44195255.7924141 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 16643 17777.2295754169 -1134.22957541690 2 17729 18690.8158377375 -961.815837737508 3 16446.1 16896.1142170079 -450.014217007912 4 15993.8 17096.7214064261 -1102.92140642607 5 16373.5 16402.2677995914 -28.7677995913770 6 17842.2 18434.3918501951 -592.191850195139 7 22321.5 19674.0857702915 2647.41422970853 8 22786.7 20910.1128760594 1876.5871239406 9 18274.1 18301.4655093036 -27.3655093036077 10 22392.9 21755.7527196678 637.14728033221 11 23899.3 23432.1697364478 467.130263552168 12 21343.5 22142.9828918718 -799.482891871844 13 22952.3 21934.9352824196 1017.36471758040 14 21374.4 23158.0092877969 -1783.60928779687 15 21164.1 20722.1072207481 441.992779251905 16 20906.5 20539.5237329529 366.976267047075 17 17877.4 18907.1231826294 -1029.72318262942 18 20664.3 21443.7664102817 -779.466410281726 19 22160 21190.4140609075 969.585939092494 20 19813.6 20701.3981731335 -887.798173133549 21 17735.4 17693.8615757411 41.5384242589451 22 19640.2 19424.7308115681 215.469188431897 23 20844.4 20692.7603181686 151.639681831429 24 19823.1 20224.5072811522 -401.407281152171 25 18594.6 19031.1472335592 -436.54723355919 26 21350.6 20283.7212876145 1066.87871238551 27 18574.1 18528.8540603731 45.2459396268812 28 18924.2 17989.1651048186 935.034895181373 29 17343.4 18044.0771847661 -700.677184766133 30 19961.2 18927.0629046191 1034.13709538091 31 19932.1 20444.6177006338 -512.517700633771 32 19464.6 19723.300908775 -258.700908774991 33 16165.4 16304.4457530732 -139.045753073231 34 17574.9 17878.3530703895 -303.453070389541 35 19795.4 19641.0310087320 154.368991268029 36 19439.5 18341.3493250300 1098.15067497004 37 17170 17929.349789123 -759.349789122983 38 21072.4 19651.7245851004 1420.67541489965 39 17751.8 17849.0174600632 -97.2174600631835 40 17515.5 16912.2405010206 603.259498979442 41 18040.3 17427.1803095559 613.11969044408 42 19090.1 18459.5364044228 630.563595577155 43 17746.5 20030.0322778638 -2283.53227786384 44 19202.1 19294.3248166616 -92.2248166615862 45 15141.6 15016.7271618821 124.872838117894 46 16258.1 16807.2633983746 -549.163398374566 47 18586.5 19359.6389366516 -773.138936651626 48 17209.4 17106.6605019460 102.739498053976 49 17838.7 16525.9381194813 1312.76188051867 50 19123.5 18865.6290017508 257.870998249224 51 16583.6 16523.6070418077 59.9929581923087 52 15991.2 16793.5492547818 -802.349254781824 53 16704.4 15558.3515234571 1146.04847654285 54 17420.4 17713.4424304812 -293.042430481198 55 17872 18692.9501903034 -820.95019030341 56 17823.2 18461.0632253705 -637.863225370472 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 20 0.957740289033793 0.0845194219324148 0.0422597109662074 21 0.96057447437089 0.07885105125822 0.03942552562911 22 0.965441708055075 0.0691165838898505 0.0345582919449253 23 0.945787363800571 0.108425272398858 0.0542126361994288 24 0.93016231054988 0.139675378900241 0.0698376894501207 25 0.894963444235863 0.210073111528274 0.105036555764137 26 0.927362708883302 0.145274582233397 0.0726372911166985 27 0.892931521021454 0.214136957957091 0.107068478978546 28 0.861698696327975 0.276602607344049 0.138301303672025 29 0.931499601516901 0.137000796966197 0.0685003984830987 30 0.948943450989225 0.102113098021551 0.0510565490107755 31 0.973355556736437 0.0532888865271269 0.0266444432635634 32 0.967497545938843 0.0650049081223145 0.0325024540611572 33 0.942428360484157 0.115143279031687 0.0575716395158435 34 0.881284141487587 0.237431717024826 0.118715858512413 35 0.778003940445852 0.443992119108296 0.221996059554148 36 0.748953002063441 0.502093995873117 0.251046997936559 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 5 0.294117647058824 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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