*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 10:27:32 -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/t1258478973qv5wgtbwct906t3.htm/, Retrieved Tue, 17 Nov 2009 18:29:44 +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/t1258478973qv5wgtbwct906t3.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:

» Textbox « » Textfile « » CSV «

15836.8 89.1 17570.4 82.6 18252.1 102.7 16196.7 91.8 16643 94.1 17729 103.1 16446.1 93.2 15993.8 91 16373.5 94.3 17842.2 99.4 22321.5 115.7 22786.7 116.8 18274.1 99.8 22392.9 96 23899.3 115.9 21343.5 109.1 22952.3 117.3 21374.4 109.8 21164.1 112.8 20906.5 110.7 17877.4 100 20664.3 113.3 22160 122.4 19813.6 112.5 17735.4 104.2 19640.2 92.5 20844.4 117.2 19823.1 109.3 18594.6 106.1 21350.6 118.8 18574.1 105.3 18924.2 106 17343.4 102 19961.2 112.9 19932.1 116.5 19464.6 114.8 16165.4 100.5 17574.9 85.4 19795.4 114.6 19439.5 109.9 17170 100.7 21072.4 115.5 17751.8 100.7 17515.5 99 18040.3 102.3 19090.1 108.8 17746.5 105.9 19202.1 113.2 15141.6 95.7 16258.1 80.9 18586.5 113.9 17209.4 98.1 17838.7 102.8 19123.5 104.7 16583.6 95.9 15991.2 94.6 16704.4 101.6 17420.4 103.9 17872 110.3 17823.2 114.1

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 5 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation uitvoer[t] = + 2131.22634960031 + 159.158963492344indproc[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) 2131.22634960031 1998.506117 1.0664 0.290658 0.145329 indproc 159.158963492344 19.039156 8.3596 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.739227801219945 R-squared 0.546457742096475 Adjusted R-squared 0.53863804799469 F-TEST (value) 69.8822402748134 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 1.53346224607276e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 1407.66632283589 Sum Squared Residuals 114928419.633887 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 15836.8 16312.2899967681 -475.489996768101 2 17570.4 15277.7567340679 2292.64326593208 3 18252.1 18476.8519002640 -224.751900264039 4 16196.7 16742.0191981975 -545.319198197486 5 16643 17108.0848142299 -465.084814229877 6 17729 18540.5154856610 -811.515485660974 7 16446.1 16964.8417470868 -518.741747086771 8 15993.8 16614.6920274036 -620.892027403612 9 16373.5 17139.9166069283 -766.416606928347 10 17842.2 17951.6273207393 -109.427320739302 11 22321.5 20545.9184256645 1775.58157433549 12 22786.7 20720.9932855061 2065.70671449391 13 18274.1 18015.2909061362 258.80909386376 14 22392.9 17410.4868448653 4982.41315513467 15 23899.3 20577.7502183630 3321.54978163702 16 21343.5 19495.4692666150 1848.03073338496 17 22952.3 20800.5727672523 2151.72723274774 18 21374.4 19606.8805410597 1767.51945894032 19 21164.1 20084.3574315367 1079.74256846329 20 20906.5 19750.1236082028 1156.37639179721 21 17877.4 18047.1226988347 -169.722698834707 22 20664.3 20163.9369132829 500.363086717116 23 22160 21612.2834810632 547.716518936785 24 19813.6 20036.609742489 -223.00974248901 25 17735.4 18715.5903455026 -980.190345502552 26 19640.2 16853.4304726421 2786.76952735787 27 20844.4 20784.656870903 59.7431290969755 28 19823.1 19527.3010593135 295.798940686491 29 18594.6 19017.992376138 -423.392376138007 30 21350.6 21039.3112124908 311.288787509223 31 18574.1 18890.6652053441 -316.565205344132 32 18924.2 19002.0764797888 -77.8764797887716 33 17343.4 18365.4406258194 -1022.04062581939 34 19961.2 20100.2733278859 -139.073327885946 35 19932.1 20673.2455964584 -741.145596458386 36 19464.6 20402.6753585214 -938.0753585214 37 16165.4 18126.7021805809 -1961.30218058088 38 17574.9 15723.4018318465 1851.49816815352 39 19795.4 20370.8435658229 -575.443565822929 40 19439.5 19622.7964374089 -183.296437408915 41 17170 18158.5339732794 -988.53397327935 42 21072.4 20514.0866329660 558.313367033961 43 17751.8 18158.5339732794 -406.73397327935 44 17515.5 17887.9637353424 -372.463735342364 45 18040.3 18413.1883148671 -372.8883148671 46 19090.1 19447.7215775673 -357.621577567337 47 17746.5 18986.1605834395 -1239.66058343954 48 19202.1 20148.0210169336 -945.921016933651 49 15141.6 17362.7391558176 -2221.13915581763 50 16258.1 15007.1864961309 1250.91350386906 51 18586.5 20259.4322913783 -1672.93229137829 52 17209.4 17744.7206681993 -535.320668199252 53 17838.7 18492.7677966133 -654.06779661327 54 19123.5 18795.1698272487 328.330172751274 55 16583.6 17394.5709485161 -810.9709485161 56 15991.2 17187.6642959761 -1196.46429597605 57 16704.4 18301.7770404225 -1597.37704042246 58 17420.4 18667.8426564548 -1247.44265645485 59 17872 19686.4600228059 -1814.46002280585 60 17823.2 20291.2640840768 -2468.06408407676 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.353971933715123 0.707943867430246 0.646028066284877 6 0.204401491262848 0.408802982525696 0.795598508737152 7 0.121664620650400 0.243329241300799 0.8783353793496 8 0.0823410919746505 0.164682183949301 0.91765890802535 9 0.0472292198941245 0.094458439788249 0.952770780105876 10 0.0286890123597905 0.0573780247195811 0.97131098764021 11 0.172184334350562 0.344368668701123 0.827815665649438 12 0.201632140418753 0.403264280837505 0.798367859581247 13 0.135914445528323 0.271828891056646 0.864085554471677 14 0.916457249095945 0.167085501808109 0.0835427509040546 15 0.966934210810225 0.0661315783795502 0.0330657891897751 16 0.966344847037512 0.0673103059249764 0.0336551529624882 17 0.973466751208746 0.053066497582509 0.0265332487912545 18 0.976664152734797 0.0466716945304059 0.0233358472652030 19 0.974783706078781 0.0504325878424376 0.0252162939212188 20 0.973919268947206 0.0521614621055873 0.0260807310527937 21 0.963966661942851 0.0720666761142977 0.0360333380571488 22 0.960409494900234 0.0791810101995318 0.0395905050997659 23 0.96677696536608 0.0664460692678403 0.0332230346339202 24 0.962800877109621 0.0743982457807579 0.0371991228903789 25 0.96218334640625 0.0756333071875005 0.0378166535937503 26 0.99566866427344 0.00866267145311933 0.00433133572655966 27 0.99509463788754 0.00981072422491919 0.00490536211245959 28 0.99409484262814 0.011810314743719 0.0059051573718595 29 0.991697597532453 0.0166048049350934 0.00830240246754668 30 0.992892007283664 0.0142159854326717 0.00710799271633583 31 0.989790935983554 0.0204181280328915 0.0102090640164458 32 0.986146183410334 0.0277076331793314 0.0138538165896657 33 0.982951131899962 0.0340977362000757 0.0170488681000378 34 0.979988387383022 0.0400232252339562 0.0200116126169781 35 0.975846694681475 0.0483066106370507 0.0241533053185254 36 0.969572600698934 0.0608547986021327 0.0304273993010663 37 0.981062917980628 0.0378741640387439 0.0189370820193720 38 0.991776615409164 0.0164467691816714 0.0082233845908357 39 0.98822685964178 0.0235462807164404 0.0117731403582202 40 0.985049840529164 0.0299003189416729 0.0149501594708365 41 0.977666598245135 0.0446668035097308 0.0223334017548654 42 0.993724256616176 0.0125514867676472 0.00627574338382362 43 0.989367781273435 0.0212644374531306 0.0106322187265653 44 0.981973611744782 0.0360527765104354 0.0180263882552177 45 0.972910635036958 0.0541787299260837 0.0270893649630418 46 0.97176744798299 0.056465104034021 0.0282325520170105 47 0.95460164287918 0.0907967142416384 0.0453983571208192 48 0.947103692211572 0.105792615576856 0.0528963077884282 49 0.985209308651037 0.0295813826979268 0.0147906913489634 50 0.977934401256405 0.0441311974871906 0.0220655987435953 51 0.95817978094062 0.0836404381187596 0.0418202190593798 52 0.920010230938511 0.159979538122978 0.079989769061489 53 0.867854780972037 0.264290438055925 0.132145219027963 54 0.996292149699036 0.00741570060192732 0.00370785030096366 55 0.986502471687345 0.0269950566253098 0.0134975283126549 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 3 0.0588235294117647 NOK 5% type I error level 23 0.450980392156863 NOK 10% type I error level 40 0.784313725490196 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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