Model 2

*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, 28 Dec 2010 20:32:48 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/28/t1293568486y93o7yuf0c3txei.htm/, Retrieved Tue, 28 Dec 2010 21:34:57 +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/2010/Dec/28/t1293568486y93o7yuf0c3txei.htm/}, year = {2010}, } @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 = {2010}, 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 «

4,24 0 4,15 0 3,93 0 3,7 0 3,7 0 3,65 0 3,55 0 3,43 0 3,47 0 3,58 0 3,67 0 3,72 0 3,8 0 3,76 0 3,63 0 3,48 0 3,41 0 3,43 0 3,5 0 3,62 0 3,58 0 3,52 0 3,45 0 3,36 0 3,27 0 3,21 0 3,19 0 3,16 0 3,12 0 3,06 0 3,01 0 2,98 0 2,97 0 3,02 0 3,07 0 3,18 0 3,29 1 3,43 1 3,61 1 3,74 1 3,87 1 3,88 1 4,09 1 4,19 1 4,2 1 4,29 1 4,37 1 4,47 1 4,61 1 4,65 1 4,69 1 4,82 1 4,86 1 4,87 1 5,01 1 5,03 1 5,13 1 5,18 1 5,21 1 5,26 1 5,25 1 5,2 1 5,16 1 5,19 1 5,39 1 5,58 1 5,76 1 5,89 1 5,98 1 6,02 1 5,62 1 4,87 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 40 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Rente[t] = + 3.47541666666667 + 1.33583333333333Dummy[t] -0.0666666666666615M1[t] -0.0766666666666652M2[t] -0.108333333333333M3[t] -0.128333333333333M4[t] -0.0849999999999992M5[t] -0.0649999999999993M6[t] + 0.0100000000000003M7[t] + 0.0466666666666675M8[t] + 0.0783333333333342M9[t] + 0.125000000000000M10[t] + 0.0883333333333339M11[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) 3.47541666666667 0.255436 13.6058 0 0 Dummy 1.33583333333333 0.141691 9.4278 0 0 M1 -0.0666666666666615 0.34707 -0.1921 0.848336 0.424168 M2 -0.0766666666666652 0.34707 -0.2209 0.825935 0.412968 M3 -0.108333333333333 0.34707 -0.3121 0.756037 0.378018 M4 -0.128333333333333 0.34707 -0.3698 0.712883 0.356442 M5 -0.0849999999999992 0.34707 -0.2449 0.807378 0.403689 M6 -0.0649999999999993 0.34707 -0.1873 0.852082 0.426041 M7 0.0100000000000003 0.34707 0.0288 0.977111 0.488556 M8 0.0466666666666675 0.34707 0.1345 0.893497 0.446749 M9 0.0783333333333342 0.34707 0.2257 0.822215 0.411108 M10 0.125000000000000 0.34707 0.3602 0.720015 0.360007 M11 0.0883333333333339 0.34707 0.2545 0.799985 0.399993 Multiple Linear Regression - Regression Statistics Multiple R 0.777527338324057 R-squared 0.604548761841292 Adjusted R-squared 0.524118001537826 F-TEST (value) 7.51638750597812 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 3.52786075907829e-08 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.601142098038308 Sum Squared Residuals 21.3209375000001 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 4.24 3.40874999999998 0.831250000000024 2 4.15 3.39875 0.751250000000002 3 3.93 3.36708333333333 0.562916666666667 4 3.7 3.34708333333333 0.352916666666666 5 3.7 3.39041666666667 0.309583333333333 6 3.65 3.41041666666667 0.239583333333333 7 3.55 3.48541666666667 0.0645833333333325 8 3.43 3.52208333333333 -0.0920833333333335 9 3.47 3.55375 -0.08375 10 3.58 3.60041666666667 -0.0204166666666671 11 3.67 3.56375 0.106249999999999 12 3.72 3.47541666666667 0.244583333333334 13 3.8 3.40875000000001 0.391249999999994 14 3.76 3.39875 0.361249999999999 15 3.63 3.36708333333333 0.262916666666666 16 3.48 3.34708333333333 0.132916666666666 17 3.41 3.39041666666667 0.0195833333333332 18 3.43 3.41041666666667 0.019583333333333 19 3.5 3.48541666666667 0.0145833333333331 20 3.62 3.52208333333333 0.0979166666666664 21 3.58 3.55375 0.0262499999999995 22 3.52 3.60041666666667 -0.0804166666666669 23 3.45 3.56375 -0.113750000000000 24 3.36 3.47541666666667 -0.115416666666667 25 3.27 3.40875000000001 -0.138750000000005 26 3.21 3.39875 -0.188750000000001 27 3.19 3.36708333333333 -0.177083333333334 28 3.16 3.34708333333333 -0.187083333333334 29 3.12 3.39041666666667 -0.270416666666667 30 3.06 3.41041666666667 -0.350416666666667 31 3.01 3.48541666666667 -0.475416666666667 32 2.98 3.52208333333333 -0.542083333333334 33 2.97 3.55375 -0.58375 34 3.02 3.60041666666667 -0.580416666666667 35 3.07 3.56375 -0.49375 36 3.18 3.47541666666667 -0.295416666666666 37 3.29 4.74458333333334 -1.45458333333334 38 3.43 4.73458333333333 -1.30458333333333 39 3.61 4.70291666666667 -1.09291666666667 40 3.74 4.68291666666667 -0.942916666666666 41 3.87 4.72625 -0.85625 42 3.88 4.74625 -0.86625 43 4.09 4.82125 -0.73125 44 4.19 4.85791666666667 -0.667916666666666 45 4.2 4.88958333333333 -0.689583333333333 46 4.29 4.93625 -0.646249999999999 47 4.37 4.89958333333333 -0.529583333333333 48 4.47 4.81125 -0.341249999999999 49 4.61 4.74458333333334 -0.134583333333337 50 4.65 4.73458333333333 -0.0845833333333329 51 4.69 4.70291666666667 -0.0129166666666657 52 4.82 4.68291666666667 0.137083333333334 53 4.86 4.72625 0.133750000000001 54 4.87 4.74625 0.123750000000001 55 5.01 4.82125 0.188750000000001 56 5.03 4.85791666666667 0.172083333333334 57 5.13 4.88958333333333 0.240416666666667 58 5.18 4.93625 0.243750000000000 59 5.21 4.89958333333333 0.310416666666667 60 5.26 4.81125 0.448750000000001 61 5.25 4.74458333333334 0.505416666666663 62 5.2 4.73458333333333 0.465416666666667 63 5.16 4.70291666666667 0.457083333333334 64 5.19 4.68291666666667 0.507083333333334 65 5.39 4.72625 0.66375 66 5.58 4.74625 0.83375 67 5.76 4.82125 0.93875 68 5.89 4.85791666666667 1.03208333333333 69 5.98 4.88958333333333 1.09041666666667 70 6.02 4.93625 1.08375 71 5.62 4.89958333333333 0.720416666666667 72 4.87 4.81125 0.0587500000000014 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.105060569844449 0.210121139688899 0.89493943015555 17 0.0493634470353885 0.0987268940707771 0.950636552964611 18 0.0204293829701914 0.0408587659403829 0.979570617029809 19 0.00677708684629807 0.0135541736925961 0.993222913153702 20 0.00248452344907401 0.00496904689814802 0.997515476550926 21 0.000775333006712286 0.00155066601342457 0.999224666993288 22 0.000217155856527484 0.000434311713054968 0.999782844143473 23 7.7346259307942e-05 0.000154692518615884 0.999922653740692 24 4.52769832019925e-05 9.0553966403985e-05 0.999954723016798 25 0.000373188621694408 0.000746377243388816 0.999626811378306 26 0.00105963573512964 0.00211927147025929 0.99894036426487 27 0.00120800474769932 0.00241600949539863 0.9987919952523 28 0.000850520164689354 0.00170104032937871 0.99914947983531 29 0.00058468736044648 0.00116937472089296 0.999415312639554 30 0.000431242500069169 0.000862485000138337 0.999568757499931 31 0.000331062856133345 0.00066212571226669 0.999668937143867 32 0.000265216314546312 0.000530432629092623 0.999734783685454 33 0.000212518569584036 0.000425037139168071 0.999787481430416 34 0.000158642793003420 0.000317285586006839 0.999841357206997 35 0.000106473403615488 0.000212946807230975 0.999893526596385 36 5.54985810002842e-05 0.000110997162000568 0.999944501419 37 6.17309067604896e-05 0.000123461813520979 0.99993826909324 38 6.9412648995117e-05 0.000138825297990234 0.999930587351005 39 8.53799026071882e-05 0.000170759805214376 0.999914620097393 40 0.000136585202339910 0.000273170404679821 0.99986341479766 41 0.000254811438324121 0.000509622876648243 0.999745188561676 42 0.000547101271140497 0.00109420254228099 0.99945289872886 43 0.00156955920079396 0.00313911840158793 0.998430440799206 44 0.00476055685752171 0.00952111371504343 0.995239443142478 45 0.0170990004048363 0.0341980008096726 0.982900999595164 46 0.0609775695841382 0.121955139168276 0.939022430415862 47 0.131249836960602 0.262499673921203 0.868750163039398 48 0.148880228593504 0.297760457187008 0.851119771406496 49 0.161313678649572 0.322627357299144 0.838686321350428 50 0.161664275607234 0.323328551214467 0.838335724392766 51 0.153635773025602 0.307271546051203 0.846364226974398 52 0.145115764420542 0.290231528841084 0.854884235579458 53 0.144806336964823 0.289612673929647 0.855193663035177 54 0.163648933974280 0.327297867948559 0.83635106602572 55 0.190852479987204 0.381704959974408 0.809147520012796 56 0.246241243913052 0.492482487826103 0.753758756086949 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 25 0.609756097560976 NOK 5% type I error level 28 0.682926829268293 NOK 10% type I error level 29 0.707317073170732 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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