Multiple Regression analysis 4a

*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: Sat, 19 Dec 2009 04:06:01 -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/Dec/19/t12612208084sqblvt4cj1uy1a.htm/, Retrieved Sat, 19 Dec 2009 12:07:01 +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/19/t12612208084sqblvt4cj1uy1a.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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122,74 95,10 96,33 109,84 97,00 96,33 101,99 112,70 95,05 125,12 102,90 96,84 103,5 97,40 96,92 102,8 111,40 97,44 118,72 87,40 97,78 119,01 96,80 97,69 118,61 114,10 96,67 120,43 110,30 98,29 111,83 103,90 98,20 116,79 101,60 98,71 131,71 94,60 98,54 120,57 95,90 98,20 117,83 104,70 100,80 130,8 102,80 101,33 107,46 98,10 101,88 112,09 113,90 101,85 129,47 80,90 102,04 119,72 95,70 102,22 134,81 113,20 102,63 135,8 105,90 102,65 129,27 108,80 102,54 126,94 102,30 102,37 153,45 99,00 102,68 121,86 100,70 102,76 133,47 115,50 102,82 135,34 100,70 103,31 117,1 109,90 103,23 120,65 114,60 103,60 132,49 85,40 103,95 137,6 100,50 103,93 138,69 114,80 104,25 125,53 116,50 104,38 133,09 112,90 104,36 129,08 102,00 104,32 145,94 106,00 104,58 129,07 105,30 104,68 139,69 118,80 104,92 142,09 106,10 105,46 137,29 109,30 105,23 127,03 117,20 105,58 137,25 92,50 105,34 156,87 104,20 105,28 150,89 112,50 105,70 139,14 122,40 105,67 158,3 113,30 105,71 149 100,00 106,19 158,3 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 Invoer[t] = -98.86710326935 + 1.58106468927319TIP[t] + 0.558446578230743CONS[t] + 15.0703390719775M1[t] + 0.0912023698377545M2[t] -17.3516358551200M3[t] + 5.66072943166297M4[t] -7.69482419975213M5[t] -26.7889968374189M6[t] + 29.169870473176M7[t] + 14.0996172288639M8[t] -13.1599163920929M9[t] -20.0903115154348M10[t] -8.88920091771722M11[t] + 0.29775784415005t + 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) -98.86710326935 159.538486 -0.6197 0.53821 0.269105 TIP 1.58106468927319 0.24129 6.5525 0 0 CONS 0.558446578230743 1.57779 0.3539 0.724841 0.362421 M1 15.0703390719775 6.282017 2.399 0.020135 0.010068 M2 0.0912023698377545 6.284795 0.0145 0.988478 0.494239 M3 -17.3516358551200 6.789906 -2.5555 0.013628 0.006814 M4 5.66072943166297 6.420293 0.8817 0.382079 0.19104 M5 -7.69482419975213 6.329107 -1.2158 0.229665 0.114833 M6 -26.7889968374189 7.03228 -3.8094 0.000376 0.000188 M7 29.169870473176 7.078168 4.1211 0.000139 6.9e-05 M8 14.0996172288639 6.575314 2.1443 0.036795 0.018397 M9 -13.1599163920929 7.466237 -1.7626 0.083961 0.041981 M10 -20.0903115154348 7.458708 -2.6935 0.009545 0.004772 M11 -8.88920091771722 6.81304 -1.3047 0.197841 0.09892 t 0.29775784415005 0.38599 0.7714 0.444022 0.222011 Multiple Linear Regression - Regression Statistics Multiple R 0.838957608214395 R-squared 0.703849868380818 Adjusted R-squared 0.622553753818689 F-TEST (value) 8.65785372612018 F-TEST (DF numerator) 14 F-TEST (DF denominator) 51 p-value 3.66045016519934e-09 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 10.3573846658034 Sum Squared Residuals 5471.04627288638 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 122.74 120.655404477625 2.08459552237498 2 109.84 108.978048529255 0.861951470745158 3 101.99 115.940872149901 -13.9508721499009 4 125.12 124.756180700990 0.363819299010295 5 103.5 103.047204848981 0.45279515101944 6 102.8 106.676087925968 -3.87608792596849 7 118.72 125.177032374755 -6.4570323747553 8 119.01 125.216284861720 -6.20628486172049 9 118.61 125.037312699545 -6.4273126995446 10 120.43 113.301313057848 7.12868694215156 11 111.83 114.631107296327 -2.80110729632685 12 116.79 120.466425027763 -3.67642502776344 13 131.71 124.672133200679 7.03786679932062 14 120.57 111.856266602146 8.71373339785355 15 117.83 110.076516590343 7.75348340965728 16 130.8 130.678593498119 0.121406501881015 17 107.46 110.496939289297 -3.03693928929685 18 112.09 116.664593188950 -4.57459318894966 19 129.47 120.852188447543 8.61781155245688 20 119.72 129.579970832706 -9.85997083270587 21 134.81 130.515790215255 4.29420978474545 22 135.8 112.352549635933 23.4474503640670 23 129.27 128.375076553087 0.894923446912506 24 126.94 127.190178916380 -0.250178916379806 25 153.45 137.513880797157 15.9361192028427 26 121.86 125.564987637191 -3.70498763719055 27 133.47 131.85317145232 1.61682854768012 28 135.34 132.037176005343 3.30282399465723 29 117.1 133.480499633133 -16.3804996331327 30 120.65 122.321714113145 -1.67171411314526 31 132.49 132.606706643494 -0.116706643493797 32 137.6 141.697119119792 -4.09711911979237 33 138.69 137.523271304626 1.16672869537395 34 125.53 133.651042052369 -8.12104205236865 35 133.09 139.446908681288 -6.35690868128815 36 129.08 131.377924466948 -2.29792446694838 37 145.94 153.215476250509 -7.27547625050866 38 129.07 137.483196767851 -8.41319676785085 39 139.69 141.816516871007 -2.12651687100658 40 142.09 145.348679600415 -3.25867960041468 41 137.29 137.221848105831 0.0681518941691958 42 127.03 131.111300659953 -4.08130065995305 43 137.25 148.181600810875 -10.9316008108748 44 156.87 151.874055480515 4.99594451948473 45 150.89 138.269664187533 12.6203358124671 46 139.14 147.272813934799 -8.13281393479876 47 158.3 144.406331567409 13.8936684325905 48 149 132.833184319494 16.1668156805059 49 158.36 165.531923878736 -7.1719238787355 50 168.06 154.455588623117 13.6044113768828 51 153.38 132.796277271565 20.5837227284355 52 173.86 168.444649629325 5.41535037067507 53 162.47 142.762775802740 19.7072241972595 54 145.17 134.812536814581 10.3574631854193 55 168.89 160.002471723333 8.88752827666701 56 166.64 151.472569705266 15.167430294734 57 140.07 151.723961593042 -11.6539615930419 58 128.84 143.162281319051 -14.3222813190511 59 123.41 129.040575901888 -5.630575901888 60 120.3 130.242287269414 -9.94228726941428 61 129.67 140.281181395294 -10.6111813952941 62 118.1 129.16191184044 -11.0619118404401 63 113.91 127.786645664865 -13.8766456648654 64 131.09 137.034720565809 -5.94472056580894 65 119.15 119.960732320019 -0.810732320018646 66 122.3 118.453767297403 3.84623270259718 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 18 0.00902711028243863 0.0180542205648773 0.990972889717561 19 0.0021344455142125 0.004268891028425 0.997865554485788 20 0.00279370851122009 0.00558741702244018 0.99720629148878 21 0.00325733306673378 0.00651466613346756 0.996742666933266 22 0.00265851119365312 0.00531702238730625 0.997341488806347 23 0.00414486555365411 0.00828973110730821 0.995855134446346 24 0.00140373411114226 0.00280746822228453 0.998596265888858 25 0.00565218734073671 0.0113043746814734 0.994347812659263 26 0.0081318872720547 0.0162637745441094 0.991868112727945 27 0.00613875857768569 0.0122775171553714 0.993861241422314 28 0.00623662795564579 0.0124732559112916 0.993763372044354 29 0.00580350313913679 0.0116070062782736 0.994196496860863 30 0.00264065969080073 0.00528131938160146 0.9973593403092 31 0.00198963331168559 0.00397926662337119 0.998010366688314 32 0.00116703877603611 0.00233407755207222 0.998832961223964 33 0.000563236718209171 0.00112647343641834 0.99943676328179 34 0.00338989814997574 0.00677979629995149 0.996610101850024 35 0.00170426516209741 0.00340853032419482 0.998295734837903 36 0.000848262497308885 0.00169652499461777 0.99915173750269 37 0.00049661421833018 0.00099322843666036 0.99950338578167 38 0.000226274177112410 0.000452548354224821 0.999773725822888 39 0.000196479255947686 0.000392958511895373 0.999803520744052 40 8.1311543453537e-05 0.000162623086907074 0.999918688456547 41 0.000261844058953794 0.000523688117907588 0.999738155941046 42 0.000449348585702633 0.000898697171405267 0.999550651414297 43 0.00563687014847038 0.0112737402969408 0.99436312985153 44 0.152278108569979 0.304556217139959 0.847721891430021 45 0.095722934067603 0.191445868135206 0.904277065932397 46 0.220144701665913 0.440289403331826 0.779855298334087 47 0.198611535681634 0.397223071363268 0.801388464318366 48 0.126464011172333 0.252928022344665 0.873535988827667 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 19 0.612903225806452 NOK 5% type I error level 26 0.838709677419355 NOK 10% type I error level 26 0.838709677419355 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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