*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: Thu, 02 Dec 2010 15:17:05 +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/02/t1291303136ic1fi02xgbqqvrb.htm/, Retrieved Thu, 02 Dec 2010 16:19:06 +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/02/t1291303136ic1fi02xgbqqvrb.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:

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8.30 3.00 3.10 4.28 2649.24 8.70 3.00 2.90 3.69 2579.39 8.90 7.00 2.40 3.54 2504.58 8.90 4.00 2.40 3.13 2462.32 8.10 -4.00 2.70 3.75 2467.38 8.00 -6.00 2.50 3.85 2446.66 8.30 8.00 2.10 3.66 2656.32 8.50 2.00 1.90 3.96 2626.15 8.70 -1.00 0.80 3.93 2482.60 8.60 -2.00 0.80 4.05 2539.91 8.30 0.00 0.30 4.19 2502.66 7.90 10.00 0.00 4.32 2466.92 7.90 3.00 -0.90 4.21 2513.17 8.10 6.00 -1.00 4.24 2443.27 8.30 7.00 -0.70 4.16 2293.41 8.10 -4.00 -1.70 4.19 2070.83 7.40 -5.00 -1.00 4.20 2029.60 7.30 -7.00 -0.20 4.46 2052.02 7.70 -10.00 0.70 4.63 1864.44 8.00 -21.00 0.60 4.33 1670.07 8.00 -22.00 1.90 4.40 1810.99 7.70 -16.00 2.10 4.58 1905.41 6.90 -25.00 2.70 4.52 1862.83 6.60 -22.00 3.20 4.04 2014.45 6.90 -22.00 4.80 4.16 2197.82 7.50 -19.00 5.50 4.73 2962.34 7.90 -21.00 5.40 4.81 3047.03 7.70 -31.00 5.90 4.75 3032.60 6.50 -28.00 5.80 4.90 3504.37 6.10 -23.00 5.10 5.12 3801.06 6.40 -17.00 4.10 4.95 3857.62 6.80 -12.00 4.40 4.76 3674.40 7.10 -14.00 3.60 4.69 3720.98 7.30 -18.00 3.50 4.58 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 6 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Werkloosheid[t] = + 11.3794637275710 + 0.0370832973532882consumerconfidence[t] + 0.0573711763273573HICP[t] -0.6802095474807OLO12[t] -0.00027370821644188Bel20[t] + 0.0121067180406699t + 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) 11.3794637275710 0.711257 15.9991 0 0 consumerconfidence 0.0370832973532882 0.010607 3.4963 0.000952 0.000476 HICP 0.0573711763273573 0.048494 1.1831 0.24197 0.120985 OLO12 -0.6802095474807 0.200528 -3.3921 0.001304 0.000652 Bel20 -0.00027370821644188 0.000124 -2.2114 0.031258 0.015629 t 0.0121067180406699 0.005399 2.2424 0.029067 0.014533 Multiple Linear Regression - Regression Statistics Multiple R 0.811558918487442 R-squared 0.658627878176506 Adjusted R-squared 0.627019348378035 F-TEST (value) 20.8370298263082 F-TEST (DF numerator) 5 F-TEST (DF denominator) 54 p-value 1.54869450597062e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.404246268307375 Sum Squared Residuals 8.82441245378367 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 8.3 8.04425536574251 0.255744634257492 2 8.7 8.46533000044976 0.234669999550237 3 8.9 8.71959186353403 0.180408136465973 4 8.9 8.91090151320876 -0.0109015132087555 5 8.1 8.2204383223081 -0.120438322308097 6 8 8.08455448987332 -0.0845544898733244 7 8.3 8.66473304969121 -0.364733049691214 8 8.5 8.24706066099253 0.252939339007474 9 8.7 8.1445062939079 0.555493706092108 10 8.6 8.0222183510133 0.577781648986695 11 8.3 7.99477237001203 0.305227629987967 12 7.9 8.28185579917052 -0.38185579917052 13 7.9 8.044909422256 -0.144909422255991 14 8.1 8.16125483262866 -0.061254832628657 15 8.3 8.32309087803526 -0.0230908780352572 16 8.1 7.91042583725361 0.189574162746386 17 7.4 7.93009197565924 -0.530091975659237 18 7.3 7.73093801949761 -0.430938019497608 19 7.7 7.61913546834148 0.0808645316585166 20 8 7.47485232813727 0.525147671862734 21 8 7.43827264786557 0.561727352134427 22 7.7 7.53607213694848 0.163927863051525 23 6.9 7.3013189533109 -0.401318953310903 24 6.6 7.73836209458893 -1.13836209458893 25 6.9 7.71044767340674 -0.810447673406744 26 7.5 7.27698925923828 0.223010740761717 27 7.9 7.13159515229072 0.768404847709278 28 7.7 6.84631666737429 0.853683332625712 29 6.5 6.7327774024492 -0.232777402449195 30 6.1 6.65928819264526 -0.559288192645261 31 6.4 6.93667820482807 -0.536678204828068 32 6.8 7.3308013959712 -0.530801395971201 33 7.1 7.2577099178452 -0.157709917845195 34 7.3 7.15676367725012 0.143236322749883 35 7.2 7.16599416645753 0.0340058335424745 36 7 6.83844098200516 0.161559017994835 37 7 7.22934172727202 -0.229341727272016 38 7 7.26446343959473 -0.264463439594728 39 7.3 7.2159932332461 0.0840067667539064 40 7.5 7.54005797527808 -0.0400579752780773 41 7.2 7.6677925186482 -0.467792518648196 42 7.7 7.52690520985393 0.173094790146069 43 8 7.79323005070713 0.206769949292875 44 7.9 7.73231850385147 0.167681496148529 45 8 7.89743192084277 0.102568079157235 46 8 7.97122034862153 0.028779651378466 47 7.9 7.71682505675644 0.183174943243558 48 7.9 8.20432781873701 -0.304327818737008 49 8 8.40951383124606 -0.409513831246057 50 8.1 8.22948455634638 -0.129484556346383 51 8.1 8.23349129813996 -0.133491298139962 52 8.2 8.37189205503645 -0.171892055036449 53 8 8.20564236443302 -0.20564236443302 54 8.3 7.92818773380636 0.371812266193642 55 8.5 7.95738523933708 0.542614760662923 56 8.6 7.94720083286249 0.652799167137508 57 8.7 8.29014033658475 0.409859663415245 58 8.7 8.60376911349435 0.0962308865056487 59 8.5 8.5519391417693 -0.0519391417692996 60 8.4 8.55870032734568 -0.158700327345682 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 9 0.111255717975783 0.222511435951565 0.888744282024217 10 0.0494034015410295 0.098806803082059 0.95059659845897 11 0.0402032430828427 0.0804064861656854 0.959796756917157 12 0.0152860893270727 0.0305721786541454 0.984713910672927 13 0.221846663097368 0.443693326194736 0.778153336902632 14 0.146066663410993 0.292133326821986 0.853933336589007 15 0.178107312592538 0.356214625185076 0.821892687407462 16 0.132631094584971 0.265262189169942 0.867368905415029 17 0.120040126726623 0.240080253453245 0.879959873273377 18 0.0843612764100094 0.168722552820019 0.91563872358999 19 0.174645826290684 0.349291652581369 0.825354173709316 20 0.232949839880233 0.465899679760465 0.767050160119767 21 0.292862294699748 0.585724589399495 0.707137705300253 22 0.291214878585694 0.582429757171388 0.708785121414306 23 0.424941129274114 0.849882258548229 0.575058870725886 24 0.557098007875757 0.885803984248487 0.442901992124243 25 0.550464721825528 0.899070556348944 0.449535278174472 26 0.652008244603039 0.695983510793922 0.347991755396961 27 0.87958442585283 0.240831148294339 0.120415574147169 28 0.998175127770254 0.00364974445949135 0.00182487222974568 29 0.99943892509718 0.00112214980563882 0.000561074902819412 30 0.999976632860215 4.67342795703104e-05 2.33671397851552e-05 31 0.999995301628852 9.3967422957218e-06 4.6983711478609e-06 32 0.99999532909873 9.34180254077517e-06 4.67090127038759e-06 33 0.999990796019227 1.84079615457820e-05 9.20398077289101e-06 34 0.999996937409998 6.12518000388444e-06 3.06259000194222e-06 35 0.999996652673265 6.69465346984614e-06 3.34732673492307e-06 36 0.99999142636527 1.71472694594685e-05 8.57363472973426e-06 37 0.999989070683046 2.18586339071971e-05 1.09293169535986e-05 38 0.999983158370902 3.36832581956459e-05 1.68416290978229e-05 39 0.99997961837498 4.07632500391899e-05 2.03816250195950e-05 40 0.99995697790447 8.60441910604174e-05 4.30220955302087e-05 41 0.999998637627237 2.72474552541688e-06 1.36237276270844e-06 42 0.999997782847953 4.43430409391904e-06 2.21715204695952e-06 43 0.999994128873505 1.17422529894523e-05 5.87112649472614e-06 44 0.999993114194322 1.37716113565778e-05 6.88580567828891e-06 45 0.99997256809898 5.48638020382063e-05 2.74319010191032e-05 46 0.999885330398453 0.000229339203094895 0.000114669601547447 47 0.999572403571444 0.000855192857111455 0.000427596428555727 48 0.999581468983295 0.000837062033409246 0.000418531016704623 49 0.99998145089466 3.70982106813052e-05 1.85491053406526e-05 50 0.999916633758335 0.00016673248333034 8.336624166517e-05 51 0.999972841724613 5.43165507735063e-05 2.71582753867531e-05 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 24 0.558139534883721 NOK 5% type I error level 25 0.581395348837209 NOK 10% type I error level 27 0.627906976744186 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal 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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