*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: Mon, 14 Dec 2009 02:45:15 -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/14/t1260784017kia6sd6al2894b5.htm/, Retrieved Mon, 14 Dec 2009 10:47:09 +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/14/t1260784017kia6sd6al2894b5.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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95,1 121,8 97,0 127,6 112,7 129,9 102,9 128,0 97,4 123,5 111,4 124,0 87,4 127,4 96,8 127,6 114,1 128,4 110,3 131,4 103,9 135,1 101,6 134,0 94,6 144,5 95,9 147,3 104,7 150,9 102,8 148,7 98,1 141,4 113,9 138,9 80,9 139,8 95,7 145,6 113,2 147,9 105,9 148,5 108,8 151,1 102,3 157,5 99,0 167,5 100,7 172,3 115,5 173,5 100,7 187,5 109,9 205,5 114,6 195,1 85,4 204,5 100,5 204,5 114,8 201,7 116,5 207,0 112,9 206,6 102,0 210,6 106,0 211,1 105,3 215,0 118,8 223,9 106,1 238,2 109,3 238,9 117,2 229,6 92,5 232,2 104,2 222,1 112,5 221,6 122,4 227,3 113,3 221,0 100,0 213,6 110,7 243,4 112,8 253,8 109,8 265,3 117,3 268,2 109,1 268,5 115,9 266,9 96,0 268,4 99,8 250,8 116,8 231,2 115,7 192,0 99,4 171,4 94,3 160,0

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 TIP[t] = + 86.9342920390978 + 0.074829895859896Grondstofprijzen[t] + 0.851428662433061M1[t] + 1.69687103936924M2[t] + 11.2453066121398M3[t] + 4.49972857657918M4[t] + 3.19197352654093M5[t] + 13.3806808412480M6[t] -13.0457135880132M7[t] -1.76095183998124M8[t] + 13.4153745476239M9[t] + 13.6635376352546M10[t] + 7.4778231978662M11[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) 86.9342920390978 2.565755 33.8825 0 0 Grondstofprijzen 0.074829895859896 0.010843 6.9011 0 0 M1 0.851428662433061 2.440093 0.3489 0.728698 0.364349 M2 1.69687103936924 2.441505 0.695 0.490471 0.245235 M3 11.2453066121398 2.444366 4.6005 3.2e-05 1.6e-05 M4 4.49972857657918 2.448604 1.8377 0.072437 0.036218 M5 3.19197352654093 2.449966 1.3029 0.198968 0.099484 M6 13.3806808412480 2.445917 5.4706 2e-06 1e-06 M7 -13.0457135880132 2.448917 -5.3271 3e-06 1e-06 M8 -1.76095183998124 2.44534 -0.7201 0.475014 0.237507 M9 13.4153745476239 2.442864 5.4917 2e-06 1e-06 M10 13.6635376352546 2.440836 5.5979 1e-06 1e-06 M11 7.4778231978662 2.440027 3.0646 0.003604 0.001802 Multiple Linear Regression - Regression Statistics Multiple R 0.923914241746214 R-squared 0.853617526101482 Adjusted R-squared 0.816243277446542 F-TEST (value) 22.8397240565969 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 1.22124532708767e-15 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 3.85788364468206 Sum Squared Residuals 699.513512147551 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 95.1 96.9000020172662 -1.80000201726620 2 97 98.1794577901898 -1.17945779018977 3 112.7 107.900002123438 4.79999787656189 4 102.9 101.012247285744 1.88775271425634 5 97.4 99.3677577043359 -1.96775770433587 6 111.4 109.593879966973 1.80612003302704 7 87.4 83.4219071836354 3.97809281636463 8 96.8 94.7216349108393 2.07836508916070 9 114.1 109.957825215132 4.14217478486757 10 110.3 110.430477990343 -0.130477990342786 11 103.9 104.521634167636 -0.621634167635952 12 101.6 96.9614980843239 4.63850191567612 13 94.6 98.5986406532859 -3.99864065328586 14 95.9 99.6536067386297 -3.75360673862973 15 104.7 109.471429936496 -4.77142993649593 16 102.8 102.561226130044 0.238773869956475 17 98.1 100.707212840228 -2.60721284022804 18 113.9 110.708845415285 3.1911545847146 19 80.9 84.3497978922981 -3.44979789229808 20 95.7 96.0685730363174 -0.368573036317430 21 113.2 111.417008184400 1.78299181559963 22 105.9 111.710069209547 -5.810069209547 23 108.8 105.718912501394 3.0810874986057 24 102.3 98.7200006370314 3.57999936296857 25 99 100.319728258063 -1.31972825806346 26 100.7 101.524354135127 -0.824354135127135 27 115.5 111.162585582930 4.33741441707042 28 100.7 105.464626089407 -4.76462608940749 29 109.9 105.503809164847 4.39619083515264 30 114.6 114.914285562612 -0.31428556261157 31 85.4 89.1912921544334 -3.79129215443336 32 100.5 100.476053902465 0.0239460975346947 33 114.8 115.442856581663 -0.642856581662782 34 116.5 116.087618117351 0.412381882649072 35 112.9 109.871971721619 3.02802827838148 36 102 102.693468107192 -0.693468107191909 37 106 103.582311717555 2.41768828244508 38 105.3 104.719590688345 0.580409311655302 39 118.8 114.934012334268 3.86598766573166 40 106.1 109.258501809504 -3.15850180950422 41 109.3 108.003127686568 1.2968723134321 42 117.2 117.495916969778 -0.295916969777974 43 92.5 91.2640802697525 1.23591973024752 44 104.2 101.793060069599 2.40693993040053 45 112.5 116.931971509275 -4.43197150927471 46 122.4 117.606665003307 4.79333499669319 47 113.3 110.949522222001 2.35047777799897 48 100 102.917957794772 -2.9179577947716 49 110.7 105.999317353830 4.70068264617044 50 112.8 107.622990647709 5.17700935229133 51 109.8 118.031970022868 -8.23197002286804 52 117.3 111.503398685301 5.7966013146989 53 109.1 110.218092604021 -1.11809260402082 54 115.9 120.287072085352 -4.38707208535209 55 96 93.9729224998807 2.02707750011928 56 99.8 103.940678080778 -4.14067808077849 57 116.8 117.650338509530 -0.850338509529715 58 115.7 114.965169679452 0.73483032054752 59 99.4 107.237959387350 -7.83795938735018 60 94.3 98.9070753766812 -4.60707537668117 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.267150750841559 0.534301501683118 0.732849249158441 17 0.169274904557696 0.338549809115393 0.830725095442304 18 0.141329520222546 0.282659040445093 0.858670479777453 19 0.166795787995846 0.333591575991692 0.833204212004154 20 0.0942509413485734 0.188501882697147 0.905749058651427 21 0.0554724129155032 0.110944825831006 0.944527587084497 22 0.0467623781325060 0.0935247562650119 0.953237621867494 23 0.0771493976134008 0.154298795226802 0.9228506023866 24 0.0662844362476261 0.132568872495252 0.933715563752374 25 0.0891222935419457 0.178244587083891 0.910877706458054 26 0.0838870477164178 0.167774095432836 0.916112952283582 27 0.143513938784107 0.287027877568214 0.856486061215893 28 0.141115084733545 0.282230169467089 0.858884915266455 29 0.265936719435244 0.531873438870488 0.734063280564756 30 0.224331684111254 0.448663368222509 0.775668315888746 31 0.195742687932275 0.39148537586455 0.804257312067725 32 0.138225739405541 0.276451478811083 0.861774260594459 33 0.104165540059717 0.208331080119433 0.895834459940283 34 0.0901301012430447 0.180260202486089 0.909869898756955 35 0.0833121965186394 0.166624393037279 0.91668780348136 36 0.0660187089315684 0.132037417863137 0.933981291068432 37 0.0592997223580482 0.118599444716096 0.940700277641952 38 0.0437702990894876 0.0875405981789751 0.956229700910512 39 0.185161256799274 0.370322513598549 0.814838743200726 40 0.246636196412494 0.493272392824988 0.753363803587506 41 0.194300465352259 0.388600930704518 0.80569953464774 42 0.219624437365133 0.439248874730266 0.780375562634867 43 0.143103422421702 0.286206844843404 0.856896577578298 44 0.460138863952493 0.920277727904986 0.539861136047507 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 2 0.0689655172413793 OK

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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