*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 14:37:11 +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/t1293546902bgu8crmkkquchtn.htm/, Retrieved Tue, 28 Dec 2010 15:35:02 +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/t1293546902bgu8crmkkquchtn.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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11100 8962 9173 8738 8459 8078 8411 8291 7810 8616 8312 9692 9911 8915 9452 9112 8472 8230 8384 8625 8221 8649 8625 10443 10357 8586 8892 8329 8101 7922 8120 7838 7735 8406 8209 9451 10041 9411 10405 8467 8464 8102 7627 7513 7510 8291 8064 9383 9706 8579 9474 8318 8213 8059 9111 7708 7680 8014 8007 8718 9486 9113 9025 8476 7952 7759 7835 7600 7651 8319 8812 8630

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Overlijdens[t] = + 9719.03333333333 + 626.820634920639M1[t] -537.753968253968M2[t] -53.9952380952378M3[t] -876.236507936508M4[t] -1164.81111111111M5[t] -1408.71904761905M6[t] -1177.79365079365M7[t] -1488.70158730159M8[t] -1642.10952380952M9[t] -1019.51746031746M10[t] -1055.92539682540M11[t] -7.92539682539685t + 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) 9719.03333333333 176.681166 55.0089 0 0 M1 626.820634920639 216.33634 2.8974 0.005272 0.002636 M2 -537.753968253968 216.113548 -2.4883 0.015679 0.007839 M3 -53.9952380952378 215.911776 -0.2501 0.803394 0.401697 M4 -876.236507936508 215.731083 -4.0617 0.000146 7.3e-05 M5 -1164.81111111111 215.571523 -5.4034 1e-06 1e-06 M6 -1408.71904761905 215.433142 -6.539 0 0 M7 -1177.79365079365 215.31598 -5.4701 1e-06 0 M8 -1488.70158730159 215.220073 -6.9171 0 0 M9 -1642.10952380952 215.14545 -7.6326 0 0 M10 -1019.51746031746 215.092131 -4.7399 1.4e-05 7e-06 M11 -1055.92539682540 215.060134 -4.9099 8e-06 4e-06 t -7.92539682539685 2.141944 -3.7001 0.000475 0.000238 Multiple Linear Regression - Regression Statistics Multiple R 0.899080149210731 R-squared 0.80834511470479 Adjusted R-squared 0.769364460068477 F-TEST (value) 20.7370841317721 F-TEST (DF numerator) 12 F-TEST (DF denominator) 59 p-value 1.11022302462516e-16 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 372.476602880371 Sum Squared Residuals 8185590.3619048 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 11100 10337.9285714286 762.071428571448 2 8962 9165.42857142857 -203.428571428571 3 9173 9641.2619047619 -468.261904761906 4 8738 8811.09523809524 -73.0952380952388 5 8459 8514.59523809524 -55.595238095239 6 8078 8262.7619047619 -184.761904761905 7 8411 8485.7619047619 -74.7619047619057 8 8291 8166.92857142857 124.071428571428 9 7810 8005.59523809524 -195.595238095238 10 8616 8620.2619047619 -4.26190476190573 11 8312 8575.92857142857 -263.928571428572 12 9692 9623.92857142857 68.0714285714281 13 9911 10242.8238095238 -331.823809523814 14 8915 9070.32380952381 -155.32380952381 15 9452 9546.15714285714 -94.1571428571432 16 9112 8715.99047619048 396.009523809523 17 8472 8419.49047619048 52.5095238095234 18 8230 8167.65714285714 62.3428571428566 19 8384 8390.65714285714 -6.65714285714329 20 8625 8071.82380952381 553.17619047619 21 8221 7910.49047619048 310.509523809523 22 8649 8525.15714285714 123.842857142857 23 8625 8480.82380952381 144.17619047619 24 10443 9528.82380952381 914.17619047619 25 10357 10147.7190476191 209.280952380948 26 8586 8975.21904761905 -389.219047619048 27 8892 9451.05238095238 -559.052380952381 28 8329 8620.88571428571 -291.885714285714 29 8101 8324.38571428571 -223.385714285714 30 7922 8072.55238095238 -150.552380952381 31 8120 8295.55238095238 -175.552380952381 32 7838 7976.71904761905 -138.719047619048 33 7735 7815.38571428571 -80.3857142857145 34 8406 8430.05238095238 -24.0523809523811 35 8209 8385.71904761905 -176.719047619048 36 9451 9433.71904761905 17.2809523809524 37 10041 10052.6142857143 -11.6142857142896 38 9411 8880.11428571429 530.885714285715 39 10405 9355.94761904762 1049.05238095238 40 8467 8525.78095238095 -58.7809523809522 41 8464 8229.28095238095 234.719047619048 42 8102 7977.44761904762 124.552380952381 43 7627 8200.44761904762 -573.447619047619 44 7513 7881.61428571429 -368.614285714286 45 7510 7720.28095238095 -210.280952380952 46 8291 8334.94761904762 -43.9476190476189 47 8064 8290.61428571429 -226.614285714286 48 9383 9338.61428571429 44.3857142857145 49 9706 9957.50952380953 -251.509523809527 50 8579 8785.00952380952 -206.009523809524 51 9474 9260.84285714286 213.157142857143 52 8318 8430.67619047619 -112.67619047619 53 8213 8134.17619047619 78.82380952381 54 8059 7882.34285714286 176.657142857143 55 9111 8105.34285714286 1005.65714285714 56 7708 7786.50952380952 -78.5095238095234 57 7680 7625.17619047619 54.8238095238099 58 8014 8239.84285714286 -225.842857142857 59 8007 8195.50952380952 -188.509523809523 60 8718 9243.50952380952 -525.509523809523 61 9486 9862.40476190477 -376.404761904765 62 9113 8689.90476190476 423.095238095239 63 9025 9165.7380952381 -140.738095238095 64 8476 8335.57142857143 140.428571428572 65 7952 8039.07142857143 -87.0714285714278 66 7759 7787.2380952381 -28.2380952380946 67 7835 8010.2380952381 -175.238095238095 68 7600 7691.40476190476 -91.4047619047612 69 7651 7530.07142857143 120.928571428572 70 8319 8144.7380952381 174.261904761906 71 8812 8100.40476190476 711.595238095239 72 8630 9148.40476190476 -518.404761904761 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.81471090995366 0.370578180092680 0.185289090046340 17 0.694180332951104 0.611639334097792 0.305819667048896 18 0.576243681670103 0.847512636659793 0.423756318329897 19 0.441267265624974 0.882534531249947 0.558732734375026 20 0.400853944653544 0.801707889307089 0.599146055346456 21 0.349172501413408 0.698345002826815 0.650827498586592 22 0.251119330592387 0.502238661184774 0.748880669407613 23 0.188553462065049 0.377106924130098 0.81144653793495 24 0.35494696693385 0.7098939338677 0.64505303306615 25 0.326697290087626 0.653394580175252 0.673302709912374 26 0.336874146675525 0.673748293351051 0.663125853324475 27 0.417199788935219 0.834399577870438 0.582800211064781 28 0.434794754774868 0.869589509549735 0.565205245225132 29 0.379755892140857 0.759511784281714 0.620244107859143 30 0.309179873811799 0.618359747623598 0.690820126188201 31 0.250745161141639 0.501490322283278 0.749254838858361 32 0.233863650057835 0.467727300115669 0.766136349942165 33 0.175136697655065 0.350273395310129 0.824863302344935 34 0.125148431475348 0.250296862950696 0.874851568524652 35 0.0945019787340984 0.189003957468197 0.905498021265902 36 0.0873181271601548 0.174636254320310 0.912681872839845 37 0.0636252466646282 0.127250493329256 0.936374753335372 38 0.141235822774877 0.282471645549753 0.858764177225123 39 0.651629456851688 0.696741086296624 0.348370543148312 40 0.57350715432292 0.852985691354161 0.426492845677081 41 0.527651154120503 0.944697691758993 0.472348845879497 42 0.452566496695224 0.905132993390447 0.547433503304776 43 0.62047618049726 0.759047639005479 0.379523819502740 44 0.598444911382948 0.803110177234104 0.401555088617052 45 0.537990891978142 0.924018216043716 0.462009108021858 46 0.44568994160696 0.89137988321392 0.55431005839304 47 0.44047620825298 0.88095241650596 0.55952379174702 48 0.448226796519614 0.896453593039228 0.551773203480386 49 0.373866251488705 0.74773250297741 0.626133748511295 50 0.379326904192027 0.758653808384053 0.620673095807973 51 0.31881855589487 0.63763711178974 0.68118144410513 52 0.240788730561599 0.481577461123199 0.7592112694384 53 0.163261393927683 0.326522787855367 0.836738606072317 54 0.106595737503559 0.213191475007118 0.893404262496441 55 0.722239093474622 0.555521813050756 0.277760906525378 56 0.626572048153422 0.746855903693156 0.373427951846578 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 0 0 OK

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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