*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: Fri, 24 Dec 2010 12:32:42 +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/24/t1293193925pst2z9ge1h5nf4t.htm/, Retrieved Fri, 24 Dec 2010 13:32:15 +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/24/t1293193925pst2z9ge1h5nf4t.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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37 30 47 35 30 43 82 40 47 19 52 136 80 42 54 66 81 63 137 72 107 58 36 52 79 77 54 84 48 96 83 66 61 53 30 74 69 59 42 65 70 100 63 105 82 81 75 102 121 98 76 77 63 37 35 23 40 29 37 51 20 28 13 22 25 13 16 13 16 17 9 17 25 14 8 7 10 7 10 3

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 7 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation Killed[t] = + 72 -10.4285714285714M1[t] -22.2857142857143M2[t] -29.9999999999999M3[t] -21.1428571428571M4[t] -25.2857142857143M5[t] -20.7142857142857M6[t] -11.1428571428571M7[t] -26M8[t] -13.1666666666666M9[t] -29.1666666666667M10[t] -32.1666666666666M11[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) 72 13.470212 5.3451 1e-06 1e-06 M1 -10.4285714285714 18.356804 -0.5681 0.571836 0.285918 M2 -22.2857142857143 18.356804 -1.214 0.228936 0.114468 M3 -29.9999999999999 18.356804 -1.6343 0.106824 0.053412 M4 -21.1428571428571 18.356804 -1.1518 0.253448 0.126724 M5 -25.2857142857143 18.356804 -1.3775 0.172888 0.086444 M6 -20.7142857142857 18.356804 -1.1284 0.263106 0.131553 M7 -11.1428571428571 18.356804 -0.607 0.545862 0.272931 M8 -26 18.356804 -1.4164 0.161232 0.080616 M9 -13.1666666666666 19.049756 -0.6912 0.49181 0.245905 M10 -29.1666666666667 19.049756 -1.5311 0.130389 0.065195 M11 -32.1666666666666 19.049756 -1.6886 0.095885 0.047942 Multiple Linear Regression - Regression Statistics Multiple R 0.283229920156028 R-squared 0.0802191876715897 Adjusted R-squared -0.0685688849109474 F-TEST (value) 0.539150660931439 F-TEST (DF numerator) 11 F-TEST (DF denominator) 68 p-value 0.869724119967225 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 32.9951454285133 Sum Squared Residuals 74030.2142857143 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 37 61.5714285714285 -24.5714285714285 2 30 49.7142857142856 -19.7142857142856 3 47 41.9999999999999 5.00000000000009 4 35 50.8571428571429 -15.8571428571429 5 30 46.7142857142858 -16.7142857142858 6 43 51.2857142857143 -8.2857142857143 7 82 60.8571428571429 21.1428571428571 8 40 46 -6 9 47 58.8333333333333 -11.8333333333333 10 19 42.8333333333333 -23.8333333333333 11 52 39.8333333333333 12.1666666666667 12 136 72 64 13 80 61.5714285714286 18.4285714285714 14 42 49.7142857142857 -7.71428571428571 15 54 42 12.0000000000000 16 66 50.8571428571429 15.1428571428571 17 81 46.7142857142857 34.2857142857143 18 63 51.2857142857143 11.7142857142857 19 137 60.8571428571429 76.1428571428571 20 72 46 26 21 107 58.8333333333333 48.1666666666667 22 58 42.8333333333333 15.1666666666667 23 36 39.8333333333333 -3.83333333333335 24 52 72 -20.0000000000000 25 79 61.5714285714286 17.4285714285714 26 77 49.7142857142857 27.2857142857143 27 54 42 12.0000000000000 28 84 50.8571428571429 33.1428571428571 29 48 46.7142857142857 1.28571428571429 30 96 51.2857142857143 44.7142857142857 31 83 60.8571428571428 22.1428571428572 32 66 46 20 33 61 58.8333333333333 2.16666666666666 34 53 42.8333333333333 10.1666666666667 35 30 39.8333333333333 -9.83333333333334 36 74 72 2.00000000000002 37 69 61.5714285714286 7.42857142857141 38 59 49.7142857142857 9.28571428571429 39 42 42 -2.97539770599542e-14 40 65 50.8571428571429 14.1428571428571 41 70 46.7142857142857 23.2857142857143 42 100 51.2857142857143 48.7142857142857 43 63 60.8571428571429 2.14285714285714 44 105 46 59 45 82 58.8333333333333 23.1666666666667 46 81 42.8333333333333 38.1666666666667 47 75 39.8333333333333 35.1666666666667 48 102 72 30 49 121 61.5714285714286 59.4285714285714 50 98 49.7142857142857 48.2857142857143 51 76 42 34.0000000000000 52 77 50.8571428571429 26.1428571428571 53 63 46.7142857142857 16.2857142857143 54 37 51.2857142857143 -14.2857142857143 55 35 60.8571428571428 -25.8571428571429 56 23 46 -23 57 40 58.8333333333333 -18.8333333333333 58 29 42.8333333333333 -13.8333333333333 59 37 39.8333333333333 -2.83333333333335 60 51 72 -21.0000000000000 61 20 61.5714285714286 -41.5714285714286 62 28 49.7142857142857 -21.7142857142857 63 13 42 -29 64 22 50.8571428571429 -28.8571428571429 65 25 46.7142857142857 -21.7142857142857 66 13 51.2857142857143 -38.2857142857143 67 16 60.8571428571429 -44.8571428571429 68 13 46 -33 69 16 58.8333333333333 -42.8333333333333 70 17 42.8333333333333 -25.8333333333333 71 9 39.8333333333333 -30.8333333333333 72 17 72 -55 73 25 61.5714285714286 -36.5714285714286 74 14 49.7142857142857 -35.7142857142857 75 8 42 -34 76 7 50.8571428571429 -43.8571428571429 77 10 46.7142857142857 -36.7142857142857 78 7 51.2857142857143 -44.2857142857143 79 10 60.8571428571429 -50.8571428571429 80 3 46 -43 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 15 0.158475561630126 0.316951123260251 0.841524438369874 16 0.123993255763458 0.247986511526917 0.876006744236542 17 0.187887423181978 0.375774846363956 0.812112576818022 18 0.120393022112806 0.240786044225611 0.879606977887194 19 0.219515918155739 0.439031836311477 0.780484081844261 20 0.184623973380724 0.369247946761449 0.815376026619276 21 0.275707866717027 0.551415733434054 0.724292133282973 22 0.250432131513488 0.500864263026976 0.749567868486512 23 0.183105851001376 0.366211702002751 0.816894148998624 24 0.339723827877663 0.679447655755325 0.660276172122337 25 0.278289346888232 0.556578693776465 0.721710653111768 26 0.274465689883425 0.54893137976685 0.725534310116575 27 0.208286391918863 0.416572783837726 0.791713608081137 28 0.197896908578411 0.395793817156823 0.802103091421589 29 0.144595596877395 0.28919119375479 0.855404403122605 30 0.170231825610318 0.340463651220635 0.829768174389682 31 0.163399393108131 0.326798786216263 0.836600606891869 32 0.127304042069895 0.254608084139789 0.872695957930105 33 0.0953491820916602 0.190698364183320 0.90465081790834 34 0.0687460649784185 0.137492129956837 0.931253935021581 35 0.0482556629361011 0.0965113258722022 0.95174433706390 36 0.0352706484903671 0.0705412969807342 0.964729351509633 37 0.0228767259116007 0.0457534518232013 0.9771232740884 38 0.0146748789959744 0.0293497579919488 0.985325121004026 39 0.00912117783686756 0.0182423556737351 0.990878822163132 40 0.0059126266204993 0.0118252532409986 0.9940873733795 41 0.00442938471156377 0.00885876942312755 0.995570615288436 42 0.0087955464316146 0.0175910928632292 0.991204453568385 43 0.0102695420582898 0.0205390841165795 0.98973045794171 44 0.0372246712135855 0.0744493424271711 0.962775328786414 45 0.037100425011708 0.074200850023416 0.962899574988292 46 0.0530312209017526 0.106062441803505 0.946968779098247 47 0.0672022039200892 0.134404407840178 0.93279779607991 48 0.0967837173589578 0.193567434717916 0.903216282641042 49 0.406877945540741 0.813755891081483 0.593122054459259 50 0.714201260148686 0.571597479702627 0.285798739851314 51 0.888107396065275 0.223785207869451 0.111892603934725 52 0.97942749695316 0.0411450060936787 0.0205725030468393 53 0.995200177276694 0.00959964544661241 0.00479982272330621 54 0.997141512820924 0.00571697435815259 0.00285848717907630 55 0.998151539862633 0.00369692027473361 0.00184846013736680 56 0.997801094056523 0.00439781188695415 0.00219890594347707 57 0.9979349989891 0.0041300020218015 0.00206500101090075 58 0.996077341343051 0.00784531731389763 0.00392265865694882 59 0.997256498940733 0.00548700211853315 0.00274350105926657 60 0.999689475613405 0.000621048773189314 0.000310524386594657 61 0.999149479444232 0.00170104111153668 0.000850520555768342 62 0.99857334375001 0.00285331249997982 0.00142665624998991 63 0.995214087637835 0.00957182472432905 0.00478591236216452 64 0.992750922919334 0.0144981541613328 0.00724907708066639 65 0.99091454754184 0.0181709049163188 0.0090854524581594 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 12 0.235294117647059 NOK 5% type I error level 21 0.411764705882353 NOK 10% type I error level 25 0.490196078431373 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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