WS7

*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, 21 Nov 2009 08:04:45 -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/Nov/21/t1258816090qtids9tojnr5fox.htm/, Retrieved Sat, 21 Nov 2009 16:08:22 +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/Nov/21/t1258816090qtids9tojnr5fox.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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10414.9 10723.8 12476.8 13938.9 12384.6 13979.8 12266.7 13807.4 12919.9 12973.9 11497.3 12509.8 12142 12934.1 13919.4 14908.3 12656.8 13772.1 12034.1 13012.6 13199.7 14049.9 10881.3 11816.5 11301.2 11593.2 13643.9 14466.2 12517 13615.9 13981.1 14733.9 14275.7 13880.7 13435 13527.5 13565.7 13584 16216.3 16170.2 12970 13260.6 14079.9 14741.9 14235 15486.5 12213.4 13154.5 12581 12621.2 14130.4 15031.6 14210.8 15452.4 14378.5 15428 13142.8 13105.9 13714.7 14716.8 13621.9 14180 15379.8 16202.2 13306.3 14392.4 14391.2 15140.6 14909.9 15960.1 14025.4 14351.3 12951.2 13230.2 14344.3 15202.1 16093.4 17056 15413.6 16077.7 14705.7 13348.2 15972.8 16402.4 16241.4 16559.1 16626.4 16579 17136.2 17561.2 15622.9 16129.6 18003.9 18484.3 16136.1 16402.6 14423.7 14032.3 16789.4 17109.1 16782.2 17157.2 14133.8 13879.8 12607 12362.4 12004.5 12683.5 12175.4 12608.8 13268 13583.7 12299.3 12846.3 11800.6 12347.1 13873.3 13967 12269.6 13114.3

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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation InIEU[t] = -1948.67388499954 + 1.09340563842981UitIEU[t] + 680.954666143251M1[t] -339.002306844012M2[t] -549.314325483949M3[t] -182.982105215105M4[t] + 1117.86368062190M5[t] + 0.843927411887669M6[t] + 219.578218092053M7[t] + 95.2438411644369M8[t] -86.0400876151622M9[t] -73.2518239774703M10[t] -252.678919640362M11[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) -1948.67388499954 579.424605 -3.3631 0.00154 0.00077 UitIEU 1.09340563842981 0.039943 27.3741 0 0 M1 680.954666143251 263.504263 2.5842 0.012927 0.006463 M2 -339.002306844012 263.947151 -1.2844 0.205312 0.102656 M3 -549.314325483949 266.737276 -2.0594 0.045021 0.022511 M4 -182.982105215105 261.29276 -0.7003 0.487195 0.243598 M5 1117.86368062190 259.350339 4.3102 8.3e-05 4.1e-05 M6 0.843927411887669 258.236303 0.0033 0.997406 0.498703 M7 219.578218092053 258.242817 0.8503 0.399481 0.199741 M8 95.2438411644369 267.10792 0.3566 0.723006 0.361503 M9 -86.0400876151622 259.217869 -0.3319 0.741424 0.370712 M10 -73.2518239774703 258.904229 -0.2829 0.778473 0.389236 M11 -252.678919640362 268.173097 -0.9422 0.350896 0.175448 Multiple Linear Regression - Regression Statistics Multiple R 0.975955859594136 R-squared 0.952489839876129 Adjusted R-squared 0.94035958622748 F-TEST (value) 78.5218403064713 F-TEST (DF numerator) 12 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 408.111714102607 Sum Squared Residuals 7828093.0458251 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 10414.9 10457.7441665374 -42.8441665374268 2 12476.8 12953.1956616658 -476.39566166579 3 12384.6 12787.6039336376 -403.003933637635 4 12266.7 12965.4330218412 -698.733021841177 5 12919.9 13354.9252080469 -435.025208046931 6 11497.3 11730.4558980416 -233.155898041644 7 12142 12413.1222011076 -271.122201107582 8 13919.4 14447.3892355681 -527.989235568103 9 12656.8 13023.7778204045 -366.97782040455 10 12034.1 12206.1245016548 -172.024501654797 11 13199.7 13160.8870747352 38.8129252648492 12 10881.3 10971.5538415064 -90.2538415063668 13 11301.2 11408.3510285882 -107.151028588239 14 13643.9 13529.7484548098 114.151545190165 15 12517 12389.7136218130 127.286378186975 16 13981.1 13978.4733458464 2.62665415359883 17 14275.7 14346.4254409751 -70.7254409750882 18 13435 12843.2148162717 591.785183728333 19 13565.7 13123.7265255231 441.973474476884 20 16216.3 15827.1578107027 389.142189297312 21 12970 12464.5008363477 505.4991636523 22 14079.9 14096.9508721915 -17.0508721914754 23 14235 14731.6736149034 -496.673614903423 24 12213.4 12434.5305857255 -221.130585725459 25 12581 12532.3720248941 48.6279751059106 26 14130.4 14147.9600027781 -17.5600027780517 27 14210.8 14397.7530767894 -186.953076789381 28 14378.5 14737.4061994805 -358.906199480536 29 13142.8 13499.2547523197 -356.454752319668 30 13714.7 14143.6021420562 -428.902142056244 31 13621.9 13775.3962860273 -153.496286027286 32 15379.8 15862.1467911324 -482.346791132442 33 13306.3 13702.0173379226 -395.717337922564 34 14391.2 14532.8917002334 -141.691700233442 35 14909.9 15249.5105252638 -339.610525263785 36 14025.4 13743.1184537983 282.28154620174 37 12951.2 13198.2560586978 -247.056058697846 38 14344.3 14334.3856641303 9.91433586966418 39 16093.4 16151.1383585754 -57.7383585754312 40 15413.6 15447.7918427684 -34.1918427683873 41 14705.7 13764.1869385112 941.513061488788 42 15972.8 15986.6466861935 -13.8466861935425 43 16241.4 16376.7176404157 -135.317640415656 44 16626.4 16274.1420356928 352.257964307206 45 17136.2 17166.8011249790 -30.6011249789598 46 15622.9 15614.2698766405 8.63012335947014 47 18003.9 18009.4850377883 -5.58503778832015 48 16136.1 15986.0214399093 150.078560090663 49 14423.7 14075.2767212824 348.423278717601 50 16789.4 16419.510216616 369.889783384012 51 16782.2 16261.7910091845 520.408990815472 52 14133.8 13044.5955900635 1089.20440993650 53 12607 12686.3076601471 -79.3076601471001 54 12004.5 11920.3804574369 84.119542563097 55 12175.4 12057.4373469264 117.962653073639 56 13268 12999.0641269040 268.935873096028 57 12299.3 12011.5028803462 287.797119653773 58 11800.6 11478.4630492798 322.136950720244 59 13873.3 13070.2437473093 803.05625269068 60 12269.6 12390.5756790606 -120.975679060578 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 0.515261006459463 0.969477987081074 0.484738993540537 17 0.341434328654986 0.682868657309972 0.658565671345014 18 0.29002842099254 0.58005684198508 0.70997157900746 19 0.237738149649579 0.475476299299159 0.762261850350421 20 0.162428255792096 0.324856511584192 0.837571744207904 21 0.458295937002299 0.916591874004598 0.541704062997701 22 0.42642931539765 0.8528586307953 0.57357068460235 23 0.568820627237988 0.862358745524024 0.431179372762012 24 0.514766810729963 0.970466378540074 0.485233189270037 25 0.414558823434049 0.829117646868097 0.585441176565952 26 0.325233699454398 0.650467398908796 0.674766300545602 27 0.285961601221351 0.571923202442701 0.71403839877865 28 0.293794155887772 0.587588311775543 0.706205844112228 29 0.292272950216142 0.584545900432284 0.707727049783858 30 0.358117533759115 0.71623506751823 0.641882466240885 31 0.289248788541297 0.578497577082593 0.710751211458703 32 0.329237612418603 0.658475224837206 0.670762387581397 33 0.345479842837439 0.690959685674878 0.654520157162561 34 0.270494757236543 0.540989514473086 0.729505242763457 35 0.308658665894037 0.617317331788074 0.691341334105963 36 0.261548914855178 0.523097829710355 0.738451085144822 37 0.258965908763230 0.517931817526460 0.74103409123677 38 0.220651040761485 0.441302081522969 0.779348959238515 39 0.20302372828006 0.40604745656012 0.79697627171994 40 0.375004893836461 0.750009787672922 0.624995106163539 41 0.910267958866024 0.179464082267951 0.0897320411339757 42 0.839944931946726 0.320110136106548 0.160055068053274 43 0.720007027639395 0.559985944721211 0.279992972360605 44 0.636223141853016 0.727553716293968 0.363776858146984 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 = 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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