*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: Wed, 18 Nov 2009 07:31:41 -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/18/t1258554808ou9noef5dsgbnm7.htm/, Retrieved Wed, 18 Nov 2009 15:33:40 +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/18/t1258554808ou9noef5dsgbnm7.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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785.8 35 819.3 31.3 849.4 30 880.4 31.3 900.1 33 937.2 31.3 948.9 29 952.6 28.7 947.3 28 974.2 29.7 1000.8 30.7 1032.8 24 1050.7 29 1057.3 33 1075.4 28 1118.4 28.7 1179.8 31.7 1227 34 1257.8 35.3 1251.5 27 1236.3 31.3 1170.6 38.7 1213.1 37.3 1265.5 37.3 1300.8 37.7 1348.4 34.7 1371.9 34.7 1403.3 33.7 1451.8 38.3 1474.2 38 1438.2 38.3 1513.6 42.7 1562.2 41.7 1546.2 39.7 1527.5 39.3 1418.7 39.3 1448.5 37.7 1492.1 38.3 1395.4 37.7 1403.7 37 1316.6 34.3 1274.5 29.7 1264.4 34.7 1323.9 32 1332.1 30.3 1250.2 28.3 1096.7 31.3 1080.8 17.7 1039.2 15.7 792 14.3 746.6 13.3 688.8 11 715.8 2.7 672.9 3.3 629.5 3.7 681.2 1.4 755.4 7.1 760.6 8.1 765.9 12.4 836.8 12.4 904.9 9.2

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 3 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Herdiv[t] = + 105.726577629394 + 27.5215172223384handact[t] -30.9077305549567M1[t] -56.3118969397406M2[t] -35.2907042334095M3[t] -21.4849018494376M4[t] -6.61039049880582M5[t] + 9.71272774076114M6[t] -33.9403029532002M7[t] + 45.1164842309389M8[t] + 22.5052769924888M9[t] -45.7537785237274M10[t] -109.474555417731M11[t] + 8.38280450496339t + 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) 105.726577629394 81.328204 1.3 0.199941 0.09997 handact 27.5215172223384 1.511728 18.2053 0 0 M1 -30.9077305549567 64.298413 -0.4807 0.632966 0.316483 M2 -56.3118969397406 67.484319 -0.8344 0.408252 0.204126 M3 -35.2907042334095 67.404271 -0.5236 0.603039 0.30152 M4 -21.4849018494376 67.3278 -0.3191 0.751058 0.375529 M5 -6.61039049880582 67.258776 -0.0983 0.922126 0.461063 M6 9.71272774076114 67.211274 0.1445 0.885715 0.442858 M7 -33.9403029532002 67.140684 -0.5055 0.615563 0.307782 M8 45.1164842309389 67.126486 0.6721 0.504803 0.252402 M9 22.5052769924888 67.070132 0.3355 0.738705 0.369352 M10 -45.7537785237274 67.113441 -0.6817 0.498751 0.249375 M11 -109.474555417731 67.261988 -1.6276 0.110299 0.05515 t 8.38280450496339 0.963828 8.6974 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.937311753740401 R-squared 0.878553323699907 Adjusted R-squared 0.844961689829668 F-TEST (value) 26.1539324670445 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 105.977470162103 Sum Squared Residuals 527867.536552091 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 785.8 1046.45475436124 -260.654754361239 2 819.3 927.60377875877 -108.30377875877 3 849.4 921.229803581025 -71.8298035810251 4 880.4 979.196382859 -98.7963828590005 5 900.1 1049.24027799257 -149.140277992571 6 937.2 1027.15962145913 -89.9596214591257 7 948.9 928.58990565875 20.3100943412503 8 952.6 1007.77304218115 -55.1730421811506 9 947.3 974.279577392027 -26.9795773920271 10 974.2 961.18990565875 13.0100943412507 11 1000.8 933.373450492048 67.426549507952 12 1032.8 866.836645025075 165.963354974925 13 1050.7 981.919305086773 68.7806949132266 14 1057.3 1074.98401209631 -17.6840120963064 15 1075.4 966.78042319591 108.619576804091 16 1118.4 1008.23409214048 110.165907859519 17 1179.8 1114.05595966309 65.7440403369086 18 1227 1202.061372019 24.9386279810000 19 1257.8 1202.56911821904 55.2308817809581 20 1251.5 1061.58011696274 189.919883037264 21 1236.3 1165.69423828530 70.6057617146957 22 1170.6 1309.47721471936 -138.877214719356 23 1213.1 1215.60911821904 -2.50911821904183 24 1265.5 1333.46647814174 -67.9664781417357 25 1300.8 1321.95015898068 -21.1501589806779 26 1348.4 1222.36424543384 126.035754566158 27 1371.9 1251.76824264514 120.131757354863 28 1403.3 1246.43533231173 156.864667688266 29 1451.8 1396.29162739009 55.5083726099149 30 1474.2 1412.74109496791 61.4589050320859 31 1438.2 1385.72732394562 52.4726760543826 32 1513.6 1594.26159141301 -80.661591413009 33 1562.2 1552.51167145718 9.6883285428162 34 1546.2 1437.59238600125 108.607613998746 35 1527.5 1371.24580672328 156.254193276721 36 1418.7 1489.10316664597 -70.4031666459729 37 1448.5 1422.54381304024 25.9561869597616 38 1492.1 1422.03536149382 70.0646385061792 39 1395.4 1434.92644837171 -39.5264483717124 40 1403.7 1437.84999320501 -34.1499932050108 41 1316.6 1386.79921256029 -70.1992125602924 42 1274.5 1284.90615608207 -10.4061560820662 43 1264.4 1387.24351600476 -122.84351600476 44 1323.9 1400.37501119355 -76.4750111935489 45 1332.1 1339.36002918209 -7.2600291820873 46 1250.2 1224.44074372616 25.7592562738425 47 1096.7 1251.66732300413 -154.967323004133 48 1080.8 995.232048703025 85.5679512969751 49 1039.2 917.664088208355 121.535911791645 50 792 862.11260221726 -70.1126022172607 51 746.6 863.995082206217 -117.395082206217 52 688.8 822.884199483774 -134.084199483774 53 715.8 617.71292239396 98.0870776060394 54 672.9 658.931755471894 13.968244528106 55 629.5 634.670136171831 -5.17013617183116 56 681.2 658.810238249555 22.3897617504446 57 755.4 801.454483683398 -46.0544836833976 58 760.6 769.099749894483 -8.49974989448316 59 765.9 832.104301561498 -66.2043015614982 60 836.8 949.961661484192 -113.161661484192 61 904.9 839.367880322716 65.5321196772839 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0092996600793034 0.0185993201586068 0.990700339920697 18 0.00453680010147977 0.00907360020295954 0.99546319989852 19 0.00131235039447105 0.0026247007889421 0.99868764960553 20 0.00070103072915786 0.00140206145831572 0.999298969270842 21 0.000142430463551736 0.000284860927103471 0.999857569536448 22 0.00133101692370086 0.00266203384740172 0.998668983076299 23 0.000798203034892902 0.00159640606978580 0.999201796965107 24 0.000447844287574643 0.000895688575149286 0.999552155712425 25 0.00103040876373838 0.00206081752747675 0.998969591236262 26 0.000501923346387768 0.00100384669277554 0.999498076653612 27 0.000218107831960038 0.000436215663920076 0.99978189216804 28 9.0415740734423e-05 0.000180831481468846 0.999909584259266 29 3.94271370946234e-05 7.88542741892467e-05 0.999960572862905 30 1.19423373520128e-05 2.38846747040255e-05 0.999988057662648 31 1.63354133621231e-05 3.26708267242461e-05 0.999983664586638 32 1.62294634663001e-05 3.24589269326002e-05 0.999983770536534 33 6.13657403089166e-05 0.000122731480617833 0.99993863425969 34 0.000105028850707121 0.000210057701414243 0.999894971149293 35 0.000297342587900748 0.000594685175801497 0.9997026574121 36 0.00501346777590459 0.0100269355518092 0.994986532224095 37 0.0388596352086286 0.0777192704172572 0.961140364791371 38 0.119813055390055 0.239626110780111 0.880186944609945 39 0.404856934662577 0.809713869325154 0.595143065337423 40 0.817380914315745 0.365238171368510 0.182619085684255 41 0.906191930285913 0.187616139428174 0.0938080697140869 42 0.898791373615794 0.202417252768413 0.101208626384206 43 0.86492287502317 0.270154249953659 0.135077124976830 44 0.760793923324338 0.478412153351324 0.239206076675662 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 18 0.642857142857143 NOK 5% type I error level 20 0.714285714285714 NOK 10% type I error level 21 0.75 NOK

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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