*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, 30 Nov 2010 12:49:11 +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/Nov/30/t1291121360z0i06biirca5313.htm/, Retrieved Tue, 30 Nov 2010 13:49:20 +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/Nov/30/t1291121360z0i06biirca5313.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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162556 807 213118 6282154 29790 444 81767 4321023 87550 412 153198 4111912 84738 428 -26007 223193 54660 315 126942 1491348 42634 168 157214 1629616 40949 263 129352 1398893 45187 267 234817 1926517 37704 228 60448 983660 16275 129 47818 1443586 25830 104 245546 1073089 12679 122 48020 984885 18014 393 -1710 1405225 43556 190 32648 227132 24811 280 95350 929118 6575 63 151352 1071292 7123 102 288170 638830 21950 265 114337 856956 37597 234 37884 992426 17821 277 122844 444477 12988 73 82340 857217 22330 67 79801 711969 13326 103 165548 702380 16189 290 116384 358589 7146 83 134028 297978 15824 56 63838 585715 27664 236 74996 657954 11920 73 31080 209458 8568 34 32168 786690 14416 139 49857 439798 3369 26 87161 688779 11819 70 106113 574339 6984 40 80570 741409 4519 42 102129 597793 2220 12 301670 644190 18562 211 102313 377934 10327 74 88577 640273 5336 80 112477 697458 2365 83 191778 550608 4069 131 79804 207393 8636 203 128294 301607 13718 56 96448 345783 4525 89 93 etc...

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 6 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation Wealth[t] = -208139.364750439 + 16.9933350616200Costs[t] + 2823.29907158168Orders[t] + 2.96778676492997Dividends[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) -208139.364750439 187885.154935 -1.1078 0.272683 0.136342 Costs 16.9933350616200 6.082125 2.794 0.007115 0.003557 Orders 2823.29907158168 1139.558844 2.4775 0.016272 0.008136 Dividends 2.96778676492997 1.264912 2.3462 0.022529 0.011264 Multiple Linear Regression - Regression Statistics Multiple R 0.813960082483913 R-squared 0.662531015877218 Adjusted R-squared 0.644452320299212 F-TEST (value) 36.6470585788959 F-TEST (DF numerator) 3 F-TEST (DF denominator) 56 p-value 3.06643599401468e-13 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 615026.420022537 Sum Squared Residuals 21182419850241.3 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 6282154 5465120.34006103 817033.659938973 2 4321023 1794303.89492552 2526719.10507448 3 4111912 2897485.33419979 1214426.66580021 4 223193 2363030.63394254 -2139837.63394254 5 1491348 1986792.32477968 -495444.324779681 6 1629616 1457246.35475409 172369.645245908 7 1398893 1614137.52213104 -215244.522131043 8 1926517 2010446.10357185 -83929.1035718543 9 983660 1255686.30309999 -272026.303099992 10 1443586 574546.371136885 869039.628863115 11 1073089 1253149.75231720 -180060.752317196 12 984885 494274.737680744 490610.262319256 13 1405225 1202460.19281315 202764.807186847 14 227132 1165341.46309544 -938209.463095436 15 929118 1286984.47954236 -357866.479542358 16 1071292 530640.11723504 540651.88276496 17 638830 1056107.77824468 -417277.778244681 18 856956 1252366.42916306 -395410.429163063 19 992426 1203842.67011401 -211416.670114009 20 444477 1241327.49956187 -796850.499561874 21 857217 463038.465479679 394178.534520321 22 711969 597315.196599686 114653.803400314 23 702380 800424.78601425 -98044.7860142493 24 358589 1231125.36217042 -872536.362170424 25 297978 545395.355071211 -247417.355071211 26 585715 408325.48877281 177389.511227190 27 657954 1150834.97351018 -492880.973510182 28 209458 292760.834063558 -83302.8340635582 29 786690 128919.463145566 657770.536854434 30 439798 577240.069186842 -137442.069186842 31 688779 181192.219151344 507586.780848656 32 574339 505256.55434058 69082.44565942 33 741409 262588.629833591 478820.370166409 34 597793 290329.171914986 307463.828085014 35 644190 758757.661321762 -114567.661321762 36 377934 1006650.19204737 -628716.192047366 37 640273 439152.586005158 201120.413994842 38 697458 442208.748823928 255249.251176072 39 550608 635539.905816312 -84931.9058163116 40 207393 467699.948980964 -260306.948980964 41 301607 892494.023592718 -590887.023592718 42 345783 469317.051537405 -123534.051537405 43 501749 398440.137979007 103308.862020993 44 379983 505812.472701587 -125829.472701587 45 387475 185863.618582216 201611.381417784 46 377305 227228.475457171 150076.524542829 47 370837 638237.615061221 -267400.615061221 48 430866 746370.19884005 -315504.19884005 49 469107 400728.87891856 68378.1210814396 50 194493 173176.486666095 21316.5133339053 51 530670 420456.433054972 110213.566945028 52 518365 646287.62614559 -127922.626145590 53 491303 750051.880769504 -258748.880769504 54 527021 422936.828340085 104084.171659915 55 233773 657650.833809051 -423877.833809051 56 405972 231834.557003176 174137.442996824 57 652925 21919.5131042276 631005.486895772 58 446211 276161.149249518 170049.850750482 59 341340 252947.460910526 88392.5390894737 60 387699 449778.843657147 -62079.8436571471 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 7 0.99998628962267 2.74207546592847e-05 1.37103773296423e-05 8 0.9999999749859 5.00281992988091e-08 2.50140996494046e-08 9 0.999999928000545 1.43998910371050e-07 7.19994551855249e-08 10 0.99999999982863 3.42739934188767e-10 1.71369967094384e-10 11 0.999999999853546 2.92907768330632e-10 1.46453884165316e-10 12 0.99999999990105 1.97898417300082e-10 9.89492086500412e-11 13 0.99999999999984 3.21049579707001e-13 1.60524789853500e-13 14 0.999999999999994 1.23490097576876e-14 6.17450487884378e-15 15 0.999999999999999 2.82308629336348e-15 1.41154314668174e-15 16 1 1.74928813788186e-16 8.74644068940932e-17 17 1 5.94739334580066e-17 2.97369667290033e-17 18 1 1.84647638129524e-17 9.23238190647622e-18 19 1 4.17225952419241e-17 2.08612976209621e-17 20 1 2.85290061122656e-17 1.42645030561328e-17 21 1 1.62802092691359e-17 8.14010463456796e-18 22 1 7.38364354121738e-17 3.69182177060869e-17 23 1 2.81086919613416e-16 1.40543459806708e-16 24 1 3.98336256364578e-16 1.99168128182289e-16 25 1 1.20285731834408e-15 6.01428659172041e-16 26 0.999999999999997 5.71438076303763e-15 2.85719038151881e-15 27 0.999999999999995 1.06924773859255e-14 5.34623869296275e-15 28 0.999999999999995 9.42329924843332e-15 4.71164962421666e-15 29 0.999999999999996 7.00685719276781e-15 3.50342859638390e-15 30 0.999999999999978 4.3505631998752e-14 2.1752815999376e-14 31 0.999999999999955 8.9713724908023e-14 4.48568624540115e-14 32 0.999999999999758 4.84834162084435e-13 2.42417081042217e-13 33 0.999999999999779 4.42664483307746e-13 2.21332241653873e-13 34 0.999999999999195 1.61012538951492e-12 8.05062694757459e-13 35 0.999999999995863 8.27318569482826e-12 4.13659284741413e-12 36 0.999999999980896 3.82088779317985e-11 1.91044389658993e-11 37 0.999999999968132 6.37362755131817e-11 3.18681377565908e-11 38 0.99999999998231 3.53802332311806e-11 1.76901166155903e-11 39 0.999999999921325 1.57350722456760e-10 7.86753612283801e-11 40 0.999999999836978 3.26044716003191e-10 1.63022358001595e-10 41 0.999999999306463 1.38707481634215e-09 6.93537408171077e-10 42 0.999999996097243 7.80551440642881e-09 3.90275720321441e-09 43 0.999999979938937 4.01221263343036e-08 2.00610631671518e-08 44 0.99999988718195 2.25636100351071e-07 1.12818050175535e-07 45 0.99999940421086 1.19157828047061e-06 5.95789140235307e-07 46 0.9999970444191 5.91116180190128e-06 2.95558090095064e-06 47 0.999986803743412 2.63925131760436e-05 1.31962565880218e-05 48 0.999936350969869 0.000127298060262370 6.36490301311848e-05 49 0.999700198580782 0.000599602838435658 0.000299801419217829 50 0.999711219481754 0.00057756103649106 0.00028878051824553 51 0.998822831647214 0.00235433670557135 0.00117716835278567 52 0.99898558285177 0.00202883429646108 0.00101441714823054 53 0.994943139672307 0.0101137206553852 0.0050568603276926 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 46 0.97872340425532 NOK 5% type I error level 47 1 NOK 10% type I error level 47 1 NOK

Charts produced by software:

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Parameters (Session):

par1 = 4 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 4 ; par2 = Do not include Seasonal 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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