final

*Unverified author*

R Software Module: rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Thu, 27 Nov 2008 03:16:48 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/27/t12277810862bc3eosbl9bml3e.htm/, Retrieved Thu, 27 Nov 2008 10:18:06 +0000

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/2008/Nov/27/t12277810862bc3eosbl9bml3e.htm/}, year = {2008}, } @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 = {2008}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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User-defined keywords:

Dataseries X:

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9492.49 0 9682.35 0 9762.12 0 10124.63 0 10540.05 0 10601.61 0 10323.73 0 10418.4 0 10092.96 0 10364.91 0 10152.09 0 10032.8 0 10204.59 0 10001.6 0 10411.75 0 10673.38 0 10539.51 0 10723.78 0 10682.06 0 10283.19 0 10377.18 0 10486.64 0 10545.38 0 10554.27 0 10532.54 0 10324.31 0 10695.25 0 10827.81 0 10872.48 0 10971.19 0 11145.65 0 11234.68 0 11333.88 0 10997.97 0 11036.89 0 11257.35 0 11533.59 0 11963.12 0 12185.15 0 12377.62 0 12512.89 0 12631.48 0 12268.53 0 12754.8 0 13407.75 0 13480.21 0 13673.28 0 13239.71 0 13557.69 0 13901.28 0 13200.58 0 13406.97 1 12538.12 1 12419.57 1 12193.88 1 12656.63 1 12812.48 1 12056.67 1 11322.38 1 11530.75 1 11114.08 1

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 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation X[t] = + 8934.32837086093 -1235.85451986755Y[t] + 74.4114233811647M1[t] + 336.556910779986M2[t] + 339.777729304636M3[t] + 744.843451802796M4[t] + 590.154270327447M5[t] + 585.853088852098M6[t] + 365.879907376747M7[t] + 439.432725901398M8[t] + 501.525544426048M9[t] + 300.738362950699M10[t] + 96.2451814753494M11[t] + 73.2171814753495t + 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) 8934.32837086093 324.567301 27.5269 0 0 Y -1235.85451986755 278.153799 -4.4431 5.4e-05 2.7e-05 M1 74.4114233811647 367.392313 0.2025 0.840369 0.420185 M2 336.556910779986 385.928922 0.8721 0.387604 0.193802 M3 339.777729304636 385.632717 0.8811 0.382752 0.191376 M4 744.843451802796 385.712662 1.9311 0.059517 0.029758 M5 590.154270327447 385.05385 1.5327 0.132065 0.066033 M6 585.853088852098 384.481966 1.5237 0.134273 0.067136 M7 365.879907376747 383.997399 0.9528 0.345557 0.172778 M8 439.432725901398 383.60048 1.1455 0.257782 0.128891 M9 501.525544426048 383.291482 1.3085 0.197077 0.098538 M10 300.738362950699 383.070615 0.7851 0.43635 0.218175 M11 96.2451814753494 382.938035 0.2513 0.802652 0.401326 t 73.2171814753495 5.818306 12.5839 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.892553472677041 R-squared 0.796651701587845 Adjusted R-squared 0.740406427558952 F-TEST (value) 14.1638869281461 F-TEST (DF numerator) 13 F-TEST (DF denominator) 47 p-value 4.10116385296533e-12 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 605.408303707719 Sum Squared Residuals 17226403.0673181 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 9492.49 9081.95697571743 410.533024282568 2 9682.35 9417.31964459161 265.030355408389 3 9762.12 9493.75764459161 268.362355408389 4 10124.63 9972.04054856512 152.589451434878 5 10540.05 9890.56854856512 649.481451434878 6 10601.61 9959.48454856512 642.125451434878 7 10323.73 9812.72854856512 511.001451434878 8 10418.4 9959.49854856512 458.901451434877 9 10092.96 10094.8085485651 -1.8485485651222 10 10364.91 9967.23854856512 397.671451434878 11 10152.09 9835.96254856512 316.127451434879 12 10032.8 9812.93454856512 219.865451434877 13 10204.59 9960.56315342164 244.026846578365 14 10001.6 10295.9258222958 -294.325822295806 15 10411.75 10372.3638222958 39.3861777041938 16 10673.38 10850.6467262693 -177.266726269316 17 10539.51 10769.1747262693 -229.664726269316 18 10723.78 10838.0907262693 -114.310726269315 19 10682.06 10691.3347262693 -9.27472626931606 20 10283.19 10838.1047262693 -554.914726269315 21 10377.18 10973.4147262693 -596.234726269315 22 10486.64 10845.8447262693 -359.204726269316 23 10545.38 10714.5687262693 -169.188726269317 24 10554.27 10691.5407262693 -137.270726269315 25 10532.54 10839.1693311258 -306.629331125829 26 10324.31 11174.532 -850.222 27 10695.25 11250.97 -555.72 28 10827.81 11729.2529039735 -901.44290397351 29 10872.48 11647.7809039735 -775.30090397351 30 10971.19 11716.6969039735 -745.50690397351 31 11145.65 11569.9409039735 -424.29090397351 32 11234.68 11716.7109039735 -482.030903973509 33 11333.88 11852.0209039735 -518.14090397351 34 10997.97 11724.4509039735 -726.48090397351 35 11036.89 11593.1749039735 -556.28490397351 36 11257.35 11570.1469039735 -312.796903973509 37 11533.59 11717.7755088300 -184.185508830024 38 11963.12 12053.1381777042 -90.0181777041935 39 12185.15 12129.5761777042 55.5738222958057 40 12377.62 12607.8590816777 -230.239081677703 41 12512.89 12526.3870816777 -13.4970816777046 42 12631.48 12595.3030816777 36.1769183222954 43 12268.53 12448.5470816777 -180.017081677703 44 12754.8 12595.3170816777 159.482918322296 45 13407.75 12730.6270816777 677.122918322296 46 13480.21 12603.0570816777 877.152918322296 47 13673.28 12471.7810816777 1201.49891832230 48 13239.71 12448.7530816777 790.956918322295 49 13557.69 12596.3816865342 961.308313465782 50 13901.28 12931.7443554084 969.535644591612 51 13200.58 13008.1823554084 192.397644591611 52 13406.97 12250.6107395143 1156.35926048565 53 12538.12 12169.1387395143 368.981260485652 54 12419.57 12238.0547395143 181.515260485651 55 12193.88 12091.2987395143 102.581260485651 56 12656.63 12238.0687395143 418.561260485651 57 12812.48 12373.3787395143 439.101260485651 58 12056.67 12245.8087395143 -189.138739514348 59 11322.38 12114.5327395143 -792.152739514349 60 11530.75 12091.5047395143 -560.754739514348 61 11114.08 12239.1333443709 -1125.05334437086 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 0.0797683458997104 0.159536691799421 0.92023165410029 18 0.0407697639996177 0.0815395279992353 0.959230236000382 19 0.0151074619258308 0.0302149238516616 0.98489253807417 20 0.0149214224421208 0.0298428448842416 0.98507857755788 21 0.0051315532881593 0.0102631065763186 0.99486844671184 22 0.00207007648444674 0.00414015296889348 0.997929923515553 23 0.000808221726897157 0.00161644345379431 0.999191778273103 24 0.000424533509876725 0.00084906701975345 0.999575466490123 25 0.000254989810436986 0.000509979620873972 0.999745010189563 26 7.62195630245815e-05 0.000152439126049163 0.999923780436975 27 2.79219412529930e-05 5.58438825059859e-05 0.999972078058747 28 1.06908923154304e-05 2.13817846308609e-05 0.999989309107685 29 4.07114980227251e-06 8.14229960454502e-06 0.999995928850198 30 1.50299623663067e-06 3.00599247326133e-06 0.999998497003763 31 4.97476584079894e-07 9.94953168159788e-07 0.999999502523416 32 4.97925320752736e-07 9.95850641505472e-07 0.99999950207468 33 1.79851823834771e-06 3.59703647669542e-06 0.999998201481762 34 6.50386347954785e-07 1.30077269590957e-06 0.999999349613652 35 2.10908525903915e-07 4.21817051807829e-07 0.999999789091474 36 1.47544380638936e-07 2.95088761277872e-07 0.99999985245562 37 5.32436786639239e-07 1.06487357327848e-06 0.999999467563213 38 2.05723587027688e-05 4.11447174055375e-05 0.999979427641297 39 5.34866323471539e-05 0.000106973264694308 0.999946513367653 40 0.000887637267256075 0.00177527453451215 0.999112362732744 41 0.00198784751513542 0.00397569503027085 0.998012152484865 42 0.00315569524838085 0.0063113904967617 0.99684430475162 43 0.00693046398126485 0.0138609279625297 0.993069536018735 44 0.0621446587456313 0.124289317491263 0.937855341254369 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 21 0.75 NOK 5% type I error level 25 0.892857142857143 NOK 10% type I error level 26 0.928571428571429 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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