*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: Mon, 06 Dec 2010 14:47:05 +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/06/t1291646703883g3v5jniy9s0v.htm/, Retrieved Mon, 06 Dec 2010 15:45:13 +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/06/t1291646703883g3v5jniy9s0v.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:

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User-defined keywords:

Dataseries X:

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3484.74 13830.14 9349.44 7977 -5.6 6 1 2.77 3411.13 14153.22 9327.78 8241 -6.2 3 1 2.76 3288.18 15418.03 9753.63 8444 -7.1 2 1.2 2.76 3280.37 16666.97 10443.5 8490 -1.4 2 1.2 2.46 3173.95 16505.21 10853.87 8388 -0.1 2 0.8 2.46 3165.26 17135.96 10704.02 8099 -0.9 -8 0.7 2.47 3092.71 18033.25 11052.23 7984 0 0 0.7 2.71 3053.05 17671 10935.47 7786 0.1 -2 0.9 2.8 3181.96 17544.22 10714.03 8086 2.6 3 1.2 2.89 2999.93 17677.9 10394.48 9315 6 5 1.3 3.36 3249.57 18470.97 10817.9 9113 6.4 8 1.5 3.31 3210.52 18409.96 11251.2 9023 8.6 8 1.9 3.5 3030.29 18941.6 11281.26 9026 6.4 9 1.8 3.51 2803.47 19685.53 10539.68 9787 7.7 11 1.9 3.71 2767.63 19834.71 10483.39 9536 9.2 13 2.2 3.71 2882.6 19598.93 10947.43 9490 8.6 12 2.1 3.71 2863.36 17039.97 10580.27 9736 7.4 13 2.2 4.21 2897.06 16969.28 10582.92 9694 8.6 15 2.7 4.21 3012.61 16973.38 10654.41 9647 6.2 13 2.8 4.21 3142.95 16329.89 11014.51 9753 6 16 2.9 4.5 3032.93 16153.34 10967.87 10070 6.6 10 3.4 4.51 3045.78 15311.7 10433.56 10137 5.1 14 3 4.51 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 7 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation BEL_20[t] = + 688.098795765917 + 0.0462179954610761Nikkei[t] + 0.278030419928214DJ_Indust[t] -0.178777803993867Goudprijs[t] -57.5548412693366Conjunct_Seizoenzuiver[t] + 33.6760247240671Cons_vertrouw[t] -131.109005569773Alg_consumptie_index_BE[t] + 131.838648549116Gem_rente_kasbon_1j[t] -34.4247599390837M1[t] + 56.988069043629M2[t] -72.544498687564M3[t] -24.1245880172990M4[t] -68.2147043679782M5[t] -14.5616582959767M6[t] -131.285788333769M7[t] -116.524230423104M8[t] + 65.1267127103127M9[t] + 96.69510720441M10[t] + 87.6952746740044M11[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) 688.098795765917 899.143352 0.7653 0.449711 0.224855 Nikkei 0.0462179954610761 0.02709 1.7061 0.097682 0.048841 DJ_Indust 0.278030419928214 0.06205 4.4808 8.9e-05 4.5e-05 Goudprijs -0.178777803993867 0.051491 -3.472 0.001502 0.000751 Conjunct_Seizoenzuiver -57.5548412693366 12.588776 -4.5719 6.9e-05 3.4e-05 Cons_vertrouw 33.6760247240671 8.686369 3.8769 0.000494 0.000247 Alg_consumptie_index_BE -131.109005569773 75.27088 -1.7418 0.091145 0.045572 Gem_rente_kasbon_1j 131.838648549116 130.185368 1.0127 0.3188 0.1594 M1 -34.4247599390837 119.646909 -0.2877 0.775417 0.387708 M2 56.988069043629 118.586593 0.4806 0.634098 0.317049 M3 -72.544498687564 120.302055 -0.603 0.550746 0.275373 M4 -24.1245880172990 126.555262 -0.1906 0.850024 0.425012 M5 -68.2147043679782 127.073369 -0.5368 0.595109 0.297555 M6 -14.5616582959767 124.993304 -0.1165 0.907985 0.453992 M7 -131.285788333769 126.340208 -1.0391 0.306526 0.153263 M8 -116.524230423104 124.034076 -0.9395 0.354536 0.177268 M9 65.1267127103127 124.006179 0.5252 0.603072 0.301536 M10 96.69510720441 129.142918 0.7487 0.459479 0.22974 M11 87.6952746740044 122.460306 0.7161 0.479116 0.239558 Multiple Linear Regression - Regression Statistics Multiple R 0.94922276490454 R-squared 0.901023857413022 Adjusted R-squared 0.845349777207846 F-TEST (value) 16.1839019898036 F-TEST (DF numerator) 18 F-TEST (DF denominator) 32 p-value 2.85611534422969e-11 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 169.602470518423 Sum Squared Residuals 920479.936190486 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 3484.74 3224.64088077143 260.099119228574 2 3411.13 3209.95278468158 201.177215318422 3 3288.18 3212.88609120956 75.2939087904361 4 3280.37 3134.99638214319 145.373617856807 5 3173.95 3193.38303085782 -19.4330308578158 6 3165.26 3009.90491731214 155.355082687857 7 3092.71 3301.27426870604 -208.564268706039 8 3053.05 3214.76467480129 -161.714674801295 9 3181.96 3272.38150022858 -90.4215002285755 10 2999.93 2922.08462795288 77.8453720471175 11 3249.57 3148.76806201861 100.801937981386 12 3210.52 3040.79870095976 169.721299040245 13 3030.29 3213.49249969773 -183.202499697735 14 2803.47 3002.84415934495 -199.374159344950 15 2767.63 2851.11637451454 -83.4863745145386 16 2882.6 3039.84780185671 -157.247801856710 17 2863.36 2886.97695304247 -23.6169530424729 18 2897.06 2878.34003453593 18.7199654640731 19 3012.61 2847.7530188292 164.856981170799 20 3142.95 3051.60341578175 91.3465842182463 21 3032.93 2854.62949975961 178.300500240390 22 3045.78 2960.24639704260 85.5336029574046 23 3110.52 3027.61657014991 82.903429850085 24 3013.24 3041.02513331141 -27.7851333114125 25 2987.1 3102.68362683346 -115.583626833456 26 2995.55 3106.40613188762 -110.856131887622 27 2833.18 2807.51664806401 25.6633519359916 28 2848.96 3012.44410974976 -163.484109749757 29 2794.83 2966.54983242192 -171.719832421920 30 2845.26 3073.86057512869 -228.600575128694 31 2915.02 2965.5539739007 -50.5339739006996 32 2892.63 2834.76908184210 57.8609181579048 33 2604.42 2603.85126636338 0.568733636618269 34 2641.65 2528.84685263005 112.80314736995 35 2659.81 2558.59725077912 101.212749220876 36 2638.53 2756.04708943989 -117.517089439890 37 2720.25 2648.10313852327 72.1468614767347 38 2745.88 2729.87264474623 16.0073552537680 39 2735.7 2709.92785652090 25.7721434790966 40 2811.7 2636.34170625034 175.35829374966 41 2799.43 2584.66018367779 214.769816322209 42 2555.28 2500.75447302324 54.5255269767635 43 2304.98 2210.73873856406 94.2412614359392 44 2214.95 2202.44282757486 12.5071724251435 45 2065.81 2154.25773364843 -88.4477336484332 46 1940.49 2216.67212237447 -276.182122374472 47 2042 2326.91811705235 -284.918117052346 48 1995.37 2019.78907628894 -24.4190762889422 49 1946.81 1980.26985417412 -33.4598541741173 50 1765.9 1672.85427933962 93.0457206603824 51 1635.25 1678.49302969099 -43.2430296909856 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 22 0.188679558931162 0.377359117862323 0.811320441068838 23 0.347628123017332 0.695256246034664 0.652371876982668 24 0.453208207933719 0.906416415867437 0.546791792066281 25 0.318510749893035 0.637021499786071 0.681489250106965 26 0.429994572970301 0.859989145940602 0.570005427029699 27 0.282788979948318 0.565577959896637 0.717211020051681 28 0.374212634431992 0.748425268863984 0.625787365568008 29 0.266928233483421 0.533856466966843 0.733071766516578 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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