*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: Thu, 09 Dec 2010 19:50:41 +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/09/t12919241147gjusabds0dqp5a.htm/, Retrieved Thu, 09 Dec 2010 20:48:34 +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/09/t12919241147gjusabds0dqp5a.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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286602 283042 276687 277915 277128 277103 275037 270150 267140 264993 287259 291186 292300 288186 281477 282656 280190 280408 276836 275216 274352 271311 289802 290726 292300 278506 269826 265861 269034 264176 255198 253353 246057 235372 258556 260993 254663 250643 243422 247105 248541 245039 237080 237085 225554 226839 247934 248333 246969 245098 246263 255765 264319 268347 273046 273963 267430 271993 292710 295881 294563

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 5 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Multiple Linear Regression - Estimated Regression Equation HPC[t] = + 293568.447058824 -1766.61209150322M1[t] -12813.4241830065M2[t] -17924.9617647059M3[t] -15151.0993464052M4[t] -12720.6369281046M5[t] -13099.9745098039M6[t] -16226.7120915033M7[t] -17264.2496732026M8[t] -22662.5872549020M9[t] -24219.1248366013M10[t] -2620.06241830065M11[t] -448.462418300654t + 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) 293568.447058824 8513.552384 34.4825 0 0 M1 -1766.61209150322 9928.804936 -0.1779 0.859528 0.429764 M2 -12813.4241830065 10421.331268 -1.2295 0.224863 0.112432 M3 -17924.9617647059 10408.023114 -1.7222 0.091467 0.045734 M4 -15151.0993464052 10396.101377 -1.4574 0.151522 0.075761 M5 -12720.6369281046 10385.570833 -1.2248 0.226613 0.113307 M6 -13099.9745098039 10376.435717 -1.2625 0.212878 0.106439 M7 -16226.7120915033 10368.699718 -1.565 0.124159 0.06208 M8 -17264.2496732026 10362.365968 -1.6661 0.102217 0.051108 M9 -22662.5872549020 10357.43704 -2.188 0.033566 0.016783 M10 -24219.1248366013 10353.914941 -2.3391 0.023539 0.011769 M11 -2620.06241830065 10351.801106 -0.2531 0.80127 0.400635 t -448.462418300654 120.786951 -3.7128 0.000533 0.000267 Multiple Linear Regression - Regression Statistics Multiple R 0.593587018188936 R-squared 0.352345548162432 Adjusted R-squared 0.190431935203040 F-TEST (value) 2.17613294967854 F-TEST (DF numerator) 12 F-TEST (DF denominator) 48 p-value 0.0286157043556925 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 16366.520449259 Sum Squared Residuals 12857423597.5686 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 286602 291353.372549019 -4751.37254901937 2 283042 279858.098039216 3183.90196078429 3 276687 274298.098039216 2388.90196078429 4 277915 276623.498039216 1291.50196078430 5 277128 278605.498039216 -1477.49803921570 6 277103 277777.698039216 -674.698039215695 7 275037 274202.498039216 834.501960784299 8 270150 272716.498039216 -2566.4980392157 9 267140 266869.698039216 270.301960784298 10 264993 264864.698039216 128.301960784296 11 287259 286015.298039216 1243.70196078430 12 291186 288186.898039216 2999.1019607843 13 292300 285971.823529412 6328.17647058818 14 288186 274476.549019608 13709.4509803922 15 281477 268916.549019608 12560.4509803922 16 282656 271241.949019608 11414.0509803922 17 280190 273223.949019608 6966.05098039215 18 280408 272396.149019608 8011.85098039215 19 276836 268820.949019608 8015.05098039215 20 275216 267334.949019608 7881.05098039215 21 274352 261488.149019608 12863.8509803921 22 271311 259483.149019608 11827.8509803922 23 289802 280633.749019608 9168.25098039215 24 290726 282805.349019608 7920.65098039215 25 292300 280590.274509804 11709.7254901960 26 278506 269095 9411 27 269826 263535 6291 28 265861 265860.4 0.599999999996718 29 269034 267842.4 1191.60000000000 30 264176 267014.6 -2838.60000000000 31 255198 263439.4 -8241.4 32 253353 261953.4 -8600.4 33 246057 256106.6 -10049.6 34 235372 254101.6 -18729.6 35 258556 275252.2 -16696.2 36 260993 277423.8 -16430.8 37 254663 275208.725490196 -20545.7254901961 38 250643 263713.450980392 -13070.4509803921 39 243422 258153.450980392 -14731.4509803921 40 247105 260478.850980392 -13373.8509803921 41 248541 262460.850980392 -13919.8509803921 42 245039 261633.050980392 -16594.0509803921 43 237080 258057.850980392 -20977.8509803921 44 237085 256571.850980392 -19486.8509803922 45 225554 250725.050980392 -25171.0509803921 46 226839 248720.050980392 -21881.0509803922 47 247934 269870.650980392 -21936.6509803921 48 248333 272042.250980392 -23709.2509803921 49 246969 269827.176470588 -22858.1764705883 50 245098 258331.901960784 -13233.9019607843 51 246263 252771.901960784 -6508.9019607843 52 255765 255097.301960784 667.698039215697 53 264319 257079.301960784 7239.6980392157 54 268347 256251.501960784 12095.4980392157 55 273046 252676.301960784 20369.6980392157 56 273963 251190.301960784 22772.6980392157 57 267430 245343.501960784 22086.4980392157 58 271993 243338.501960784 28654.4980392157 59 292710 264489.101960784 28220.8980392157 60 295881 266660.701960784 29220.2980392157 61 294563 264445.627450980 30117.3725490196 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 16 6.01658023459024e-06 1.20331604691805e-05 0.999993983419765 17 3.49408884324547e-06 6.98817768649094e-06 0.999996505911157 18 2.54562690197232e-07 5.09125380394464e-07 0.99999974543731 19 8.07125049453863e-08 1.61425009890773e-07 0.999999919287495 20 4.78329676791352e-09 9.56659353582705e-09 0.999999995216703 21 1.78023099037116e-09 3.56046198074232e-09 0.99999999821977 22 2.06880556340787e-10 4.13761112681574e-10 0.99999999979312 23 3.24936681888441e-11 6.49873363776883e-11 0.999999999967506 24 6.6783307778119e-11 1.33566615556238e-10 0.999999999933217 25 3.27584220096189e-11 6.55168440192378e-11 0.999999999967242 26 3.51334674057214e-08 7.02669348114428e-08 0.999999964866533 27 6.29952550644207e-07 1.25990510128841e-06 0.99999937004745 28 9.99500574734472e-06 1.99900114946894e-05 0.999990004994253 29 1.50444291850858e-05 3.00888583701716e-05 0.999984955570815 30 4.58778401854214e-05 9.17556803708429e-05 0.999954122159815 31 0.000244896832103961 0.000489793664207922 0.999755103167896 32 0.000535222601429895 0.00107044520285979 0.99946477739857 33 0.002390383948812 0.004780767897624 0.997609616051188 34 0.00989150752885992 0.0197830150577198 0.99010849247114 35 0.0204122272921013 0.0408244545842027 0.979587772707899 36 0.0429390900327624 0.0858781800655248 0.957060909967238 37 0.0896612508838785 0.179322501767757 0.910338749116121 38 0.241067115444192 0.482134230888384 0.758932884555808 39 0.462106526575599 0.924213053151197 0.537893473424401 40 0.722385616709502 0.555228766580996 0.277614383290498 41 0.917175526155712 0.165648947688576 0.0828244738442881 42 0.99223440922818 0.0155311815436417 0.00776559077182083 43 0.993002350448917 0.0139952991021649 0.00699764955108246 44 0.997989605070092 0.00402078985981517 0.00201039492990758 45 0.998000602809076 0.00399879438184899 0.00199939719092449 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 20 0.666666666666667 NOK 5% type I error level 24 0.8 NOK 10% type I error level 25 0.833333333333333 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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