SeatbeltlawQ3GeoffreyDeMeester

*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, 25 Nov 2008 09:51:19 -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/25/t1227632536hjqrhpji41c0xut.htm/, Retrieved Tue, 25 Nov 2008 17:02:25 +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/25/t1227632536hjqrhpji41c0xut.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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1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.43 0 1.44 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.48 0 1.57 0 1.58 0 1.58 0 1.58 0 1.58 0 1.59 1 1.6 1 1.6 1 1.61 1 1.61 1 1.61 1 1.62 1 1.63 1 1.63 1 1.64 1 1.64 1 1.64 1 1.64 1 1.64 1 1.65 1 1.65 1 1.65 1 1.65 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 4 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Multiple Linear Regression - Estimated Regression Equation Y[t] = + 1.40222222222222 + 0.0783333333333335X[t] + 0.00250000000000066M1[t] + 0.0169444444444444M2[t] + 0.0163888888888888M3[t] + 0.0158333333333333M4[t] + 0.0136111111111111M5[t] + 0.0113888888888889M6[t] -0.000555555555555579M7[t] + 0.00555555555555554M8[t] + 0.00499999999999998M9[t] + 0.00444444444444443M10[t] + 0.00222222222222222M11[t] + 0.00222222222222222t + 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) 1.40222222222222 0.010685 131.2371 0 0 X 0.0783333333333335 0.009044 8.6611 0 0 M1 0.00250000000000066 0.012604 0.1983 0.843466 0.421733 M2 0.0169444444444444 0.012591 1.3457 0.183634 0.091817 M3 0.0163888888888888 0.012582 1.3026 0.197861 0.09893 M4 0.0158333333333333 0.012575 1.2591 0.213023 0.106512 M5 0.0136111111111111 0.012571 1.0828 0.283387 0.141693 M6 0.0113888888888889 0.012569 0.9061 0.368631 0.184316 M7 -0.000555555555555579 0.012564 -0.0442 0.964883 0.482441 M8 0.00555555555555554 0.012551 0.4426 0.659685 0.329843 M9 0.00499999999999998 0.012542 0.3987 0.691599 0.3458 M10 0.00444444444444443 0.012535 0.3546 0.724195 0.362098 M11 0.00222222222222222 0.01253 0.1773 0.859854 0.429927 t 0.00222222222222222 0.000188 11.8504 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.96746207394789 R-squared 0.935982864527553 Adjusted R-squared 0.921634196232005 F-TEST (value) 65.2313403061898 F-TEST (DF numerator) 13 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 0.0217009013355194 Sum Squared Residuals 0.0273138888888891 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1.43 1.40694444444444 0.0230555555555585 2 1.43 1.42361111111111 0.00638888888888877 3 1.43 1.42527777777778 0.00472222222222195 4 1.43 1.42694444444444 0.00305555555555539 5 1.43 1.42694444444444 0.00305555555555547 6 1.43 1.42694444444444 0.0030555555555554 7 1.43 1.41722222222222 0.0127777777777777 8 1.43 1.42555555555556 0.0044444444444443 9 1.43 1.42722222222222 0.00277777777777762 10 1.43 1.42888888888889 0.00111111111111095 11 1.43 1.42888888888889 0.00111111111111097 12 1.43 1.42888888888889 0.00111111111111097 13 1.43 1.43361111111111 -0.00361111111111185 14 1.43 1.45027777777778 -0.0202777777777779 15 1.43 1.45194444444444 -0.0219444444444445 16 1.43 1.45361111111111 -0.0236111111111112 17 1.43 1.45361111111111 -0.0236111111111112 18 1.43 1.45361111111111 -0.0236111111111112 19 1.44 1.44388888888889 -0.00388888888888897 20 1.48 1.45222222222222 0.0277777777777777 21 1.48 1.45388888888889 0.0261111111111111 22 1.48 1.45555555555556 0.0244444444444444 23 1.48 1.45555555555556 0.0244444444444444 24 1.48 1.45555555555556 0.0244444444444444 25 1.48 1.46027777777778 0.0197222222222216 26 1.48 1.47694444444444 0.00305555555555555 27 1.48 1.47861111111111 0.00138888888888892 28 1.48 1.48027777777778 -0.000277777777777775 29 1.48 1.48027777777778 -0.000277777777777789 30 1.48 1.48027777777778 -0.000277777777777771 31 1.48 1.47055555555556 0.00944444444444446 32 1.48 1.47888888888889 0.00111111111111112 33 1.48 1.48055555555556 -0.000555555555555545 34 1.48 1.48222222222222 -0.00222222222222221 35 1.48 1.48222222222222 -0.00222222222222222 36 1.48 1.48222222222222 -0.00222222222222221 37 1.48 1.48694444444445 -0.00694444444444504 38 1.48 1.50361111111111 -0.0236111111111111 39 1.48 1.50527777777778 -0.0252777777777777 40 1.48 1.50694444444444 -0.0269444444444444 41 1.48 1.50694444444444 -0.0269444444444444 42 1.48 1.50694444444444 -0.0269444444444444 43 1.48 1.49722222222222 -0.0172222222222221 44 1.48 1.50555555555556 -0.0255555555555555 45 1.48 1.50722222222222 -0.0272222222222221 46 1.48 1.50888888888889 -0.0288888888888888 47 1.48 1.50888888888889 -0.0288888888888888 48 1.48 1.50888888888889 -0.0288888888888888 49 1.48 1.51361111111111 -0.0336111111111116 50 1.57 1.53027777777778 0.0397222222222224 51 1.58 1.53194444444444 0.0480555555555558 52 1.58 1.53361111111111 0.0463888888888891 53 1.58 1.53361111111111 0.0463888888888891 54 1.58 1.53361111111111 0.0463888888888891 55 1.59 1.60222222222222 -0.0122222222222221 56 1.6 1.61055555555556 -0.0105555555555554 57 1.6 1.61222222222222 -0.0122222222222221 58 1.61 1.61388888888889 -0.00388888888888877 59 1.61 1.61388888888889 -0.00388888888888877 60 1.61 1.61388888888889 -0.00388888888888876 61 1.62 1.61861111111111 0.00138888888888843 62 1.63 1.63527777777778 -0.00527777777777783 63 1.63 1.63694444444444 -0.00694444444444445 64 1.64 1.63861111111111 0.00138888888888886 65 1.64 1.63861111111111 0.00138888888888886 66 1.64 1.63861111111111 0.00138888888888887 67 1.64 1.62888888888889 0.0111111111111111 68 1.64 1.63722222222222 0.00277777777777776 69 1.65 1.63888888888889 0.0111111111111111 70 1.65 1.64055555555556 0.00944444444444444 71 1.65 1.64055555555556 0.00944444444444445 72 1.65 1.64055555555556 0.00944444444444444 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 17 2.96840180793134e-41 5.93680361586267e-41 1 18 0 0 1 19 7.87177433430026e-05 0.000157435486686005 0.999921282256657 20 0.0696513324954493 0.139302664990899 0.93034866750455 21 0.146238875961257 0.292477751922515 0.853761124038743 22 0.193749666763150 0.387499333526301 0.80625033323685 23 0.224955371624205 0.449910743248410 0.775044628375795 24 0.25330333365774 0.50660666731548 0.74669666634226 25 0.251764044220457 0.503528088440914 0.748235955779543 26 0.198171190938615 0.396342381877230 0.801828809061385 27 0.148758245928046 0.297516491856092 0.851241754071954 28 0.106681073474927 0.213362146949854 0.893318926525073 29 0.0742950218427533 0.148590043685507 0.925704978157247 30 0.0506626625232637 0.101325325046527 0.949337337476736 31 0.0397203828739189 0.0794407657478379 0.960279617126081 32 0.0395261524263155 0.0790523048526311 0.960473847573684 33 0.039087356822638 0.078174713645276 0.960912643177362 34 0.0391535829011681 0.0783071658023362 0.960846417098832 35 0.0443635074989057 0.0887270149978114 0.955636492501094 36 0.0628391204694014 0.125678240938803 0.937160879530599 37 0.0909897419717145 0.181979483943429 0.909010258028286 38 0.0695280157274577 0.139056031454915 0.930471984272542 39 0.05269698659625 0.1053939731925 0.94730301340375 40 0.0416872352512527 0.0833744705025054 0.958312764748747 41 0.033513213193574 0.067026426387148 0.966486786806426 42 0.0283072983048688 0.0566145966097375 0.971692701695131 43 0.0197982603847813 0.0395965207695627 0.980201739615219 44 0.0205810870261201 0.0411621740522401 0.97941891297388 45 0.0234660017792958 0.0469320035585917 0.976533998220704 46 0.0348907731719573 0.0697815463439145 0.965109226828043 47 0.0695622865249886 0.139124573049977 0.930437713475011 48 0.248714527218984 0.497429054437968 0.751285472781016 49 0.999960351940855 7.92961182898487e-05 3.96480591449243e-05 50 0.999965543470122 6.89130597567617e-05 3.44565298783809e-05 51 0.99998696634174 2.60673165191107e-05 1.30336582595554e-05 52 0.999951599879666 9.68002406682206e-05 4.84001203341103e-05 53 0.999764051280707 0.00047189743858533 0.000235948719292665 54 0.998686915943167 0.00262616811366535 0.00131308405683268 55 0.995836263672196 0.00832747265560866 0.00416373632780433 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 10 0.256410256410256 NOK 5% type I error level 13 0.333333333333333 NOK 10% type I error level 22 0.564102564102564 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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