Seatbeltlawq3

*Unverified author*

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

Title produced by software: Multiple Regression

Date of computation: Sun, 23 Nov 2008 07:57:28 -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/23/t1227452328htis7zlfmlwekla.htm/, Retrieved Sun, 23 Nov 2008 14:58:58 +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/23/t1227452328htis7zlfmlwekla.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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Dataseries X:

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1846,5 1530,9 2796,3 2220,6 2895,6 2161,5 2472,2 1863,6 2584,4 1955,1 2630,4 1907,4 2663,1 1889,4 3176,2 2246,3 2856,7 2213 2551,4 1965 3088,7 2285,6 2628,3 1983,8 2226,2 1872,4 3023,6 2371,4 3077,9 2287 3084,1 2198,2 2990,3 2330,4 2949,6 2014,4 3014,7 2066,1 3517,7 2355,8 3121,2 2232,5 3067,4 2091,7 3174,6 2376,5 2676,3 1931,9 2424 2025,7 3195,1 2404,9 3146,6 2316,1 3506,7 2368,1 3528,5 2282,5 3365,1 2158,6 3153 2174,8 3843,3 2594,1 3123,2 2281,4 3361,1 2547,9 3481,9 2606,3 2970,5 2190,8 2537 2262,3 3257,6 2423,8 3301,3 2520,4 3391,6 2482,9 2933,6 2215,9 3283,2 2441,9 3139,7 2333,8 3486,4 2670,2 3202,2 2431 3294,4 2559,3 3550,3 2661,4 3279,3 2404,6 2678,6 2378,3 3451,4 2489,2 3977,1 2959 3814,8 2713,5 3310,5 2341,3 3971,8 2833,2 4051,9 2849,7 4057,6 2871,7 4391,4 3058,3 3628,9 2855,1 4092,2 3083,6 3822,5 2828,3

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 3 seconds R Server 'George Udny Yule' @ 72.249.76.132 Multiple Linear Regression - Estimated Regression Equation frankrijk[t] = -142.247331748287 + 1.41627277715675Nederland[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) -142.247331748287 189.244427 -0.7517 0.455295 0.227648 Nederland 1.41627277715675 0.079819 17.7435 0 0 Multiple Linear Regression - Regression Statistics Multiple R 0.918930870190701 R-squared 0.844433944189439 Adjusted R-squared 0.841751770813395 F-TEST (value) 314.831976087567 F-TEST (DF numerator) 1 F-TEST (DF denominator) 58 p-value 0 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 196.536872669440 Sum Squared Residuals 2240351.05448364 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 1846.5 2025.92466280097 -179.424662800974 2 2796.3 3002.72799720598 -206.427997205981 3 2895.6 2919.02627607602 -23.4262760760176 4 2472.2 2497.11861576102 -24.9186157610231 5 2584.4 2626.70757487087 -42.307574870865 6 2630.4 2559.15136340049 71.2486365995115 7 2663.1 2533.65845341167 129.441546588333 8 3176.2 3039.12620757891 137.07379242109 9 2856.7 2991.96432409959 -135.26432409959 10 2551.4 2640.72867536472 -89.328675364717 11 3088.7 3094.78572772117 -6.08572772116958 12 2628.3 2667.35460357526 -39.0546035752636 13 2226.2 2509.58181620000 -283.381816200003 14 3023.6 3216.30193200122 -192.701932001218 15 3077.9 3096.76850960919 -18.8685096091889 16 3084.1 2971.00348699767 113.096513002330 17 2990.3 3158.23474813779 -167.934748137792 18 2949.6 2710.69255055626 238.907449443740 19 3014.7 2783.91385313526 230.786146864736 20 3517.7 3194.20807667757 323.491923322426 21 3121.2 3019.58164325415 101.618356745853 22 3067.4 2820.17043623048 247.229563769524 23 3174.6 3223.52492316472 -48.9249231647178 24 2676.3 2593.85004644083 82.4499535591714 25 2424 2726.69643293813 -302.696432938132 26 3195.1 3263.74707003597 -68.6470700359695 27 3146.6 3137.98204742445 8.61795257554978 28 3506.7 3211.6282318366 295.071768163399 29 3528.5 3090.39528211198 438.104717888016 30 3365.1 2914.91908502226 450.180914977737 31 3153 2937.8627040122 215.137295987798 32 3843.3 3531.70587947403 311.594120525975 33 3123.2 3088.83738205711 34.3626179428885 34 3361.1 3466.27407716938 -105.174077169384 35 3481.9 3548.98440735534 -67.0844073553379 36 2970.5 2960.52306844671 9.97693155328967 37 2537 3061.78657201342 -524.786572013418 38 3257.6 3290.51462552423 -32.9146255242321 39 3301.3 3427.32657579757 -126.026575797573 40 3391.6 3374.21634665420 17.3836533458044 41 2933.6 2996.07151515334 -62.4715151533446 42 3283.2 3316.14916279077 -32.9491627907691 43 3139.7 3163.05007558012 -23.3500755801251 44 3486.4 3639.48423781565 -153.084237815653 45 3202.2 3300.71178951976 -98.5117895197605 46 3294.4 3482.41958682897 -188.019586828971 47 3550.3 3627.02103737667 -76.7210373766744 48 3279.3 3263.32218820282 15.9778117971781 49 2678.6 3226.0742141636 -547.4742141636 50 3451.4 3383.13886515028 68.2611348497175 51 3977.1 4048.50381585852 -71.4038158585219 52 3814.8 3700.80884906654 113.991150933459 53 3310.5 3173.6721214088 136.827878591199 54 3971.8 3870.3367004922 101.463299507797 55 4051.9 3893.70520131529 158.194798684711 56 4057.6 3924.86320241274 132.736797587262 57 4391.4 4189.13970263019 202.260297369813 58 3628.9 3901.35307431194 -272.453074311936 59 4092.2 4224.97140389225 -132.771403892252 60 3822.5 3863.39696388414 -40.8969638841355 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 5 0.146324834279607 0.292649668559214 0.853675165720393 6 0.146355650841050 0.292711301682099 0.85364434915895 7 0.170035207152696 0.340070414305391 0.829964792847304 8 0.145857468436277 0.291714936872553 0.854142531563723 9 0.117364369306329 0.234728738612658 0.882635630693671 10 0.0707727046121676 0.141545409224335 0.929227295387832 11 0.0378282614231861 0.0756565228463723 0.962171738576814 12 0.0192424163525751 0.0384848327051502 0.980757583647425 13 0.0416845037613645 0.083369007522729 0.958315496238636 14 0.0423070084590257 0.0846140169180515 0.957692991540974 15 0.0245487651103927 0.0490975302207854 0.975451234889607 16 0.0227030095242725 0.0454060190485450 0.977296990475727 17 0.0191535734778745 0.0383071469557490 0.980846426522126 18 0.0446225845468048 0.0892451690936097 0.955377415453195 19 0.0691179149188615 0.138235829837723 0.930882085081139 20 0.143949089417874 0.287898178835748 0.856050910582126 21 0.109861774612492 0.219723549224984 0.890138225387508 22 0.135917811254591 0.271835622509181 0.86408218874541 23 0.102226768832815 0.204453537665630 0.897773231167185 24 0.0766405982200504 0.153281196440101 0.92335940177995 25 0.129223764122373 0.258447528244746 0.870776235877627 26 0.099127317317226 0.198254634634452 0.900872682682774 27 0.0690258829997564 0.138051765999513 0.930974117000244 28 0.0984887523912492 0.196977504782498 0.901511247608751 29 0.269800704852002 0.539601409704003 0.730199295147999 30 0.591343223704659 0.817313552590682 0.408656776295341 31 0.64501397334305 0.709972053313899 0.354986026656949 32 0.738537022881328 0.522925954237345 0.261462977118672 33 0.700482936376322 0.599034127247355 0.299517063623678 34 0.677189119093553 0.645621761812895 0.322810880906447 35 0.631160062095561 0.737679875808877 0.368839937904439 36 0.590001101019487 0.819997797961026 0.409998898980513 37 0.89182916590465 0.2163416681907 0.10817083409535 38 0.852744031675636 0.294511936648727 0.147255968324364 39 0.818675372742511 0.362649254514977 0.181324627257489 40 0.766666190429562 0.466667619140876 0.233333809570438 41 0.70359966021912 0.59280067956176 0.29640033978088 42 0.631236423743068 0.737527152513863 0.368763576256932 43 0.559700461325475 0.88059907734905 0.440299538674525 44 0.511557242705201 0.976885514589598 0.488442757294799 45 0.428907201106457 0.857814402212913 0.571092798893543 46 0.388858959863897 0.777717919727793 0.611141040136103 47 0.308080975016284 0.616161950032569 0.691919024983716 48 0.239919952334012 0.479839904668025 0.760080047665988 49 0.853832627738549 0.292334744522903 0.146167372261451 50 0.780511417123605 0.438977165752789 0.219488582876395 51 0.701969259465014 0.596061481069972 0.298030740534986 52 0.597344203793003 0.805311592413994 0.402655796206997 53 0.478054092061 0.956108184122 0.521945907939 54 0.364501824792925 0.72900364958585 0.635498175207075 55 0.323476634624454 0.646953269248907 0.676523365375546 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 4 0.0784313725490196 NOK 10% type I error level 8 0.156862745098039 NOK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; 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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