R version 2.15.2 (2012-10-26) -- "Trick or Treat" Copyright (C) 2012 The R Foundation for Statistical Computing ISBN 3-900051-07-0 Platform: i686-pc-linux-gnu (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > x <- array(list(1966 + ,1 + ,41 + ,1966 + ,2 + ,39 + ,1966 + ,3 + ,50 + ,1966 + ,4 + ,40 + ,1966 + ,5 + ,43 + ,1966 + ,6 + ,38 + ,1966 + ,7 + ,44 + ,1966 + ,8 + ,35 + ,1966 + ,9 + ,39 + ,1966 + ,10 + ,35 + ,1966 + ,11 + ,29 + ,1966 + ,12 + ,49 + ,1967 + ,1 + ,50 + ,1967 + ,2 + ,59 + ,1967 + ,3 + ,63 + ,1967 + ,4 + ,32 + ,1967 + ,5 + ,39 + ,1967 + ,6 + ,47 + ,1967 + ,7 + ,53 + ,1967 + ,8 + ,60 + ,1967 + ,9 + ,57 + ,1967 + ,10 + ,52 + ,1967 + ,11 + ,70 + ,1967 + ,12 + ,90 + ,1968 + ,1 + ,74 + ,1968 + ,2 + ,62 + ,1968 + ,3 + ,55 + ,1968 + ,4 + ,84 + ,1968 + ,5 + ,94 + ,1968 + ,6 + ,70 + ,1968 + ,7 + ,108 + ,1968 + ,8 + ,139 + ,1968 + ,9 + ,120 + ,1968 + ,10 + ,97 + ,1968 + ,11 + ,126 + ,1968 + ,12 + ,149 + ,1969 + ,1 + ,158 + ,1969 + ,2 + ,124 + ,1969 + ,3 + ,140 + ,1969 + ,4 + ,109 + ,1969 + ,5 + ,114 + ,1969 + ,6 + ,77 + ,1969 + ,7 + ,120 + ,1969 + ,8 + ,133 + ,1969 + ,9 + ,110 + ,1969 + ,10 + ,92 + ,1969 + ,11 + ,97 + ,1969 + ,12 + ,78 + ,1970 + ,1 + ,99 + ,1970 + ,2 + ,107 + ,1970 + ,3 + ,112 + ,1970 + ,4 + ,90 + ,1970 + ,5 + ,98 + ,1970 + ,6 + ,125 + ,1970 + ,7 + ,155 + ,1970 + ,8 + ,190 + ,1970 + ,9 + ,236 + ,1970 + ,10 + ,189 + ,1970 + ,11 + ,174 + ,1970 + ,12 + ,178 + ,1971 + ,1 + ,136 + ,1971 + ,2 + ,161 + ,1971 + ,3 + ,171 + ,1971 + ,4 + ,149 + ,1971 + ,5 + ,184 + ,1971 + ,6 + ,155 + ,1971 + ,7 + ,276 + ,1971 + ,8 + ,224 + ,1971 + ,9 + ,213 + ,1971 + ,10 + ,279 + ,1971 + ,11 + ,268 + ,1971 + ,12 + ,287 + ,1972 + ,1 + ,238 + ,1972 + ,2 + ,213 + ,1972 + ,3 + ,257 + ,1972 + ,4 + ,293 + ,1972 + ,5 + ,212 + ,1972 + ,6 + ,246 + ,1972 + ,7 + ,353 + ,1972 + ,8 + ,339 + ,1972 + ,9 + ,308 + ,1972 + ,10 + ,247 + ,1972 + ,11 + ,257 + ,1972 + ,12 + ,322 + ,1973 + ,1 + ,298 + ,1973 + ,2 + ,273 + ,1973 + ,3 + ,312 + ,1973 + ,4 + ,249 + ,1973 + ,5 + ,286 + ,1973 + ,6 + ,279 + ,1973 + ,7 + ,309 + ,1973 + ,8 + ,401 + ,1973 + ,9 + ,309 + ,1973 + ,10 + ,328 + ,1973 + ,11 + ,353 + ,1973 + ,12 + ,354 + ,1974 + ,1 + ,327 + ,1974 + ,2 + ,324 + ,1974 + ,3 + ,285 + ,1974 + ,4 + ,243 + ,1974 + ,5 + ,241 + ,1974 + ,6 + ,287 + ,1974 + ,7 + ,355 + ,1974 + ,8 + ,460 + ,1974 + ,9 + ,364 + ,1974 + ,10 + ,487 + ,1974 + ,11 + ,452 + ,1974 + ,12 + ,391 + ,1975 + ,1 + ,500 + ,1975 + ,2 + ,451 + ,1975 + ,3 + ,375 + ,1975 + ,4 + ,372 + ,1975 + ,5 + ,302 + ,1975 + ,6 + ,316 + ,1975 + ,7 + ,398 + ,1975 + ,8 + ,394 + ,1975 + ,9 + ,431 + ,1975 + ,10 + ,431) + ,dim=c(3 + ,118) + ,dimnames=list(c('year' + ,'month' + ,'robberies') + ,1:118)) > y <- array(NA,dim=c(3,118),dimnames=list(c('year','month','robberies'),1:118)) > for (i in 1:dim(x)[1]) + { + for (j in 1:dim(x)[2]) + { + y[i,j] <- as.numeric(x[i,j]) + } + } > par3 = 'No Linear Trend' > par2 = 'Do not include Seasonal Dummies' > par1 = '1' > par3 <- 'No Linear Trend' > par2 <- 'Do not include Seasonal Dummies' > par1 <- '1' > #'GNU S' R Code compiled by R2WASP v. 1.0.44 () > #Author: Prof. Dr. P. Wessa > #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/ > #Source of accompanying publication: Office for Research, Development, and Education > #Technical description: Write here your technical program description (don't use hard returns!) > library(lattice) > library(lmtest) Loading required package: zoo Attaching package: 'zoo' The following object(s) are masked from 'package:base': as.Date, as.Date.numeric > 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 year month robberies 1 1966 1 41 2 1966 2 39 3 1966 3 50 4 1966 4 40 5 1966 5 43 6 1966 6 38 7 1966 7 44 8 1966 8 35 9 1966 9 39 10 1966 10 35 11 1966 11 29 12 1966 12 49 13 1967 1 50 14 1967 2 59 15 1967 3 63 16 1967 4 32 17 1967 5 39 18 1967 6 47 19 1967 7 53 20 1967 8 60 21 1967 9 57 22 1967 10 52 23 1967 11 70 24 1967 12 90 25 1968 1 74 26 1968 2 62 27 1968 3 55 28 1968 4 84 29 1968 5 94 30 1968 6 70 31 1968 7 108 32 1968 8 139 33 1968 9 120 34 1968 10 97 35 1968 11 126 36 1968 12 149 37 1969 1 158 38 1969 2 124 39 1969 3 140 40 1969 4 109 41 1969 5 114 42 1969 6 77 43 1969 7 120 44 1969 8 133 45 1969 9 110 46 1969 10 92 47 1969 11 97 48 1969 12 78 49 1970 1 99 50 1970 2 107 51 1970 3 112 52 1970 4 90 53 1970 5 98 54 1970 6 125 55 1970 7 155 56 1970 8 190 57 1970 9 236 58 1970 10 189 59 1970 11 174 60 1970 12 178 61 1971 1 136 62 1971 2 161 63 1971 3 171 64 1971 4 149 65 1971 5 184 66 1971 6 155 67 1971 7 276 68 1971 8 224 69 1971 9 213 70 1971 10 279 71 1971 11 268 72 1971 12 287 73 1972 1 238 74 1972 2 213 75 1972 3 257 76 1972 4 293 77 1972 5 212 78 1972 6 246 79 1972 7 353 80 1972 8 339 81 1972 9 308 82 1972 10 247 83 1972 11 257 84 1972 12 322 85 1973 1 298 86 1973 2 273 87 1973 3 312 88 1973 4 249 89 1973 5 286 90 1973 6 279 91 1973 7 309 92 1973 8 401 93 1973 9 309 94 1973 10 328 95 1973 11 353 96 1973 12 354 97 1974 1 327 98 1974 2 324 99 1974 3 285 100 1974 4 243 101 1974 5 241 102 1974 6 287 103 1974 7 355 104 1974 8 460 105 1974 9 364 106 1974 10 487 107 1974 11 452 108 1974 12 391 109 1975 1 500 110 1975 2 451 111 1975 3 375 112 1975 4 372 113 1975 5 302 114 1975 6 316 115 1975 7 398 116 1975 8 394 117 1975 9 431 118 1975 10 431 > k <- length(x[1,]) > df <- as.data.frame(x) > (mylm <- lm(df)) Call: lm(formula = df) Coefficients: (Intercept) month robberies 1967.10365 -0.12590 0.02103 > (mysum <- summary(mylm)) Call: lm(formula = df) Residuals: Min 1Q Median 3Q Max -2.49232 -0.61260 0.03958 0.64792 2.45784 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.967e+03 2.266e-01 8682.475 < 2e-16 *** month -1.259e-01 2.663e-02 -4.728 6.48e-06 *** robberies 2.103e-02 7.139e-04 29.457 < 2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 0.9818 on 115 degrees of freedom Multiple R-squared: 0.8832, Adjusted R-squared: 0.8811 F-statistic: 434.7 on 2 and 115 DF, p-value: < 2.2e-16 > 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 + } [,1] [,2] [,3] [1,] 3.647200e-39 7.294401e-39 1.000000e+00 [2,] 3.589064e-56 7.178128e-56 1.000000e+00 [3,] 3.528266e-63 7.056531e-63 1.000000e+00 [4,] 8.907975e-78 1.781595e-77 1.000000e+00 [5,] 6.985235e-91 1.397047e-90 1.000000e+00 [6,] 2.715776e-108 5.431553e-108 1.000000e+00 [7,] 2.921237e-112 5.842473e-112 1.000000e+00 [8,] 8.326836e-05 1.665367e-04 9.999167e-01 [9,] 8.824840e-05 1.764968e-04 9.999118e-01 [10,] 3.709382e-05 7.418765e-05 9.999629e-01 [11,] 7.602752e-04 1.520550e-03 9.992397e-01 [12,] 1.467584e-03 2.935168e-03 9.985324e-01 [13,] 1.661496e-03 3.322992e-03 9.983385e-01 [14,] 1.353010e-03 2.706019e-03 9.986470e-01 [15,] 7.927303e-04 1.585461e-03 9.992073e-01 [16,] 4.657325e-04 9.314650e-04 9.995343e-01 [17,] 3.075150e-04 6.150301e-04 9.996925e-01 [18,] 1.524284e-04 3.048568e-04 9.998476e-01 [19,] 1.296807e-04 2.593614e-04 9.998703e-01 [20,] 1.743663e-04 3.487326e-04 9.998256e-01 [21,] 3.646490e-04 7.292979e-04 9.996354e-01 [22,] 9.775865e-04 1.955173e-03 9.990224e-01 [23,] 6.220992e-04 1.244198e-03 9.993779e-01 [24,] 4.020232e-04 8.040465e-04 9.995980e-01 [25,] 4.294451e-04 8.588902e-04 9.995706e-01 [26,] 3.680908e-04 7.361816e-04 9.996319e-01 [27,] 9.747422e-04 1.949484e-03 9.990253e-01 [28,] 7.129577e-04 1.425915e-03 9.992870e-01 [29,] 5.339317e-04 1.067863e-03 9.994661e-01 [30,] 3.883662e-04 7.767323e-04 9.996116e-01 [31,] 4.856021e-04 9.712041e-04 9.995144e-01 [32,] 7.130421e-04 1.426084e-03 9.992870e-01 [33,] 7.779854e-04 1.555971e-03 9.992220e-01 [34,] 7.976487e-04 1.595297e-03 9.992024e-01 [35,] 1.292395e-03 2.584790e-03 9.987076e-01 [36,] 1.721244e-03 3.442489e-03 9.982788e-01 [37,] 1.030801e-02 2.061602e-02 9.896920e-01 [38,] 1.067052e-02 2.134104e-02 9.893295e-01 [39,] 9.438025e-03 1.887605e-02 9.905620e-01 [40,] 1.221637e-02 2.443274e-02 9.877836e-01 [41,] 2.585400e-02 5.170799e-02 9.741460e-01 [42,] 3.898149e-02 7.796297e-02 9.610185e-01 [43,] 8.596721e-02 1.719344e-01 9.140328e-01 [44,] 1.574986e-01 3.149972e-01 8.425014e-01 [45,] 2.067810e-01 4.135621e-01 7.932190e-01 [46,] 2.378105e-01 4.756209e-01 7.621895e-01 [47,] 3.431802e-01 6.863605e-01 6.568198e-01 [48,] 4.132699e-01 8.265398e-01 5.867301e-01 [49,] 3.986425e-01 7.972849e-01 6.013575e-01 [50,] 3.571967e-01 7.143933e-01 6.428033e-01 [51,] 3.604531e-01 7.209062e-01 6.395469e-01 [52,] 5.036595e-01 9.926810e-01 4.963405e-01 [53,] 4.718461e-01 9.436921e-01 5.281539e-01 [54,] 4.278786e-01 8.557571e-01 5.721214e-01 [55,] 3.829670e-01 7.659340e-01 6.170330e-01 [56,] 4.045521e-01 8.091042e-01 5.954479e-01 [57,] 3.839914e-01 7.679829e-01 6.160086e-01 [58,] 3.565725e-01 7.131450e-01 6.434275e-01 [59,] 3.516218e-01 7.032436e-01 6.483782e-01 [60,] 3.172147e-01 6.344294e-01 6.827853e-01 [61,] 3.077104e-01 6.154208e-01 6.922896e-01 [62,] 4.697085e-01 9.394171e-01 5.302915e-01 [63,] 4.457584e-01 8.915168e-01 5.542416e-01 [64,] 4.063941e-01 8.127882e-01 5.936059e-01 [65,] 4.844551e-01 9.689102e-01 5.155449e-01 [66,] 5.095501e-01 9.808998e-01 4.904499e-01 [67,] 5.731215e-01 8.537570e-01 4.268785e-01 [68,] 5.684957e-01 8.630085e-01 4.315043e-01 [69,] 5.495619e-01 9.008762e-01 4.504381e-01 [70,] 5.645754e-01 8.708493e-01 4.354246e-01 [71,] 6.461180e-01 7.077640e-01 3.538820e-01 [72,] 6.376843e-01 7.246315e-01 3.623157e-01 [73,] 6.266282e-01 7.467437e-01 3.733718e-01 [74,] 8.055839e-01 3.888322e-01 1.944161e-01 [75,] 8.846488e-01 2.307024e-01 1.153512e-01 [76,] 9.051699e-01 1.896602e-01 9.483010e-02 [77,] 9.003980e-01 1.992039e-01 9.960195e-02 [78,] 8.958831e-01 2.082339e-01 1.041169e-01 [79,] 9.215045e-01 1.569909e-01 7.849547e-02 [80,] 9.312180e-01 1.375640e-01 6.878200e-02 [81,] 9.344248e-01 1.311504e-01 6.557519e-02 [82,] 9.500611e-01 9.987780e-02 4.993890e-02 [83,] 9.526029e-01 9.479415e-02 4.739708e-02 [84,] 9.564577e-01 8.708467e-02 4.354233e-02 [85,] 9.583840e-01 8.323206e-02 4.161603e-02 [86,] 9.624223e-01 7.515549e-02 3.757775e-02 [87,] 9.852069e-01 2.958618e-02 1.479309e-02 [88,] 9.858599e-01 2.828012e-02 1.414006e-02 [89,] 9.875882e-01 2.482357e-02 1.241178e-02 [90,] 9.914976e-01 1.700478e-02 8.502390e-03 [91,] 9.959846e-01 8.030892e-03 4.015446e-03 [92,] 9.956441e-01 8.711860e-03 4.355930e-03 [93,] 9.956620e-01 8.675922e-03 4.337961e-03 [94,] 9.956570e-01 8.685918e-03 4.342959e-03 [95,] 9.962881e-01 7.423842e-03 3.711921e-03 [96,] 9.973217e-01 5.356635e-03 2.678317e-03 [97,] 9.984000e-01 3.200035e-03 1.600018e-03 [98,] 9.990341e-01 1.931714e-03 9.658570e-04 [99,] 9.991008e-01 1.798463e-03 8.992314e-04 [100,] 9.994162e-01 1.167505e-03 5.837525e-04 [101,] 9.993018e-01 1.396482e-03 6.982410e-04 [102,] 9.995028e-01 9.944446e-04 4.972223e-04 [103,] 1.000000e+00 1.148043e-95 5.740217e-96 [104,] 1.000000e+00 1.776377e-78 8.881887e-79 [105,] 1.000000e+00 3.240242e-64 1.620121e-64 [106,] 1.000000e+00 1.386228e-59 6.931142e-60 [107,] 1.000000e+00 4.682369e-38 2.341185e-38 > postscript(file="/var/wessaorg/rcomp/tmp/1it5l1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') > points(x[,1]-mysum$resid) > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/2wbbo1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/35wb01354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/4twz11354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/5r6591354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') > qqline(mysum$resid) > grid() > dev.off() null device 1 > (myerror <- as.ts(mysum$resid)) Time Series: Start = 1 End = 118 Frequency = 1 1 2 3 4 5 6 -1.83994534 -1.67198492 -1.77740329 -1.44120976 -1.37839502 -1.14734719 7 8 9 10 11 12 -1.14761987 -0.83245548 -0.79066988 -0.58065118 -0.32857420 -0.62325481 13 14 15 16 17 18 -1.02920758 -1.09256768 -1.05078208 -0.27297666 -0.29427847 -0.33660943 19 20 21 22 23 24 -0.33688211 -0.35818392 -0.16919436 0.06185348 -0.19076886 -0.48544947 25 26 27 28 29 30 -0.53390689 -0.15565509 0.11745102 -0.36649183 -0.45088106 0.17972040 31 32 33 34 35 36 -0.49348469 -1.01948582 -0.49403005 0.11554227 -0.36840058 -0.72616860 37 38 39 40 41 42 -1.30035447 -0.45946164 -0.67002569 0.10777973 0.12853619 1.03251644 43 44 45 46 47 48 0.25416566 0.10668901 0.71626133 1.22068796 1.24144442 1.76690019 49 50 51 52 53 54 0.94036466 0.89803371 0.91879017 1.50733335 1.46500239 1.02311782 55 56 57 58 59 60 0.51814583 -0.09197185 -0.93341004 0.18086159 0.62220080 0.66398640 61 62 63 64 65 66 1.16228656 0.76246026 0.67807103 1.26661421 0.65649654 1.39224368 67 68 69 70 71 72 -1.02637985 0.19303747 0.55026013 -0.71176082 -0.35453816 -0.62818963 73 74 75 76 77 78 0.01731450 0.66894509 -0.13043483 -0.76158164 1.06768067 0.47859214 79 80 81 82 83 84 -1.64562347 -1.22531339 -0.44750797 0.96117159 0.87678236 -0.36420945 85 86 87 88 89 90 -0.24443378 0.40719682 -0.28703741 1.16370042 0.51152447 0.78463059 91 92 93 94 95 96 0.27965860 -1.52911994 0.53146289 0.25781142 -0.14201488 -0.03714187 97 98 99 100 101 102 0.14572123 0.33471079 1.28074931 2.28987525 2.45783568 1.61639748 103 104 105 106 107 108 0.31231826 -1.76983907 0.37486031 -2.08582150 -1.22389953 0.18478003 109 110 111 112 113 114 -2.49231963 -1.33598972 0.38812690 0.57711647 2.17505827 2.00655248 115 116 117 118 0.40806533 0.61808403 -0.03409193 0.09181022 > postscript(file="/var/wessaorg/rcomp/tmp/618kk1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > dum <- cbind(lag(myerror,k=1),myerror) > dum Time Series: Start = 0 End = 118 Frequency = 1 lag(myerror, k = 1) myerror 0 -1.83994534 NA 1 -1.67198492 -1.83994534 2 -1.77740329 -1.67198492 3 -1.44120976 -1.77740329 4 -1.37839502 -1.44120976 5 -1.14734719 -1.37839502 6 -1.14761987 -1.14734719 7 -0.83245548 -1.14761987 8 -0.79066988 -0.83245548 9 -0.58065118 -0.79066988 10 -0.32857420 -0.58065118 11 -0.62325481 -0.32857420 12 -1.02920758 -0.62325481 13 -1.09256768 -1.02920758 14 -1.05078208 -1.09256768 15 -0.27297666 -1.05078208 16 -0.29427847 -0.27297666 17 -0.33660943 -0.29427847 18 -0.33688211 -0.33660943 19 -0.35818392 -0.33688211 20 -0.16919436 -0.35818392 21 0.06185348 -0.16919436 22 -0.19076886 0.06185348 23 -0.48544947 -0.19076886 24 -0.53390689 -0.48544947 25 -0.15565509 -0.53390689 26 0.11745102 -0.15565509 27 -0.36649183 0.11745102 28 -0.45088106 -0.36649183 29 0.17972040 -0.45088106 30 -0.49348469 0.17972040 31 -1.01948582 -0.49348469 32 -0.49403005 -1.01948582 33 0.11554227 -0.49403005 34 -0.36840058 0.11554227 35 -0.72616860 -0.36840058 36 -1.30035447 -0.72616860 37 -0.45946164 -1.30035447 38 -0.67002569 -0.45946164 39 0.10777973 -0.67002569 40 0.12853619 0.10777973 41 1.03251644 0.12853619 42 0.25416566 1.03251644 43 0.10668901 0.25416566 44 0.71626133 0.10668901 45 1.22068796 0.71626133 46 1.24144442 1.22068796 47 1.76690019 1.24144442 48 0.94036466 1.76690019 49 0.89803371 0.94036466 50 0.91879017 0.89803371 51 1.50733335 0.91879017 52 1.46500239 1.50733335 53 1.02311782 1.46500239 54 0.51814583 1.02311782 55 -0.09197185 0.51814583 56 -0.93341004 -0.09197185 57 0.18086159 -0.93341004 58 0.62220080 0.18086159 59 0.66398640 0.62220080 60 1.16228656 0.66398640 61 0.76246026 1.16228656 62 0.67807103 0.76246026 63 1.26661421 0.67807103 64 0.65649654 1.26661421 65 1.39224368 0.65649654 66 -1.02637985 1.39224368 67 0.19303747 -1.02637985 68 0.55026013 0.19303747 69 -0.71176082 0.55026013 70 -0.35453816 -0.71176082 71 -0.62818963 -0.35453816 72 0.01731450 -0.62818963 73 0.66894509 0.01731450 74 -0.13043483 0.66894509 75 -0.76158164 -0.13043483 76 1.06768067 -0.76158164 77 0.47859214 1.06768067 78 -1.64562347 0.47859214 79 -1.22531339 -1.64562347 80 -0.44750797 -1.22531339 81 0.96117159 -0.44750797 82 0.87678236 0.96117159 83 -0.36420945 0.87678236 84 -0.24443378 -0.36420945 85 0.40719682 -0.24443378 86 -0.28703741 0.40719682 87 1.16370042 -0.28703741 88 0.51152447 1.16370042 89 0.78463059 0.51152447 90 0.27965860 0.78463059 91 -1.52911994 0.27965860 92 0.53146289 -1.52911994 93 0.25781142 0.53146289 94 -0.14201488 0.25781142 95 -0.03714187 -0.14201488 96 0.14572123 -0.03714187 97 0.33471079 0.14572123 98 1.28074931 0.33471079 99 2.28987525 1.28074931 100 2.45783568 2.28987525 101 1.61639748 2.45783568 102 0.31231826 1.61639748 103 -1.76983907 0.31231826 104 0.37486031 -1.76983907 105 -2.08582150 0.37486031 106 -1.22389953 -2.08582150 107 0.18478003 -1.22389953 108 -2.49231963 0.18478003 109 -1.33598972 -2.49231963 110 0.38812690 -1.33598972 111 0.57711647 0.38812690 112 2.17505827 0.57711647 113 2.00655248 2.17505827 114 0.40806533 2.00655248 115 0.61808403 0.40806533 116 -0.03409193 0.61808403 117 0.09181022 -0.03409193 118 NA 0.09181022 > dum1 <- dum[2:length(myerror),] > dum1 lag(myerror, k = 1) myerror [1,] -1.67198492 -1.83994534 [2,] -1.77740329 -1.67198492 [3,] -1.44120976 -1.77740329 [4,] -1.37839502 -1.44120976 [5,] -1.14734719 -1.37839502 [6,] -1.14761987 -1.14734719 [7,] -0.83245548 -1.14761987 [8,] -0.79066988 -0.83245548 [9,] -0.58065118 -0.79066988 [10,] -0.32857420 -0.58065118 [11,] -0.62325481 -0.32857420 [12,] -1.02920758 -0.62325481 [13,] -1.09256768 -1.02920758 [14,] -1.05078208 -1.09256768 [15,] -0.27297666 -1.05078208 [16,] -0.29427847 -0.27297666 [17,] -0.33660943 -0.29427847 [18,] -0.33688211 -0.33660943 [19,] -0.35818392 -0.33688211 [20,] -0.16919436 -0.35818392 [21,] 0.06185348 -0.16919436 [22,] -0.19076886 0.06185348 [23,] -0.48544947 -0.19076886 [24,] -0.53390689 -0.48544947 [25,] -0.15565509 -0.53390689 [26,] 0.11745102 -0.15565509 [27,] -0.36649183 0.11745102 [28,] -0.45088106 -0.36649183 [29,] 0.17972040 -0.45088106 [30,] -0.49348469 0.17972040 [31,] -1.01948582 -0.49348469 [32,] -0.49403005 -1.01948582 [33,] 0.11554227 -0.49403005 [34,] -0.36840058 0.11554227 [35,] -0.72616860 -0.36840058 [36,] -1.30035447 -0.72616860 [37,] -0.45946164 -1.30035447 [38,] -0.67002569 -0.45946164 [39,] 0.10777973 -0.67002569 [40,] 0.12853619 0.10777973 [41,] 1.03251644 0.12853619 [42,] 0.25416566 1.03251644 [43,] 0.10668901 0.25416566 [44,] 0.71626133 0.10668901 [45,] 1.22068796 0.71626133 [46,] 1.24144442 1.22068796 [47,] 1.76690019 1.24144442 [48,] 0.94036466 1.76690019 [49,] 0.89803371 0.94036466 [50,] 0.91879017 0.89803371 [51,] 1.50733335 0.91879017 [52,] 1.46500239 1.50733335 [53,] 1.02311782 1.46500239 [54,] 0.51814583 1.02311782 [55,] -0.09197185 0.51814583 [56,] -0.93341004 -0.09197185 [57,] 0.18086159 -0.93341004 [58,] 0.62220080 0.18086159 [59,] 0.66398640 0.62220080 [60,] 1.16228656 0.66398640 [61,] 0.76246026 1.16228656 [62,] 0.67807103 0.76246026 [63,] 1.26661421 0.67807103 [64,] 0.65649654 1.26661421 [65,] 1.39224368 0.65649654 [66,] -1.02637985 1.39224368 [67,] 0.19303747 -1.02637985 [68,] 0.55026013 0.19303747 [69,] -0.71176082 0.55026013 [70,] -0.35453816 -0.71176082 [71,] -0.62818963 -0.35453816 [72,] 0.01731450 -0.62818963 [73,] 0.66894509 0.01731450 [74,] -0.13043483 0.66894509 [75,] -0.76158164 -0.13043483 [76,] 1.06768067 -0.76158164 [77,] 0.47859214 1.06768067 [78,] -1.64562347 0.47859214 [79,] -1.22531339 -1.64562347 [80,] -0.44750797 -1.22531339 [81,] 0.96117159 -0.44750797 [82,] 0.87678236 0.96117159 [83,] -0.36420945 0.87678236 [84,] -0.24443378 -0.36420945 [85,] 0.40719682 -0.24443378 [86,] -0.28703741 0.40719682 [87,] 1.16370042 -0.28703741 [88,] 0.51152447 1.16370042 [89,] 0.78463059 0.51152447 [90,] 0.27965860 0.78463059 [91,] -1.52911994 0.27965860 [92,] 0.53146289 -1.52911994 [93,] 0.25781142 0.53146289 [94,] -0.14201488 0.25781142 [95,] -0.03714187 -0.14201488 [96,] 0.14572123 -0.03714187 [97,] 0.33471079 0.14572123 [98,] 1.28074931 0.33471079 [99,] 2.28987525 1.28074931 [100,] 2.45783568 2.28987525 [101,] 1.61639748 2.45783568 [102,] 0.31231826 1.61639748 [103,] -1.76983907 0.31231826 [104,] 0.37486031 -1.76983907 [105,] -2.08582150 0.37486031 [106,] -1.22389953 -2.08582150 [107,] 0.18478003 -1.22389953 [108,] -2.49231963 0.18478003 [109,] -1.33598972 -2.49231963 [110,] 0.38812690 -1.33598972 [111,] 0.57711647 0.38812690 [112,] 2.17505827 0.57711647 [113,] 2.00655248 2.17505827 [114,] 0.40806533 2.00655248 [115,] 0.61808403 0.40806533 [116,] -0.03409193 0.61808403 [117,] 0.09181022 -0.03409193 > z <- as.data.frame(dum1) > z lag(myerror, k = 1) myerror 1 -1.67198492 -1.83994534 2 -1.77740329 -1.67198492 3 -1.44120976 -1.77740329 4 -1.37839502 -1.44120976 5 -1.14734719 -1.37839502 6 -1.14761987 -1.14734719 7 -0.83245548 -1.14761987 8 -0.79066988 -0.83245548 9 -0.58065118 -0.79066988 10 -0.32857420 -0.58065118 11 -0.62325481 -0.32857420 12 -1.02920758 -0.62325481 13 -1.09256768 -1.02920758 14 -1.05078208 -1.09256768 15 -0.27297666 -1.05078208 16 -0.29427847 -0.27297666 17 -0.33660943 -0.29427847 18 -0.33688211 -0.33660943 19 -0.35818392 -0.33688211 20 -0.16919436 -0.35818392 21 0.06185348 -0.16919436 22 -0.19076886 0.06185348 23 -0.48544947 -0.19076886 24 -0.53390689 -0.48544947 25 -0.15565509 -0.53390689 26 0.11745102 -0.15565509 27 -0.36649183 0.11745102 28 -0.45088106 -0.36649183 29 0.17972040 -0.45088106 30 -0.49348469 0.17972040 31 -1.01948582 -0.49348469 32 -0.49403005 -1.01948582 33 0.11554227 -0.49403005 34 -0.36840058 0.11554227 35 -0.72616860 -0.36840058 36 -1.30035447 -0.72616860 37 -0.45946164 -1.30035447 38 -0.67002569 -0.45946164 39 0.10777973 -0.67002569 40 0.12853619 0.10777973 41 1.03251644 0.12853619 42 0.25416566 1.03251644 43 0.10668901 0.25416566 44 0.71626133 0.10668901 45 1.22068796 0.71626133 46 1.24144442 1.22068796 47 1.76690019 1.24144442 48 0.94036466 1.76690019 49 0.89803371 0.94036466 50 0.91879017 0.89803371 51 1.50733335 0.91879017 52 1.46500239 1.50733335 53 1.02311782 1.46500239 54 0.51814583 1.02311782 55 -0.09197185 0.51814583 56 -0.93341004 -0.09197185 57 0.18086159 -0.93341004 58 0.62220080 0.18086159 59 0.66398640 0.62220080 60 1.16228656 0.66398640 61 0.76246026 1.16228656 62 0.67807103 0.76246026 63 1.26661421 0.67807103 64 0.65649654 1.26661421 65 1.39224368 0.65649654 66 -1.02637985 1.39224368 67 0.19303747 -1.02637985 68 0.55026013 0.19303747 69 -0.71176082 0.55026013 70 -0.35453816 -0.71176082 71 -0.62818963 -0.35453816 72 0.01731450 -0.62818963 73 0.66894509 0.01731450 74 -0.13043483 0.66894509 75 -0.76158164 -0.13043483 76 1.06768067 -0.76158164 77 0.47859214 1.06768067 78 -1.64562347 0.47859214 79 -1.22531339 -1.64562347 80 -0.44750797 -1.22531339 81 0.96117159 -0.44750797 82 0.87678236 0.96117159 83 -0.36420945 0.87678236 84 -0.24443378 -0.36420945 85 0.40719682 -0.24443378 86 -0.28703741 0.40719682 87 1.16370042 -0.28703741 88 0.51152447 1.16370042 89 0.78463059 0.51152447 90 0.27965860 0.78463059 91 -1.52911994 0.27965860 92 0.53146289 -1.52911994 93 0.25781142 0.53146289 94 -0.14201488 0.25781142 95 -0.03714187 -0.14201488 96 0.14572123 -0.03714187 97 0.33471079 0.14572123 98 1.28074931 0.33471079 99 2.28987525 1.28074931 100 2.45783568 2.28987525 101 1.61639748 2.45783568 102 0.31231826 1.61639748 103 -1.76983907 0.31231826 104 0.37486031 -1.76983907 105 -2.08582150 0.37486031 106 -1.22389953 -2.08582150 107 0.18478003 -1.22389953 108 -2.49231963 0.18478003 109 -1.33598972 -2.49231963 110 0.38812690 -1.33598972 111 0.57711647 0.38812690 112 2.17505827 0.57711647 113 2.00655248 2.17505827 114 0.40806533 2.00655248 115 0.61808403 0.40806533 116 -0.03409193 0.61808403 117 0.09181022 -0.03409193 > 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() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/7fi0h1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/8s07c1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') > grid() > dev.off() null device 1 > postscript(file="/var/wessaorg/rcomp/tmp/9begw1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) > opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) > plot(mylm, las = 1, sub='Residual Diagnostics') > par(opar) > dev.off() null device 1 > if (n > n25) { + postscript(file="/var/wessaorg/rcomp/tmp/10hmia1354888648.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) + plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') + grid() + dev.off() + } null device 1 > > #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab > load(file="/var/wessaorg/rcomp/createtable") > > a<-table.start() > a<-table.row.start(a) > a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) > a<-table.row.end(a) > myeq <- colnames(x)[1] > myeq <- paste(myeq, '[t] = ', sep='') > for (i in 1:k){ + if (mysum$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="/var/wessaorg/rcomp/tmp/112d8w1354888648.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
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="/var/wessaorg/rcomp/tmp/12k9w21354888648.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="/var/wessaorg/rcomp/tmp/13s4gs1354888648.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
Forecast', 1, TRUE) > a<-table.element(a, 'Residuals
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="/var/wessaorg/rcomp/tmp/14k2fq1354888648.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="/var/wessaorg/rcomp/tmp/15odme1354888648.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="/var/wessaorg/rcomp/tmp/1653sl1354888648.tab") + } > > try(system("convert tmp/1it5l1354888648.ps tmp/1it5l1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/2wbbo1354888648.ps tmp/2wbbo1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/35wb01354888648.ps tmp/35wb01354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/4twz11354888648.ps tmp/4twz11354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/5r6591354888648.ps tmp/5r6591354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/618kk1354888648.ps tmp/618kk1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/7fi0h1354888648.ps tmp/7fi0h1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/8s07c1354888648.ps tmp/8s07c1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/9begw1354888648.ps tmp/9begw1354888648.png",intern=TRUE)) character(0) > try(system("convert tmp/10hmia1354888648.ps tmp/10hmia1354888648.png",intern=TRUE)) character(0) > > > proc.time() user system elapsed 6.697 1.160 7.906