Estimates values for a QQ plot of Empirical values against Theoretical values from a normal distribution, for either the chain points or the distances between successive points. Optionally, returns a plot as well as the values.
calc_qqplot(chain, change = TRUE, plot = FALSE)Arguments
- chain
Vector of n length, where n is the number of trials or sampler iterations
- change
Boolean. If false, it calculates a qqplot of the given chain. If true, it creates a chain of step sizes.
- plot
Boolean. Whether to plot the QQ plot or just return the values.
Value
A list with the theoretical and empirical quantiles, and the intercept and slope of the line connecting the points
Examples
set.seed(1)
chain1 <- sampler_mh(1, "norm", c(0,1), diag(1))
calc_qqplot(chain1[[1]], plot = TRUE)
#> $theoretical_quantiles
#> [1] -1.074714782 0.638771407 -0.370976632 0.787336268 -1.338171109
#> [6] -0.715830857 1.044643681 -0.734957149 -0.368353090 -1.622976959
#> [11] -0.365732081 -0.363113582 -0.397356492 0.881034550 -0.360497570
#> [16] 1.362562203 1.226684092 -0.357884023 -0.355272919 -0.352664234
#> [21] -2.073528010 -0.944207666 -0.626797795 -0.475530917 -0.350057947
#> [26] -0.347454035 1.455069402 -0.344852478 1.553789633 -0.342253252
#> [31] -0.644792622 -0.339656337 -1.690621630 -0.337061710 1.587433632
#> [36] 1.274896040 -0.334469350 -0.831538303 -0.331879236 -1.587433632
#> [41] -0.329291347 1.083486871 -1.514063341 -0.326705661 -0.324122158
#> [46] -0.321540816 0.478276292 -0.318961615 -0.316384534 1.869282096
#> [51] 0.511511186 0.932789543 -1.092343136 -0.497596702 -0.313809552
#> [56] 0.757616913 -0.492057923 -1.308759482 -2.033190945 -0.311236650
#> [61] 1.216350538 -0.606056812 1.061709585 0.794035138 1.521817797
#> [66] -0.308665806 0.738170977 -1.291642616 0.459132795 -0.306097000
#> [71] 0.576869863 -1.828672528 0.681427269 1.469342258 1.221501011
#> [76] 0.489294194 0.497596702 -1.105790508 -0.303530213 -0.300965424
#> [81] -0.298402614 -0.884652492 -1.434200160 1.841873565 -1.096803562
#> [86] -0.588484353 -0.295841762 -0.675258978 0.597247529 -0.494825415
#> [91] 1.767026136 -1.242434627 -0.293282848 1.161701358 0.722176892
#> [96] -1.128658237 -0.754356164 0.503150790 1.242434627 -2.141198121
#> [101] 0.774043308 -0.290725853 -1.394239291 -0.288170758 1.191068771
#> [106] 0.514305920 -0.751103416 -0.929010441 -1.211232131 2.704408084
#> [111] 0.464584912 -0.285617543 0.899241670 -0.467316148 -0.283066188
#> [116] -2.095032169 -0.280516675 -1.061709585 -0.277968984 0.873833032
#> [121] -0.275423095 2.095032169 -0.272878991 -0.270336652 1.308759482
#> [126] -0.528340607 -0.267796058 -1.344194096 -0.712668633 -1.057414228
#> [131] -0.770741421 -0.265257192 -0.262720035 -0.260184568 -0.257650772
#> [136] -0.255118629 -0.252588121 -0.459132795 1.855403612 -1.201089411
#> [141] -0.914024804 -0.400009445 0.863114909 -0.250059230 -0.247531936
#> [146] -0.245006223 0.467316148 -0.852495034 -0.838482930 -0.242482072
#> [151] 2.052942017 -0.764162713 -0.239959464 -0.807541042 1.003254620
#> [156] -0.975276216 1.387792002 0.866676551 -0.635769475 -0.237438383
#> [161] -0.234918810 0.545321024 -0.232400727 -0.229884118 0.450980074
#> [166] -0.568209866 1.978269267 -0.227368963 -1.387792002 -0.224855246
#> [171] 0.728552146 -0.440156108 -0.533983596 -0.222342948 -0.434763480
#> [176] -0.472789121 1.019600667 -1.156903404 -0.551016041 0.963516541
#> [181] -0.219832054 0.456411856 1.604951862 -0.217322544 -0.653868576
#> [186] -0.553870253 -0.214814402 -0.212307611 -0.445561566 -0.641779106
#> [191] -0.209802154 -0.453694292 1.079090447 0.831538303 -0.207298013
#> [196] -0.848976393 -0.681427269 -0.204795171 -0.202293611 -0.899241670
#> [201] -1.700941053 -0.767447915 -1.375067692 2.166106753 -1.274896040
#> [206] -0.199793316 1.087904337 -0.197294270 -0.725360834 -0.194796456
#> [211] 0.856024262 -0.192299856 -1.152131935 -1.019600667 -0.585573341
#> [216] 1.394239291 -0.189804454 -0.187310234 0.835005583 -0.594321404
#> [221] 0.519907490 0.591400360 0.848976393 -0.424015853 -0.738170977
#> [226] 1.326268632 -0.184817178 -0.841970446 -0.182325270 -0.870249220
#> [231] 0.548166310 -1.498821892 0.777353656 -1.237150322 -0.925244560
#> [236] 0.807541042 1.928737641 -0.955750235 -0.500371817 -0.179834494
#> [241] 0.877428103 -0.177344834 -1.191068771 -0.174856272 0.914024804
#> [246] -0.672184455 -0.172368792 1.133303079 -0.169882379 -0.814349482
#> [251] -0.167397015 0.891923351 -0.164912685 -0.582667283 -1.670506678
#> [256] -0.162429373 -0.159947061 0.461857138 -0.157465735 -0.154985378
#> [261] 0.706365453 0.609003688 -1.413937500 1.913231090 -0.152505974
#> [266] -2.052942017 1.995913821 1.066024621 -0.150027508 -2.619818643
#> [271] -0.571091767 0.725360834 1.007315900 1.506398875 -0.559592274
#> [276] -0.147549962 -2.220380319 -1.011393864 -0.145073322 0.744621629
#> [281] -0.142597571 1.427380718 0.910310379 0.582667283 -1.280438370
#> [286] -0.140122695 -1.476592340 -0.137648676 1.074714782 1.011393864
#> [291] -0.135175499 0.810940563 -0.132703149 -0.130231610 -0.127760866
#> [296] -1.441086959 -0.486534197 -0.125290901 0.492057923 -0.122821701
#> [301] -0.856024262 2.395056799 -1.044643681 -0.859564183 -0.120353250
#> [306] -0.810940563 0.568209866 1.803187654 1.036223787 -0.117885531
#> [311] -2.395056799 -0.780672545 0.979226190 1.498821892 0.647812006
#> [316] -0.115418530 -1.562035738 -0.413316983 -0.112952232 -0.835005583
#> [321] -0.110486620 -0.108021680 -1.124037618 -1.083486871 -0.105557396
#> [326] 0.797397964 -0.103093753 1.320387223 -0.415987220 -0.100630735
#> [331] -0.098168328 1.690621630 -0.095706516 0.656905865 -2.117551154
#> [336] -0.910310379 -0.093245284 1.413937500 -1.048881526 -0.090784616
#> [341] -0.088324498 1.258499567 -0.085864915 -0.083405850 -0.080947290
#> [346] -0.078489220 1.375067692 0.453694292 -0.076031623 -0.073574486
#> [351] -0.461857138 -0.963516541 -0.071117792 -0.483777902 -0.068661528
#> [356] 1.350266243 0.821195882 -1.087904337 -1.303011399 -0.066205678
#> [361] -1.613898866 -0.063750227 2.974721001 -0.061295161 -0.058840464
#> [366] -3.296918935 0.975276216 -0.056386121 -0.659949227 0.565332676
#> [371] -0.053932118 -0.542480146 -0.051478440 -1.015488716 0.533983596
#> [376] -0.722176892 -0.049025072 1.448042793 2.073528010 -0.046571998
#> [381] 1.596131519 -1.070359597 -0.044119205 -1.427380718 0.500371817
#> [386] 0.999209820 -0.902918945 0.828080992 0.483777902 -1.176258257
#> [391] 0.754356164 -0.620844627 -0.971341400 -0.041666678 -0.525525421
#> [396] -1.462168597 0.606056812 -0.039214400 -0.036762359 -0.034310539
#> [401] -0.464584912 0.770741421 1.700941053 1.070359597 -0.690728667
#> [406] -0.794035138 -0.031858925 0.470050875 -0.600178776 1.027876723
#> [411] 0.995181302 -0.029407502 0.951888623 -1.680479163 0.817767890
#> [416] -0.026956256 -0.024505173 -0.022054236 -0.019603432 -1.722140952
#> [421] -0.407985313 1.711444857 -1.053138293 -0.017152745 -0.629782717
#> [426] -1.326268632 1.332196279 -1.469342258 -0.014702162 -0.012251667
#> [431] -1.778822805 1.040424514 2.550634966 -2.814350831 -0.703224371
#> [436] 0.626797795 2.033190945 -0.009801245 -0.007350882 -0.531159987
#> [441] 0.929010441 1.263927335 -0.709513519 -0.517104677 -0.004900564
#> [446] 0.747858595 1.211232131 -0.002450274 0.000000000 -2.282109209
#> [451] 1.105790508 0.002450274 0.004900564 -1.604951862 0.007350882
#> [456] 2.014202572 0.666054377 -1.855403612 1.344194096 -1.961219934
#> [461] 0.009801245 -0.951888623 0.012251667 -0.450980074 -0.650837306
#> [466] 0.014702162 2.250173597 1.147386553 -1.660697611 1.722140952
#> [471] -0.744621629 0.017152745 0.019603432 -1.166526206 0.472789121
#> [476] -0.983191502 -0.706365453 0.925244560 -1.448042793 1.883530256
#> [481] 0.703224371 1.166526206 0.921491755 -2.192436603 1.286020313
#> [486] 0.481025277 -0.647812006 0.505933654 0.022054236 -1.995913821
#> [491] 0.712668633 0.024505173 0.884652492 -1.545647850 -0.522714393
#> [496] 1.434200160 -1.258499567 0.026956256 -0.747858595 -0.386772374
#> [501] 0.525525421 2.814350831 -1.356388589 -1.632190810 0.029407502
#> [506] 0.824633551 -1.381401890 0.031858925 0.034310539 1.545647850
#> [511] 0.036762359 -0.959626153 0.039214400 0.041666678 1.407310665
#> [516] 1.944722329 0.684521150 -0.448269175 -2.974721001 -1.186103008
#> [521] 0.508720442 0.044119205 1.053138293 1.110317650 0.046571998
#> [526] 0.049025072 1.314551136 -1.578854208 -1.913231090 0.614913381
#> [531] 0.553870253 -0.687621597 1.961219934 0.051478440 0.053932118
#> [536] -0.760885738 0.056386121 -0.700090213 0.588484353 0.058840464
#> [541] -0.508720442 0.061295161 -0.932789543 0.522714393 0.063750227
#> [546] -1.711444857 -0.800769832 -0.514305920 0.066205678 1.462168597
#> [551] 0.068661528 1.381401890 -0.576869863 -0.597247529 0.071117792
#> [556] -0.656905865 1.152131935 -1.420627017 0.073574486 0.076031623
#> [561] 1.622976959 -0.456411856 -1.263927335 -0.719000255 -1.841873565
#> [566] 0.841970446 1.483920879 -0.684521150 0.078489220 1.537607255
#> [571] 0.080947290 -0.503150790 2.282109209 0.083405850 -1.570389449
#> [576] 0.715830857 -0.777353656 0.085864915 -0.609003688 -0.442857219
#> [581] -1.883530256 0.600178776 0.088324498 1.137972502 1.186103008
#> [586] 0.090784616 0.852495034 -0.797397964 0.644792622 -0.489294194
#> [591] 1.124037618 0.093245284 0.095706516 0.764162713 -0.611955863
#> [596] -1.506398875 -0.389414298 -1.744144364 1.613898866 -1.553789633
#> [601] 1.790872342 -1.314551136 -1.040424514 0.971341400 0.983191502
#> [606] 1.632190810 -2.353995718 0.594321404 0.098168328 0.100630735
#> [611] 1.247753855 -0.917751883 -2.316557308 0.103093753 0.105557396
#> [616] -0.728552146 0.536811468 0.641779106 0.623818448 0.108021680
#> [621] 1.032041267 0.751103416 0.110486620 2.353995718 1.491329994
#> [626] 0.556728985 0.112952232 -1.815782684 0.115418530 0.117885531
#> [631] 0.120353250 0.122821701 0.125290901 0.617876287 -1.269392597
#> [636] 0.127760866 0.814349482 0.902918945 -1.641545347 0.130231610
#> [641] -1.027876723 -1.196064078 1.828672528 0.132703149 1.237150322
#> [646] 1.441086959 -0.548166310 0.135175499 0.137648676 0.140122695
#> [651] 0.690728667 -2.704408084 0.142597571 -1.066024621 1.680479163
#> [656] -0.638771407 0.629782717 1.356388589 -0.556728985 0.145073322
#> [661] 1.101285917 0.669116273 0.147549962 -0.731750895 -1.171378363
#> [666] -1.928737641 0.734957149 0.672184455 0.150027508 -1.733037780
#> [671] 1.119440874 -0.392058943 0.719000255 -0.410649689 -0.987172334
#> [676] -0.821195882 0.731750895 0.152505974 -0.787336268 1.114867663
#> [681] 0.700090213 1.171378363 -1.362562203 1.338171109 0.659949227
#> [686] 0.632773261 0.154985378 0.157465735 1.142666869 0.559592274
#> [691] 0.159947061 0.162429373 -1.596131519 0.870249220 0.164912685
#> [696] -0.565332676 0.167397015 0.955750235 0.169882379 -1.137972502
#> [701] -0.579766137 0.172368792 1.231900339 -0.817767890 -1.350266243
#> [706] 1.297306048 -0.863114909 0.693842421 0.174856272 -0.678339898
#> [711] 0.177344834 0.179834494 1.641545347 0.182325270 0.662998713
#> [716] -0.895576515 -0.591400360 -1.483920879 -0.940388005 0.184817178
#> [721] -0.402665216 0.187310234 0.189804454 -0.617876287 0.192299856
#> [726] 0.194796456 0.906608471 1.303011399 -1.400745061 1.778822805
#> [731] -1.181166323 0.197294270 0.967421566 0.199793316 -1.978269267
#> [736] 0.531159987 0.202293611 0.204795171 0.585573341 0.207298013
#> [741] -0.470050875 1.128658237 -0.948041153 -0.967421566 1.514063341
#> [746] 0.579766137 -0.741392447 1.529664857 1.201089411 -1.142666869
#> [751] 0.209802154 -0.545321024 -1.944722329 0.517104677 0.212307611
#> [756] 0.709513519 -0.666054377 1.476592340 -1.003254620 0.214814402
#> [761] 0.217322544 -0.603115189 -1.032041267 0.219832054 2.619818643
#> [766] -0.757616913 0.222342948 -1.651045778 0.767447915 -1.767026136
#> [771] 0.224855246 0.227368963 0.229884118 -0.873833032 0.687621597
#> [776] 0.551016041 0.232400727 0.234918810 0.237438383 -0.381496592
#> [781] 0.573978420 0.239959464 0.242482072 0.542480146 0.845468232
#> [786] 0.245006223 0.940388005 0.611955863 0.486534197 0.675258978
#> [791] 0.247531936 -0.999209820 0.250059230 1.368788190 0.252588121
#> [796] -0.866676551 -1.231900339 1.570389449 -1.221501011 1.176258257
#> [801] 0.255118629 0.257650772 0.260184568 1.291642616 -0.845468232
#> [806] -1.790872342 2.192436603 0.494825415 -2.491856901 1.015488716
#> [811] -0.437458204 2.316557308 0.262720035 -0.784000055 -1.529664857
#> [816] -1.368788190 0.265257192 0.620844627 0.804150828 1.181166323
#> [821] 0.267796058 -0.384133146 -0.505933654 0.270336652 1.670506678
#> [826] -1.206145261 0.838482930 0.272878991 0.275423095 -0.790681268
#> [831] -1.755470364 1.280438370 -0.373602730 0.948041153 1.048881526
#> [836] 0.696962916 0.277968984 -1.079090447 1.023729930 -1.226684092
#> [841] -0.936582015 -0.478276292 0.280516675 0.283066188 -1.161701358
#> [846] 0.285617543 0.288170758 -1.216350538 -1.119440874 1.755470364
#> [851] -0.405323831 -1.286020313 1.269392597 0.290725853 0.293282848
#> [856] 0.295841762 0.298402614 1.733037780 0.300965424 0.303530213
#> [861] -1.247753855 0.528340607 0.539643639 0.475530917 -0.536811468
#> [866] 0.306097000 0.800769832 0.308665806 -0.632773261 -0.891923351
#> [871] -0.511511186 -0.539643639 0.311236650 0.678339898 0.313809552
#> [876] 0.316384534 -1.869282096 -0.877428103 0.318961615 -0.828080992
#> [881] 2.220380319 1.651045778 0.321540816 0.324122158 1.578854208
#> [886] -1.455069402 -0.519907490 0.326705661 -0.562460158 1.096803562
#> [891] 0.329291347 0.562460158 -0.662998713 0.331879236 -0.669116273
#> [896] 0.959626153 -1.491329994 1.660697611 -0.824633551 0.760885738
#> [901] -0.921491755 -2.250173597 -1.407310665 2.440603181 -2.550634966
#> [906] 1.206145261 0.334469350 -0.573978420 0.337061710 1.815782684
#> [911] 0.339656337 0.991168871 -0.774043308 0.342253252 0.917751883
#> [916] -0.693842421 0.344852478 0.347454035 0.350057947 0.352664234
#> [921] 0.987172334 0.355272919 -0.426698123 0.357884023 -1.101285917
#> [926] -0.991168871 0.859564183 -0.995181302 -0.421336629 0.571091767
#> [931] 0.936582015 -0.696962916 -0.888282052 3.296918935 0.360497570
#> [936] -1.898171383 -0.804150828 0.363113582 0.365732081 0.368353090
#> [941] 0.370976632 0.373602730 0.376231407 -0.979226190 2.117551154
#> [946] 0.741392447 0.378862687 -1.320387223 -1.332196279 0.381496592
#> [951] -0.378862687 0.384133146 0.386772374 -1.036223787 1.156903404
#> [956] 2.141198121 -0.623818448 -1.521817797 0.389414298 1.092343136
#> [961] 0.790681268 -2.166106753 1.196064078 0.392058943 0.394706333
#> [966] -0.481025277 0.635769475 0.397356492 0.400009445 0.888282052
#> [971] 0.402665216 0.944207666 -0.429383467 -1.114867663 0.895576515
#> [976] -1.023729930 0.780672545 1.744144364 0.405323831 0.407985313
#> [981] 0.410649689 -1.537607255 -1.007315900 1.057414228 -1.253108624
#> [986] -2.440603181 0.650837306 -0.394706333 1.898171383 -1.133303079
#> [991] 0.413316983 1.420627017 -1.297306048 -0.432071910 0.415987220
#> [996] 0.418660427 0.421336629 0.424015853 -0.881034550 0.426698123
#> [1001] 1.562035738 0.429383467 0.784000055 0.603115189 -0.376231407
#> [1006] -0.418660427 0.432071910 0.434763480 0.437458204 -1.803187654
#> [1011] 0.440156108 1.400745061 -0.906608471 0.442857219 0.653868576
#> [1016] -0.614913381 0.445561566 -1.110317650 0.448269175 2.491856901
#> [1021] -1.147386553 1.253108624 -2.014202572
#>
#> $empirical_quantiles
#> [1] -0.626453811 0.183643324 0.000000000 0.329507772 -0.928567035
#> [6] -0.294720447 0.575781352 -0.305388387 0.000000000 -1.147657009
#> [11] 0.000000000 0.000000000 -0.016190263 0.435683299 0.000000000
#> [16] 0.918977372 0.782136301 0.000000000 0.000000000 0.000000000
#> [21] -1.470752384 -0.478150055 -0.235706556 -0.102787727 0.000000000
#> [26] 0.000000000 0.992160365 0.000000000 1.100025372 0.000000000
#> [31] -0.253361680 0.000000000 -1.166570547 0.000000000 1.156536997
#> [36] 0.832047129 0.000000000 -0.376702719 0.000000000 -1.129363096
#> [41] 0.000000000 0.618243294 -1.044134626 0.000000000 0.000000000
#> [46] 0.000000000 0.028002159 0.000000000 0.000000000 1.465554862
#> [51] 0.065288182 0.475509529 -0.649010078 -0.119168762 0.000000000
#> [56] 0.291446236 -0.117753598 -0.912068367 -1.437586241 0.000000000
#> [61] 0.772142186 -0.219515627 0.593946188 0.332950371 1.063099837
#> [66] 0.000000000 0.267098791 -0.873262112 0.008370960 0.000000000
#> [71] 0.119717641 -1.276592208 0.229019591 0.996543929 0.781859185
#> [76] 0.042115873 0.046580303 -0.654584644 0.000000000 0.000000000
#> [81] 0.000000000 -0.412519887 -0.972286836 1.432282239 -0.650696353
#> [86] -0.207380744 0.000000000 -0.279113303 0.138052709 -0.118792026
#> [91] 1.343038825 -0.803213217 0.000000000 0.712666307 0.262645459
#> [96] -0.681660479 -0.324270272 0.060160440 0.797916438 -1.518394082
#> [101] 0.306557861 0.000000000 -0.956891881 0.000000000 0.741276305
#> [106] 0.068511533 -0.323750755 -0.463530401 -0.767790185 2.087166546
#> [111] 0.017395620 0.000000000 0.450187101 -0.096524923 0.000000000
#> [116] -1.487460310 0.000000000 -0.621266695 0.000000000 0.425100377
#> [121] 0.000000000 1.680278205 0.000000000 0.000000000 0.885778374
#> [126] -0.144399602 0.000000000 -0.928971079 -0.294196454 -0.614950271
#> [131] -0.334000842 0.000000000 0.000000000 0.000000000 0.000000000
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#> [141] -0.430211754 -0.016748256 0.402011779 0.000000000 0.000000000
#> [146] 0.000000000 0.017636546 -0.389908629 -0.381076051 0.000000000
#> [151] 1.586588433 -0.330907801 0.000000000 -0.365401797 0.541327336
#> [156] -0.501378318 0.926062725 0.420694643 -0.238456353 0.000000000
#> [161] 0.000000000 0.095056227 0.000000000 0.000000000 0.002131860
#> [166] -0.193972745 1.576158181 0.000000000 -0.953203145 0.000000000
#> [171] 0.263175646 -0.061707422 -0.147270790 0.000000000 -0.059723276
#> [176] -0.098178744 0.560820729 -0.705928586 -0.161178506 0.501321828
#> [181] 0.000000000 0.005641985 1.162964556 0.000000000 -0.255670709
#> [186] -0.166121037 0.000000000 0.000000000 -0.069654813 -0.247664342
#> [191] 0.000000000 -0.082523762 0.606073431 0.374724407 0.000000000
#> [196] -0.389237182 -0.284330662 0.000000000 0.000000000 -0.422184010
#> [201] -1.189113295 -0.331032979 -0.939829327 1.702570586 -0.851857092
#> [206] 0.000000000 0.621054203 0.000000000 -0.298909313 0.000000000
#> [211] 0.398130155 0.000000000 -0.701231669 -0.580614304 -0.206144567
#> [216] 0.945184953 0.000000000 0.000000000 0.376370292 -0.213885951
#> [221] 0.070366141 0.134447661 0.390565942 -0.050565701 -0.305815420
#> [226] 0.893673702 0.000000000 -0.383632106 0.000000000 -0.395702923
#> [231] 0.097396655 -1.024548480 0.323006503 -0.797276101 -0.454136909
#> [236] 0.344795124 1.539648088 -0.483974930 -0.121010111 0.000000000
#> [241] 0.434536656 0.000000000 -0.756647609 0.000000000 0.456135603
#> [246] -0.273157993 0.000000000 0.679230774 0.000000000 -0.367450756
#> [251] 0.000000000 0.443805326 0.000000000 -0.201961742 -1.158015254
#> [256] 0.000000000 0.000000000 0.014646812 0.000000000 0.000000000
#> [261] 0.249196012 0.149220736 -0.963233180 1.473881181 0.000000000
#> [266] -1.452028290 1.577891795 0.596234109 0.000000000 -1.918909820
#> [271] -0.195258846 0.262665243 0.543657859 1.041060298 -0.169318332
#> [276] 0.000000000 -1.637421952 -0.572542604 0.000000000 0.277914132
#> [281] 0.000000000 0.976202525 0.456008669 0.128855402 -0.869460351
#> [286] 0.000000000 -1.001801335 0.000000000 0.604309409 0.548787588
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#> [296] -0.972442936 -0.110158762 0.000000000 0.045010598 0.000000000
#> [301] -0.390009563 1.895654774 -0.602997304 -0.390867821 0.000000000
#> [306] -0.366630946 0.116413613 1.384253158 0.574220913 0.000000000
#> [311] -1.800826318 -0.339880639 0.523620590 1.017754227 0.193725667
#> [316] 0.000000000 -1.105305910 -0.025162639 0.000000000 -0.380824536
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#> [351] -0.093557640 -0.490086292 0.000000000 -0.109655699 0.000000000
#> [356] 0.915182505 0.364384593 -0.635865043 -0.886443308 0.000000000
#> [361] -1.146814136 0.000000000 2.350554326 0.000000000 0.000000000
#> [366] -1.972934934 0.514671633 0.000000000 -0.256854125 0.111106430
#> [371] 0.000000000 -0.154671706 0.000000000 -0.576506933 0.077303123
#> [376] -0.296868642 0.000000000 0.991601036 1.593967454 0.000000000
#> [381] 1.159424527 -0.625227429 0.000000000 -0.967239458 0.047488592
#> [386] 0.539054406 -0.422372408 0.374118395 0.032637295 -0.737327525
#> [391] 0.290666645 -0.233427178 -0.498888219 0.000000000 -0.144226557
#> [396] -0.981224119 0.143247631 0.000000000 0.000000000 0.000000000
#> [401] -0.094497345 0.303360961 1.281737421 0.602222795 -0.287813744
#> [406] -0.346637445 0.000000000 0.018607400 -0.218964232 0.564268161
#> [411] 0.537326132 0.000000000 0.496960952 -1.160655001 0.358774234
#> [416] 0.000000000 0.000000000 0.000000000 0.000000000 -1.215364041
#> [421] -0.022558628 1.293879968 -0.606727941 0.000000000 -0.237653068
#> [426] -0.926858157 0.900434636 -0.994193629 0.000000000 0.000000000
#> [431] -1.258948697 0.575620289 2.024842045 -1.962353191 -0.291748602
#> [436] 0.167679934 1.584629079 0.000000000 0.000000000 -0.144874874
#> [441] 0.468971760 0.806123264 -0.293294934 -0.134841264 0.000000000
#> [446] 0.287667139 0.768278218 0.000000000 0.000000000 -1.687801029
#> [451] 0.647645994 0.000000000 0.000000000 -1.136733853 0.000000000
#> [456] 1.584192142 0.221703816 -1.291719044 0.909670446 -1.398754027
#> [461] 0.000000000 -0.483882474 0.000000000 -0.076825771 -0.255510379
#> [466] 0.000000000 1.763586348 0.689600222 -1.157180172 1.301554937
#> [471] -0.319786166 0.000000000 0.000000000 -0.731194999 0.019752007
#> [476] -0.510742458 -0.291842736 0.465214906 -0.973902306 1.466199919
#> [481] 0.243863295 0.713033195 0.464459771 -1.593286302 0.847792797
#> [486] 0.030101166 -0.255248113 0.060921227 0.000000000 -1.429916216
#> [491] 0.254137143 0.000000000 0.438821912 -1.084720001 -0.141585732
#> [496] 0.976327473 -0.843339880 0.000000000 -0.322470342 -0.010258765
#> [501] 0.071280652 2.189752359 -0.937000891 -1.152157056 0.000000000
#> [506] 0.371912476 -0.943514417 0.000000000 0.000000000 1.077850323
#> [511] 0.000000000 -0.484069527 0.000000000 0.000000000 0.959394327
#> [516] 1.556052636 0.229284475 -0.075445931 -1.967195349 -0.755903643
#> [521] 0.065051010 0.000000000 0.580318685 0.655051998 0.000000000
#> [526] 0.000000000 0.886390001 -1.123456937 -1.344130123 0.156056926
#> [531] 0.102051958 -0.287458172 1.568364734 0.000000000 0.000000000
#> [536] -0.327812680 0.000000000 -0.291724771 0.130953101 0.000000000
#> [541] -0.130950479 0.000000000 -0.463956220 0.070659825 0.000000000
#> [546] -1.197934626 -0.354781330 -0.132857466 0.000000000 0.992288426
#> [551] 0.000000000 0.925084797 -0.198620810 -0.214708418 0.000000000
#> [556] -0.256392295 0.690795904 -0.967062668 0.000000000 0.000000000
#> [561] 1.183724120 -0.088616917 -0.845654313 -0.295005034 -1.290769688
#> [566] 0.384543716 1.004804339 -0.285965791 0.000000000 1.072472006
#> [571] 0.000000000 -0.124261326 1.768873624 0.000000000 -1.110366445
#> [576] 0.254403389 -0.339676972 0.000000000 -0.219755198 -0.062720778
#> [581] -1.309429950 0.139327027 0.000000000 0.687525073 0.738242550
#> [586] 0.000000000 0.391413340 -0.354592006 0.188238853 -0.111586803
#> [591] 0.675743917 0.000000000 0.000000000 0.293623431 -0.220894598
#> [596] -1.029391655 -0.010925691 -1.222331968 1.169122592 -1.086908817
#> [601] 1.379236132 -0.919674583 -0.599628395 0.512773055 0.527988783
#> [606] 1.188247324 -1.726630596 0.137021552 0.000000000 0.000000000
#> [611] 0.802137876 -0.430536942 -1.709276181 0.000000000 0.000000000
#> [616] -0.299019664 0.080999364 0.183661843 0.166255035 0.000000000
#> [621] 0.566183078 0.290325674 0.000000000 1.800112333 1.011440176
#> [626] 0.102573846 0.000000000 -1.272369672 0.000000000 0.000000000
#> [631] 0.000000000 0.000000000 0.000000000 0.157560555 -0.847190495
#> [636] 0.000000000 0.353536709 0.450424514 -1.154918660 0.000000000
#> [641] -0.589627963 -0.765889998 1.416440853 0.000000000 0.796092713
#> [646] 0.986428344 -0.157827180 0.000000000 0.000000000 0.000000000
#> [651] 0.231852545 -1.951783301 0.000000000 -0.623049782 1.248358506
#> [656] -0.247078230 0.176417798 0.915848207 -0.167523856 0.000000000
#> [661] 0.634702931 0.222146147 0.000000000 -0.303177624 -0.733571785
#> [666] -1.381854714 0.266352192 0.222370495 0.000000000 -1.215755063
#> [671] 0.660531281 -0.013255700 0.261106083 -0.024543857 -0.526152469
#> [676] -0.370993056 0.264422549 0.000000000 -0.340236065 0.659201499
#> [681] 0.237829400 0.715275947 -0.938483039 0.908747388 0.207849948
#> [686] 0.178014002 0.000000000 0.000000000 0.689243733 0.106191316
#> [691] 0.000000000 0.000000000 -1.133916661 0.421335268 0.000000000
#> [696] -0.189474330 0.000000000 0.500172741 0.000000000 -0.693889397
#> [701] -0.199064505 0.000000000 0.794146066 -0.367550766 -0.934517579
#> [706] 0.877708267 -0.392230913 0.235175025 0.000000000 -0.283552997
#> [711] 0.000000000 0.000000000 1.193691666 0.000000000 0.214421481
#> [716] -0.419643268 -0.212739735 -1.020660780 -0.466438215 0.000000000
#> [721] -0.019955117 0.000000000 0.000000000 -0.227754971 0.000000000
#> [726] 0.000000000 0.455876742 0.878110263 -0.958463923 1.354397332
#> [731] -0.747766705 0.000000000 0.505067590 0.000000000 -1.419873383
#> [736] 0.074778333 0.000000000 0.000000000 0.129420458 0.000000000
#> [741] -0.097765133 0.676452747 -0.482652526 -0.497700719 1.048909929
#> [746] 0.121058163 -0.313292885 1.066352402 0.755509155 -0.697318199
#> [751] 0.000000000 -0.156764310 -1.389802635 0.069395647 0.000000000
#> [756] 0.250419911 -0.264423950 0.998154445 -0.540872745 0.000000000
#> [761] 0.000000000 -0.219049185 -0.591428470 0.000000000 2.036103609
#> [766] -0.326489593 0.000000000 -1.155943109 0.294808760 -1.252355924
#> [771] 0.000000000 0.000000000 0.000000000 -0.398376014 0.229467460
#> [776] 0.100254667 0.000000000 0.000000000 0.000000000 -0.006368929
#> [781] 0.118853245 0.000000000 0.000000000 0.085578656 0.387769029
#> [786] 0.000000000 0.485388565 0.151856040 0.041998754 0.223422312
#> [791] 0.000000000 -0.539542776 0.000000000 0.923313589 0.000000000
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#> [806] -1.263656166 1.718926338 0.046567748 -1.845609422 0.555737185
#> [811] -0.060119191 1.769289381 0.000000000 -0.340080187 -1.061509942
#> [816] -0.939173204 0.000000000 0.158199488 0.340690847 0.735364418
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#> [841] -0.465728889 -0.104852065 0.000000000 0.000000000 -0.718511452
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#> [851] -0.020293545 -0.872179536 0.822826091 0.000000000 0.000000000
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#> [871] -0.132499628 -0.153078892 0.000000000 0.225088397 0.000000000
#> [876] 0.000000000 -1.306214904 -0.406815143 0.000000000 -0.375580746
#> [881] 1.741510530 1.204177513 0.000000000 0.000000000 1.135799570
#> [886] -0.981075755 -0.139221405 0.000000000 -0.184970096 0.633953390
#> [891] 0.000000000 0.108808268 -0.261264878 0.000000000 -0.271064090
#> [896] 0.500359049 -1.021747370 1.218305379 -0.371810022 0.291790766
#> [901] -0.442317719 -1.638007733 -0.959316423 1.923163653 -1.856829628
#> [906] 0.760994764 0.000000000 -0.195988199 0.000000000 1.398718955
#> [911] 0.000000000 0.529627475 -0.339343445 0.000000000 0.456530316
#> [916] -0.291160144 0.000000000 0.000000000 0.000000000 0.000000000
#> [921] 0.528971601 0.000000000 -0.053178475 0.000000000 -0.650810638
#> [926] -0.530295274 0.401480746 -0.538301076 -0.044228378 0.118845015
#> [931] 0.482247223 -0.291324805 -0.416276480 2.390576700 0.000000000
#> [936] -1.336053745 -0.365131612 0.000000000 0.000000000 0.000000000
#> [941] 0.000000000 0.000000000 0.000000000 -0.503130035 1.680361859
#> [946] 0.275330300 0.000000000 -0.926404248 -0.928557925 0.000000000
#> [951] -0.005667893 0.000000000 0.000000000 -0.599075968 0.696845859
#> [956] 1.699970673 -0.235347706 -1.049652040 0.000000000 0.624332984
#> [961] 0.331725219 -1.576233560 0.742589846 0.000000000 0.000000000
#> [966] -0.107877789 0.181994495 0.000000000 0.000000000 0.443393864
#> [971] 0.000000000 0.489449364 -0.054002596 -0.668147317 0.445807957
#> [976] -0.582069807 0.323837305 1.316167163 0.000000000 0.000000000
#> [981] 0.000000000 -1.073772410 -0.552358286 0.590461401 -0.842691810
#> [986] -1.838814903 0.195880789 -0.015519729 1.467632026 -0.691064579
#> [991] 0.000000000 0.964313072 -0.885634952 -0.058414484 0.000000000
#> [996] 0.000000000 0.000000000 0.000000000 -0.409796840 0.000000000
#> [1001] 1.113110482 0.000000000 0.327991438 0.140094492 -0.002555836
#> [1006] -0.038227771 0.000000000 0.000000000 0.000000000 -1.269333501
#> [1011] 0.000000000 0.949049121 -0.422709861 0.000000000 0.200478092
#> [1016] -0.226224485 0.000000000 -0.662115621 0.000000000 1.998830635
#> [1021] -0.697496645 0.803540155 -1.434221772
#>
#> $intercept
#> [1] -0.02661962
#>
#> $slope
#> [1] 0.369933
#>