Is there a significant change (i.e., increase or decrease) in mean annual air temperature at Banner Summit over the last 30 years (from 1990 to 2020)?
require(readr)
require(snotelr)
require(lubridate)
require(dplyr)
require(ggplot2)Import data
snotel_312 <- read_csv("~/Desktop/ENVS 511/Week 5/snotel_312.csv")## Rows: 15257 Columns: 18
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (5): network, state, site_name, description, county
## dbl (10): latitude, longitude, elev, site_id, snow_water_equivalent, precip...
## date (3): start, end, date
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
banner <- snotel_312Format date, create year column, extract years 1990 - 2020
banner$date <- ymd(banner$date)
banner$year <- year(banner$date)
banner1 <- banner %>% filter(year >= 1990 & year <= 2020)Create density plot:
banner1$year1 <- as.factor(banner1$year)
ggplot(banner1, aes(x = temperature_mean, color = year, group = year)) +
geom_density(size = 1) +
labs(x = "Mean Temperature", y = "Density") +
theme(text = element_text(size = 20))
Create boxplot:
ggplot(banner1, aes(x = year, y = temperature_mean, color = year, group = year1)) +
geom_boxplot(size = 1) +
labs(y = "Mean Temperature", x = "Year") +
theme(text = element_text(size = 20))
Run anova analysis:
model1 <- aov(temperature_mean ~ year1, data = banner1)
summary(model1)## Df Sum Sq Mean Sq F value Pr(>F)
## year1 30 5804 193.47 2.807 5.17e-07 ***
## Residuals 11236 774398 68.92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 56 observations deleted due to missingness
Statistically significant result. Therefore, posthoc pairwise comparison:
posthoc <- TukeyHSD(model1)
posthoc## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = temperature_mean ~ year1, data = banner1)
##
## $year1
## diff lwr upr p adj
## 1991-1990 0.157913299 -2.160992239 2.4768188 1.0000000
## 1992-1990 0.317873674 -2.024203580 2.6599509 1.0000000
## 1993-1990 -0.709155380 -3.059906070 1.6415953 0.9999997
## 1994-1990 0.989832078 -1.340460296 3.3201245 0.9995127
## 1995-1990 0.278842390 -2.036880010 2.5945648 1.0000000
## 1996-1990 0.105887828 -2.208254425 2.4200301 1.0000000
## 1997-1990 -0.159267804 -2.479776444 2.1612408 1.0000000
## 1998-1990 0.559390336 -1.756332065 2.8751127 1.0000000
## 1999-1990 0.700000000 -1.617310143 3.0173101 0.9999997
## 2000-1990 1.350897185 -0.964825215 3.6666196 0.9417569
## 2001-1990 1.635006774 -0.680715626 3.9507292 0.6782864
## 2002-1990 1.016650610 -1.299071791 3.3323730 0.9991128
## 2003-1990 1.789253349 -0.526469051 4.1049757 0.4709992
## 2004-1990 1.474193839 -0.839948414 3.7883361 0.8564363
## 2005-1990 1.294732801 -1.020989599 3.6104552 0.9648413
## 2006-1990 1.439390336 -0.876332065 3.7551127 0.8861779
## 2007-1990 1.958516484 -0.358793660 4.2758266 0.2700392
## 2008-1990 0.780204768 -1.533937486 3.0943470 0.9999957
## 2009-1990 0.726239651 -1.589482750 3.0419621 0.9999992
## 2010-1990 1.061582117 -1.254140284 3.3773045 0.9981175
## 2011-1990 0.545143760 -1.770578640 2.8608662 1.0000000
## 2012-1990 1.650969795 -0.663172458 3.9651120 0.6559749
## 2013-1990 1.233088966 -1.082633435 3.5488114 0.9813572
## 2014-1990 1.805691706 -0.510030695 4.1214141 0.4492738
## 2015-1990 2.511171158 0.195448757 4.8268936 0.0156285
## 2016-1990 1.892226626 -0.421915628 4.2063689 0.3398444
## 2017-1990 1.608705404 -0.707016996 3.9244278 0.7117412
## 2018-1990 1.638020473 -0.677701928 3.9537429 0.6743815
## 2019-1990 0.902951980 -1.412770421 3.2186744 0.9999063
## 2020-1990 1.449876899 -0.864265354 3.7640192 0.8771050
## 1992-1991 0.159960375 -2.183695414 2.5036162 1.0000000
## 1993-1991 -0.867068678 -3.219392083 1.4852547 0.9999704
## 1994-1991 0.831918779 -1.499960107 3.1637977 0.9999852
## 1995-1991 0.120929092 -2.196389796 2.4382480 1.0000000
## 1996-1991 -0.052025471 -2.367765301 2.2637144 1.0000000
## 1997-1991 -0.317181103 -2.639282940 2.0049207 1.0000000
## 1998-1991 0.401477037 -1.915841851 2.7187959 1.0000000
## 1999-1991 0.542086701 -1.776818836 2.8609922 1.0000000
## 2000-1991 1.192983886 -1.124335002 3.5103028 0.9883749
## 2001-1991 1.477093475 -0.840225413 3.7944124 0.8556568
## 2002-1991 0.858737311 -1.458581577 3.1760562 0.9999669
## 2003-1991 1.631340051 -0.685978837 3.9486589 0.6844656
## 2004-1991 1.316280540 -0.999459290 3.6320204 0.9569961
## 2005-1991 1.136819503 -1.180499385 3.4541384 0.9943446
## 2006-1991 1.281477037 -1.035841851 3.5987959 0.9693659
## 2007-1991 1.800603185 -0.518302353 4.1195087 0.4592295
## 2008-1991 0.622291469 -1.693448361 2.9380313 1.0000000
## 2009-1991 0.568326352 -1.748992536 2.8856452 1.0000000
## 2010-1991 0.903668818 -1.413650070 3.2209877 0.9999061
## 2011-1991 0.387230462 -1.930088426 2.7045493 1.0000000
## 2012-1991 1.493056496 -0.822683334 3.8087963 0.8400610
## 2013-1991 1.075175667 -1.242143221 3.3924946 0.9976950
## 2014-1991 1.647778407 -0.669540481 3.9650973 0.6631376
## 2015-1991 2.353257859 0.035938971 4.6705767 0.0408577
## 2016-1991 1.734313327 -0.581426503 4.0500532 0.5451483
## 2017-1991 1.450792105 -0.866526783 3.7681110 0.8779727
## 2018-1991 1.480107174 -0.837211714 3.7974261 0.8529562
## 2019-1991 0.745038681 -1.572280207 3.0623576 0.9999985
## 2020-1991 1.291963600 -1.023776230 3.6077034 0.9657684
## 1993-1992 -1.027029053 -3.402198178 1.3481401 0.9993249
## 1994-1992 0.671958404 -1.682964548 3.0268814 0.9999999
## 1995-1992 -0.039031283 -2.379537595 2.3014750 1.0000000
## 1996-1992 -0.211985846 -2.550928755 2.1269571 1.0000000
## 1997-1992 -0.477141478 -2.822383451 1.8681005 1.0000000
## 1998-1992 0.241516662 -2.098989650 2.5820230 1.0000000
## 1999-1992 0.382126326 -1.959950927 2.7242036 1.0000000
## 2000-1992 1.033023511 -1.307482801 3.3735298 0.9990246
## 2001-1992 1.317133100 -1.023373212 3.6576394 0.9619035
## 2002-1992 0.698776936 -1.641729376 3.0392832 0.9999997
## 2003-1992 1.471379676 -0.869126636 3.8118860 0.8730724
## 2004-1992 1.156320165 -1.182622744 3.4952631 0.9936305
## 2005-1992 0.976859128 -1.363647184 3.3173654 0.9996488
## 2006-1992 1.121516662 -1.218989650 3.4620230 0.9960945
## 2007-1992 1.640642810 -0.701434444 3.9827201 0.6947476
## 2008-1992 0.462331094 -1.876611815 2.8012740 1.0000000
## 2009-1992 0.408365977 -1.932140335 2.7488723 1.0000000
## 2010-1992 0.743708443 -1.596797869 3.0842148 0.9999989
## 2011-1992 0.227270087 -2.113236226 2.5677764 1.0000000
## 2012-1992 1.333096122 -1.005846787 3.6720390 0.9555705
## 2013-1992 0.915215292 -1.425291020 3.2557216 0.9999008
## 2014-1992 1.487818032 -0.852688280 3.8283243 0.8592094
## 2015-1992 2.193297484 -0.147208828 4.5338038 0.1069561
## 2016-1992 1.574352952 -0.764589957 3.9132959 0.7714790
## 2017-1992 1.290831731 -1.049674582 3.6313380 0.9703931
## 2018-1992 1.320146799 -1.020359513 3.6606531 0.9608242
## 2019-1992 0.585078306 -1.755428006 2.9255846 1.0000000
## 2020-1992 1.132003225 -1.206939684 3.4709461 0.9954233
## 1994-1993 1.698987458 -0.664561793 4.0625367 0.6394109
## 1995-1993 0.987997770 -1.361187779 3.3371833 0.9995948
## 1996-1993 0.815043208 -1.532584718 3.1626711 0.9999918
## 1997-1993 0.549887575 -1.804016173 2.9037913 1.0000000
## 1998-1993 1.268545715 -1.080639834 3.6177313 0.9775017
## 1999-1993 1.409155380 -0.941595311 3.7599061 0.9214002
## 2000-1993 2.060052565 -0.289132985 4.4092381 0.2013886
## 2001-1993 2.344162154 -0.005023396 4.6933477 0.0513894
## 2002-1993 1.725805989 -0.623379560 4.0749915 0.5901439
## 2003-1993 2.498408729 0.149223180 4.8475943 0.0211376
## 2004-1993 2.183349218 -0.164278707 4.5309771 0.1157997
## 2005-1993 2.003888181 -0.345297368 4.3530737 0.2518439
## 2006-1993 2.148545715 -0.200639834 4.4977313 0.1370701
## 2007-1993 2.667671863 0.316921173 5.0184226 0.0072692
## 2008-1993 1.489360147 -0.858267778 3.8369881 0.8617831
## 2009-1993 1.435395030 -0.913790519 3.7845806 0.9040523
## 2010-1993 1.770737496 -0.578448053 4.1199230 0.5298992
## 2011-1993 1.254299140 -1.094886409 3.6034847 0.9806600
## 2012-1993 2.360125175 0.012497249 4.7077531 0.0466808
## 2013-1993 1.942244345 -0.406941204 4.2914299 0.3157483
## 2014-1993 2.514847085 0.165661536 4.8640326 0.0191225
## 2015-1993 3.220326537 0.871140988 5.5695121 0.0001096
## 2016-1993 2.601382005 0.253754080 4.9490099 0.0109761
## 2017-1993 2.317860784 -0.031324765 4.6670463 0.0592161
## 2018-1993 2.347175852 -0.002009697 4.6963614 0.0505519
## 2019-1993 1.612107359 -0.737078190 3.9612929 0.7357850
## 2020-1993 2.159032279 -0.188595647 4.5066602 0.1297670
## 1995-1994 -0.710989688 -3.039703171 1.6177238 0.9999996
## 1996-1994 -0.883944250 -3.211086407 1.4431979 0.9999449
## 1997-1994 -1.149099882 -3.482572959 1.1843732 0.9940029
## 1998-1994 -0.430441742 -2.759155225 1.8982717 1.0000000
## 1999-1994 -0.289832078 -2.620124452 2.0404603 1.0000000
## 2000-1994 0.361065107 -1.967648376 2.6897786 1.0000000
## 2001-1994 0.645174696 -1.683538787 2.9738882 1.0000000
## 2002-1994 0.026818532 -2.301894951 2.3555320 1.0000000
## 2003-1994 0.799421271 -1.529292212 3.1281348 0.9999936
## 2004-1994 0.484361761 -1.842780396 2.8115039 1.0000000
## 2005-1994 0.304900723 -2.023812760 2.6336142 1.0000000
## 2006-1994 0.449558258 -1.879155225 2.7782717 1.0000000
## 2007-1994 0.968684405 -1.361607969 3.2989768 0.9996745
## 2008-1994 -0.209627310 -2.536769467 2.1175148 1.0000000
## 2009-1994 -0.263592427 -2.592305910 2.0651211 1.0000000
## 2010-1994 0.071750038 -2.256963445 2.4004635 1.0000000
## 2011-1994 -0.444688318 -2.773401801 1.8840252 1.0000000
## 2012-1994 0.661137717 -1.666004440 2.9882799 0.9999999
## 2013-1994 0.243256888 -2.085456595 2.5719704 1.0000000
## 2014-1994 0.815859628 -1.512853856 3.1445731 0.9999900
## 2015-1994 1.521339080 -0.807374403 3.8500526 0.8207136
## 2016-1994 0.902394548 -1.424747609 3.2295367 0.9999162
## 2017-1994 0.618873326 -1.709840157 2.9475868 1.0000000
## 2018-1994 0.648188395 -1.680525088 2.9769019 1.0000000
## 2019-1994 -0.086880099 -2.415593582 2.2418334 1.0000000
## 2020-1994 0.460044821 -1.867097336 2.7871870 1.0000000
## 1996-1995 -0.172954562 -2.485506898 2.1395978 1.0000000
## 1997-1995 -0.438110195 -2.757033282 1.8808129 1.0000000
## 1998-1995 0.280547945 -2.033585623 2.5946815 1.0000000
## 1999-1995 0.421157610 -1.894564791 2.7368800 1.0000000
## 2000-1995 1.072054795 -1.242078774 3.3861884 0.9977532
## 2001-1995 1.356164384 -0.957969185 3.6702980 0.9386646
## 2002-1995 0.737808219 -1.576325349 3.0519418 0.9999988
## 2003-1995 1.510410959 -0.803722609 3.8245445 0.8221248
## 2004-1995 1.195351448 -1.117200887 3.5079038 0.9876812
## 2005-1995 1.015890411 -1.298243157 3.3300240 0.9991138
## 2006-1995 1.160547945 -1.153585623 3.4746815 0.9920877
## 2007-1995 1.679674093 -0.636048307 3.9953965 0.6192567
## 2008-1995 0.501362377 -1.811189958 2.8139147 1.0000000
## 2009-1995 0.447397260 -1.866736308 2.7615308 1.0000000
## 2010-1995 0.782739726 -1.531393842 3.0968733 0.9999954
## 2011-1995 0.266301370 -2.047832198 2.5804349 1.0000000
## 2012-1995 1.372127405 -0.940424931 3.6846797 0.9296357
## 2013-1995 0.954246575 -1.359886993 3.2683801 0.9997206
## 2014-1995 1.526849315 -0.787284253 3.8409829 0.8052234
## 2015-1995 2.232328767 -0.081804801 4.5464623 0.0775766
## 2016-1995 1.613384235 -0.699168100 3.9259366 0.7030928
## 2017-1995 1.329863014 -0.984270555 3.6439966 0.9510221
## 2018-1995 1.359178082 -0.954955486 3.6733117 0.9371185
## 2019-1995 0.624109589 -1.690023979 2.9382432 1.0000000
## 2020-1995 1.171034509 -1.141517827 3.4835868 0.9908620
## 1997-1996 -0.265155632 -2.582500755 2.0521895 1.0000000
## 1998-1996 0.453502508 -1.859049828 2.7660548 1.0000000
## 1999-1996 0.594112172 -1.720030081 2.9082544 1.0000000
## 2000-1996 1.245009357 -1.067542979 3.5575617 0.9783845
## 2001-1996 1.529118946 -0.783433390 3.8416713 0.8017188
## 2002-1996 0.910762782 -1.401789554 3.2233151 0.9998857
## 2003-1996 1.683365521 -0.629186814 3.9959179 0.6111803
## 2004-1996 1.368306011 -0.942664010 3.6792760 0.9312399
## 2005-1996 1.188844973 -1.123707362 3.5013973 0.9886097
## 2006-1996 1.333502508 -0.979049828 3.6460548 0.9490264
## 2007-1996 1.852628655 -0.461513598 4.1667709 0.3876038
## 2008-1996 0.674316940 -1.636653081 2.9852870 0.9999998
## 2009-1996 0.620351823 -1.692200513 2.9329042 1.0000000
## 2010-1996 0.955694288 -1.356858047 3.2682466 0.9997087
## 2011-1996 0.439255932 -1.873296403 2.7518083 1.0000000
## 2012-1996 1.545081967 -0.765888054 3.8560520 0.7832239
## 2013-1996 1.127201138 -1.185351198 3.4397535 0.9948836
## 2014-1996 1.699803878 -0.612748458 4.0123562 0.5889073
## 2015-1996 2.405283330 0.092730994 4.7178357 0.0293366
## 2016-1996 1.786338798 -0.524631223 4.0973088 0.4699899
## 2017-1996 1.502817576 -0.809734760 3.8153699 0.8286485
## 2018-1996 1.532132645 -0.780419691 3.8446850 0.7985033
## 2019-1996 0.797064152 -1.515488184 3.1096165 0.9999930
## 2020-1996 1.343989071 -0.966980950 3.6549591 0.9437610
## 1998-1997 0.718658140 -1.600264948 3.0375812 0.9999994
## 1999-1997 0.859267804 -1.461240836 3.1797764 0.9999674
## 2000-1997 1.510164989 -0.808758099 3.8290881 0.8254847
## 2001-1997 1.794274578 -0.524648510 4.1131977 0.4676175
## 2002-1997 1.175918414 -1.143004674 3.4948415 0.9906698
## 2003-1997 1.948521153 -0.370401934 4.2674442 0.2817994
## 2004-1997 1.633461643 -0.683883480 3.9508068 0.6817591
## 2005-1997 1.454000605 -0.864922482 3.7729237 0.8761907
## 2006-1997 1.598658140 -0.720264948 3.9175812 0.7268948
## 2007-1997 2.117784288 -0.202724353 4.4382929 0.1399653
## 2008-1997 0.939472572 -1.377872551 3.2568177 0.9997983
## 2009-1997 0.885507455 -1.433415633 3.2044305 0.9999386
## 2010-1997 1.220849921 -1.098073167 3.5397730 0.9840484
## 2011-1997 0.704411564 -1.614511523 3.0233347 0.9999996
## 2012-1997 1.810237599 -0.507107524 4.1275827 0.4449774
## 2013-1997 1.392356770 -0.926566318 3.7112799 0.9200155
## 2014-1997 1.964959510 -0.353963578 4.2838826 0.2648790
## 2015-1997 2.670438962 0.351515874 4.9893620 0.0055738
## 2016-1997 2.051494430 -0.265850693 4.3688396 0.1855390
## 2017-1997 1.767973208 -0.550949879 4.0868963 0.5027898
## 2018-1997 1.797288277 -0.521634811 4.1162114 0.4636265
## 2019-1997 1.062219784 -1.256703304 3.3811429 0.9981423
## 2020-1997 1.609144703 -0.708200420 3.9264898 0.7125992
## 1999-1998 0.140609664 -2.175112736 2.4563321 1.0000000
## 2000-1998 0.791506849 -1.522626719 3.1056404 0.9999941
## 2001-1998 1.075616438 -1.238517130 3.3897500 0.9976253
## 2002-1998 0.457260274 -1.856873294 2.7713938 1.0000000
## 2003-1998 1.229863014 -1.084270555 3.5439966 0.9818415
## 2004-1998 0.914803503 -1.397748833 3.2273558 0.9998752
## 2005-1998 0.735342466 -1.578791103 3.0494760 0.9999989
## 2006-1998 0.880000000 -1.434133568 3.1941336 0.9999436
## 2007-1998 1.399126148 -0.916596253 3.7148485 0.9145784
## 2008-1998 0.220814432 -2.091737904 2.5333668 1.0000000
## 2009-1998 0.166849315 -2.147284253 2.4809829 1.0000000
## 2010-1998 0.502191781 -1.811941788 2.8163253 1.0000000
## 2011-1998 -0.014246575 -2.328380144 2.2998870 1.0000000
## 2012-1998 1.091579460 -1.220972876 3.4041318 0.9969377
## 2013-1998 0.673698630 -1.640434938 2.9878322 0.9999999
## 2014-1998 1.246301370 -1.067832198 3.5604349 0.9782824
## 2015-1998 1.951780822 -0.362352746 4.2659144 0.2742070
## 2016-1998 1.332836290 -0.979716046 3.6453886 0.9493224
## 2017-1998 1.049315068 -1.264818500 3.3634486 0.9984380
## 2018-1998 1.078630137 -1.235503431 3.3927637 0.9975122
## 2019-1998 0.343561644 -1.970571925 2.6576952 1.0000000
## 2020-1998 0.890486563 -1.422065772 3.2030389 0.9999272
## 2000-1999 0.650897185 -1.664825215 2.9666196 0.9999999
## 2001-1999 0.935006774 -1.380715626 3.2507292 0.9998136
## 2002-1999 0.316650610 -1.999071791 2.6323730 1.0000000
## 2003-1999 1.089253349 -1.226469051 3.4049757 0.9971083
## 2004-1999 0.774193839 -1.539948414 3.0883361 0.9999964
## 2005-1999 0.594732801 -1.720989599 2.9104552 1.0000000
## 2006-1999 0.739390336 -1.576332065 3.0551127 0.9999987
## 2007-1999 1.258516484 -1.058793660 3.5758266 0.9757375
## 2008-1999 0.080204768 -2.233937486 2.3943470 1.0000000
## 2009-1999 0.026239651 -2.289482750 2.3419621 1.0000000
## 2010-1999 0.361582117 -1.954140284 2.6773045 1.0000000
## 2011-1999 -0.154856240 -2.470578640 2.1608662 1.0000000
## 2012-1999 0.950969795 -1.363172458 3.2651120 0.9997383
## 2013-1999 0.533088966 -1.782633435 2.8488114 1.0000000
## 2014-1999 1.105691706 -1.210030695 3.4214141 0.9963116
## 2015-1999 1.811171158 -0.504551243 4.1268936 0.4420999
## 2016-1999 1.192226626 -1.121915628 3.5063689 0.9882511
## 2017-1999 0.908705404 -1.407016996 3.2244278 0.9998936
## 2018-1999 0.938020473 -1.377701928 3.2537429 0.9998016
## 2019-1999 0.202951980 -2.112770421 2.5186744 1.0000000
## 2020-1999 0.749876899 -1.564265354 3.0640192 0.9999982
## 2001-2000 0.284109589 -2.030023979 2.5982432 1.0000000
## 2002-2000 -0.334246575 -2.648380144 1.9798870 1.0000000
## 2003-2000 0.438356164 -1.875777404 2.7524897 1.0000000
## 2004-2000 0.123296654 -2.189255682 2.4358490 1.0000000
## 2005-2000 -0.056164384 -2.370297952 2.2579692 1.0000000
## 2006-2000 0.088493151 -2.225640418 2.4026267 1.0000000
## 2007-2000 0.607619299 -1.708103102 2.9233417 1.0000000
## 2008-2000 -0.570692417 -2.883244753 1.7418599 1.0000000
## 2009-2000 -0.624657534 -2.938791103 1.6894760 1.0000000
## 2010-2000 -0.289315068 -2.603448637 2.0248185 1.0000000
## 2011-2000 -0.805753425 -3.119886993 1.5083801 0.9999912
## 2012-2000 0.300072610 -2.012479726 2.6126249 1.0000000
## 2013-2000 -0.117808219 -2.431941788 2.1963253 1.0000000
## 2014-2000 0.454794521 -1.859339048 2.7689281 1.0000000
## 2015-2000 1.160273973 -1.153859596 3.4744075 0.9921157
## 2016-2000 0.541329441 -1.771222895 2.8538818 1.0000000
## 2017-2000 0.257808219 -2.056325349 2.5719418 1.0000000
## 2018-2000 0.287123288 -2.027010281 2.6012569 1.0000000
## 2019-2000 -0.447945205 -2.762078774 1.8661884 1.0000000
## 2020-2000 0.098979714 -2.213572622 2.4115320 1.0000000
## 2002-2001 -0.618356164 -2.932489733 1.6957774 1.0000000
## 2003-2001 0.154246575 -2.159886993 2.4683801 1.0000000
## 2004-2001 -0.160812935 -2.473365271 2.1517394 1.0000000
## 2005-2001 -0.340273973 -2.654407541 1.9738596 1.0000000
## 2006-2001 -0.195616438 -2.509750007 2.1185171 1.0000000
## 2007-2001 0.323509709 -1.992212691 2.6392321 1.0000000
## 2008-2001 -0.854802006 -3.167354342 1.4577503 0.9999686
## 2009-2001 -0.908767123 -3.222900692 1.4053664 0.9998920
## 2010-2001 -0.573424658 -2.887558226 1.7407089 1.0000000
## 2011-2001 -1.089863014 -3.403996582 1.2242706 0.9970487
## 2012-2001 0.015963021 -2.296589315 2.3285154 1.0000000
## 2013-2001 -0.401917808 -2.716051377 1.9122158 1.0000000
## 2014-2001 0.170684932 -2.143448637 2.4848185 1.0000000
## 2015-2001 0.876164384 -1.437969185 3.1902980 0.9999484
## 2016-2001 0.257219852 -2.055332484 2.5697722 1.0000000
## 2017-2001 -0.026301370 -2.340434938 2.2878322 1.0000000
## 2018-2001 0.003013699 -2.311119870 2.3171473 1.0000000
## 2019-2001 -0.732054795 -3.046188363 1.5820788 0.9999990
## 2020-2001 -0.185129875 -2.497682211 2.1274225 1.0000000
## 2003-2002 0.772602740 -1.541530829 3.0867363 0.9999965
## 2004-2002 0.457543229 -1.855009107 2.7700956 1.0000000
## 2005-2002 0.278082192 -2.036051377 2.5922158 1.0000000
## 2006-2002 0.422739726 -1.891393842 2.7368733 1.0000000
## 2007-2002 0.941865874 -1.373856527 3.2575883 0.9997853
## 2008-2002 -0.236445842 -2.548998178 2.0761065 1.0000000
## 2009-2002 -0.290410959 -2.604544527 2.0237226 1.0000000
## 2010-2002 0.044931507 -2.269202061 2.3590651 1.0000000
## 2011-2002 -0.471506849 -2.785640418 1.8426267 1.0000000
## 2012-2002 0.634319186 -1.678233150 2.9468715 1.0000000
## 2013-2002 0.216438356 -2.097695212 2.5305719 1.0000000
## 2014-2002 0.789041096 -1.525092472 3.1031747 0.9999945
## 2015-2002 1.494520548 -0.819613020 3.8086541 0.8376847
## 2016-2002 0.875576016 -1.436976320 3.1881284 0.9999484
## 2017-2002 0.592054795 -1.722078774 2.9061884 1.0000000
## 2018-2002 0.621369863 -1.692763705 2.9355034 1.0000000
## 2019-2002 -0.113698630 -2.427832198 2.2004349 1.0000000
## 2020-2002 0.433226289 -1.879326046 2.7457786 1.0000000
## 2004-2003 -0.315059510 -2.627611846 1.9974928 1.0000000
## 2005-2003 -0.494520548 -2.808654116 1.8196130 1.0000000
## 2006-2003 -0.349863014 -2.663996582 1.9642706 1.0000000
## 2007-2003 0.169263134 -2.146459266 2.4849855 1.0000000
## 2008-2003 -1.009048581 -3.321600917 1.3035038 0.9992051
## 2009-2003 -1.063013699 -3.377147267 1.2511199 0.9980516
## 2010-2003 -0.727671233 -3.041804801 1.5864623 0.9999991
## 2011-2003 -1.244109589 -3.558243157 1.0700240 0.9787865
## 2012-2003 -0.138283554 -2.450835890 2.1742688 1.0000000
## 2013-2003 -0.556164384 -2.870297952 1.7579692 1.0000000
## 2014-2003 0.016438356 -2.297695212 2.3305719 1.0000000
## 2015-2003 0.721917808 -1.592215760 3.0360514 0.9999993
## 2016-2003 0.102973276 -2.209579059 2.4155256 1.0000000
## 2017-2003 -0.180547945 -2.494681514 2.1335856 1.0000000
## 2018-2003 -0.151232877 -2.465366445 2.1629007 1.0000000
## 2019-2003 -0.886301370 -3.200434938 1.4278322 0.9999347
## 2020-2003 -0.339376450 -2.651928786 1.9731759 1.0000000
## 2005-2004 -0.179461038 -2.492013373 2.1330913 1.0000000
## 2006-2004 -0.034803503 -2.347355839 2.2777488 1.0000000
## 2007-2004 0.484322645 -1.829819609 2.7984649 1.0000000
## 2008-2004 -0.693989071 -3.004959092 1.6169810 0.9999997
## 2009-2004 -0.747954188 -3.060506524 1.5645981 0.9999983
## 2010-2004 -0.412611722 -2.725164058 1.8999406 1.0000000
## 2011-2004 -0.929050079 -3.241602414 1.3835023 0.9998309
## 2012-2004 0.176775956 -2.134194065 2.4877460 1.0000000
## 2013-2004 -0.241104873 -2.553657209 2.0714475 1.0000000
## 2014-2004 0.331497867 -1.981054469 2.6440502 1.0000000
## 2015-2004 1.036977319 -1.275575017 3.3495297 0.9987118
## 2016-2004 0.418032787 -1.892937234 2.7290028 1.0000000
## 2017-2004 0.134511565 -2.178040771 2.4470639 1.0000000
## 2018-2004 0.163826634 -2.148725702 2.4763790 1.0000000
## 2019-2004 -0.571241859 -2.883794195 1.7413105 1.0000000
## 2020-2004 -0.024316940 -2.335286961 2.2866531 1.0000000
## 2006-2005 0.144657534 -2.169476034 2.4587911 1.0000000
## 2007-2005 0.663783682 -1.651938718 2.9795061 0.9999999
## 2008-2005 -0.514528034 -2.827080369 1.7980243 1.0000000
## 2009-2005 -0.568493151 -2.882626719 1.7456404 1.0000000
## 2010-2005 -0.233150685 -2.547284253 2.0809829 1.0000000
## 2011-2005 -0.749589041 -3.063722609 1.5645445 0.9999983
## 2012-2005 0.356236994 -1.956315342 2.6687893 1.0000000
## 2013-2005 -0.061643836 -2.375777404 2.2524897 1.0000000
## 2014-2005 0.510958904 -1.803174664 2.8250925 1.0000000
## 2015-2005 1.216438356 -1.097695212 3.5305719 0.9843885
## 2016-2005 0.597493824 -1.715058511 2.9100462 1.0000000
## 2017-2005 0.313972603 -2.000160966 2.6281062 1.0000000
## 2018-2005 0.343287671 -1.970845897 2.6574212 1.0000000
## 2019-2005 -0.391780822 -2.705914390 1.9223527 1.0000000
## 2020-2005 0.155144098 -2.157408238 2.4676964 1.0000000
## 2007-2006 0.519126148 -1.796596253 2.8348485 1.0000000
## 2008-2006 -0.659185568 -2.971737904 1.6533668 0.9999999
## 2009-2006 -0.713150685 -3.027284253 1.6009829 0.9999994
## 2010-2006 -0.377808219 -2.691941788 1.9363253 1.0000000
## 2011-2006 -0.894246575 -3.208380144 1.4198870 0.9999218
## 2012-2006 0.211579460 -2.100972876 2.5241318 1.0000000
## 2013-2006 -0.206301370 -2.520434938 2.1078322 1.0000000
## 2014-2006 0.366301370 -1.947832198 2.6804349 1.0000000
## 2015-2006 1.071780822 -1.242352746 3.3859144 0.9977628
## 2016-2006 0.452836290 -1.859716046 2.7653886 1.0000000
## 2017-2006 0.169315068 -2.144818500 2.4834486 1.0000000
## 2018-2006 0.198630137 -2.115503431 2.5127637 1.0000000
## 2019-2006 -0.536438356 -2.850571925 1.7776952 1.0000000
## 2020-2006 0.010486563 -2.302065772 2.3230389 1.0000000
## 2008-2007 -1.178311716 -3.492453969 1.1358305 0.9900910
## 2009-2007 -1.232276833 -3.547999233 1.0834456 0.9815235
## 2010-2007 -0.896934367 -3.212656767 1.4187880 0.9999181
## 2011-2007 -1.413372723 -3.729095124 0.9023497 0.9051372
## 2012-2007 -0.307546688 -2.621688942 2.0065956 1.0000000
## 2013-2007 -0.725427518 -3.041149918 1.5902949 0.9999992
## 2014-2007 -0.152824778 -2.468547178 2.1628976 1.0000000
## 2015-2007 0.552654674 -1.763067726 2.8683771 1.0000000
## 2016-2007 -0.066289858 -2.380432111 2.2478524 1.0000000
## 2017-2007 -0.349811079 -2.665533480 1.9659113 1.0000000
## 2018-2007 -0.320496011 -2.636218411 1.9952264 1.0000000
## 2019-2007 -1.055564504 -3.371286904 1.2601579 0.9982910
## 2020-2007 -0.508639584 -2.822781838 1.8055027 1.0000000
## 2009-2008 -0.053965117 -2.366517453 2.2585872 1.0000000
## 2010-2008 0.281377349 -2.031174987 2.5939297 1.0000000
## 2011-2008 -0.235061008 -2.547613343 2.0774913 1.0000000
## 2012-2008 0.870765027 -1.440204994 3.1817350 0.9999533
## 2013-2008 0.452884198 -1.859668138 2.7654365 1.0000000
## 2014-2008 1.025486938 -1.287065398 3.3380393 0.9989402
## 2015-2008 1.730966390 -0.581585946 4.0435187 0.5464563
## 2016-2008 1.112021858 -1.198948163 3.4229919 0.9958238
## 2017-2008 0.828500636 -1.484051700 3.1410530 0.9999838
## 2018-2008 0.857815705 -1.454736631 3.1703680 0.9999662
## 2019-2008 0.122747212 -2.189805124 2.4352995 1.0000000
## 2020-2008 0.669672131 -1.641297890 2.9806422 0.9999999
## 2010-2009 0.335342466 -1.978791103 2.6494760 1.0000000
## 2011-2009 -0.181095890 -2.495229459 2.1330377 1.0000000
## 2012-2009 0.924730144 -1.387822191 3.2372825 0.9998457
## 2013-2009 0.506849315 -1.807284253 2.8209829 1.0000000
## 2014-2009 1.079452055 -1.234681514 3.3935856 0.9974805
## 2015-2009 1.784931507 -0.529202061 4.0990651 0.4751223
## 2016-2009 1.165986975 -1.146565361 3.4785393 0.9914286
## 2017-2009 0.882465753 -1.431667815 3.1965993 0.9999403
## 2018-2009 0.911780822 -1.402352746 3.2259144 0.9998847
## 2019-2009 0.176712329 -2.137421240 2.4908459 1.0000000
## 2020-2009 0.723637248 -1.588915087 3.0361896 0.9999992
## 2011-2010 -0.516438356 -2.830571925 1.7976952 1.0000000
## 2012-2010 0.589387679 -1.723164657 2.9019400 1.0000000
## 2013-2010 0.171506849 -2.142626719 2.4856404 1.0000000
## 2014-2010 0.744109589 -1.570023979 3.0582432 0.9999985
## 2015-2010 1.449589041 -0.864544527 3.7637226 0.8773336
## 2016-2010 0.830644509 -1.481907826 3.1431968 0.9999829
## 2017-2010 0.547123288 -1.767010281 2.8612569 1.0000000
## 2018-2010 0.576438356 -1.737695212 2.8905719 1.0000000
## 2019-2010 -0.158630137 -2.472763705 2.1555034 1.0000000
## 2020-2010 0.388294783 -1.924257553 2.7008471 1.0000000
## 2012-2011 1.105826035 -1.206726301 3.4183784 0.9962222
## 2013-2011 0.687945205 -1.626188363 3.0020788 0.9999998
## 2014-2011 1.260547945 -1.053585623 3.5746815 0.9747714
## 2015-2011 1.966027397 -0.348106171 4.2801610 0.2597237
## 2016-2011 1.347082865 -0.965469470 3.6596352 0.9427148
## 2017-2011 1.063561644 -1.250571925 3.3776952 0.9980345
## 2018-2011 1.092876712 -1.221256856 3.4070103 0.9969123
## 2019-2011 0.357808219 -1.956325349 2.6719418 1.0000000
## 2020-2011 0.904733139 -1.407819197 3.2172855 0.9998998
## 2013-2012 -0.417880829 -2.730433165 1.8946715 1.0000000
## 2014-2012 0.154721910 -2.157830425 2.4672742 1.0000000
## 2015-2012 0.860201362 -1.452350973 3.1727537 0.9999642
## 2016-2012 0.241256831 -2.069713191 2.5522269 1.0000000
## 2017-2012 -0.042264391 -2.354816727 2.2702879 1.0000000
## 2018-2012 -0.012949323 -2.325501658 2.2996030 1.0000000
## 2019-2012 -0.748017816 -3.060570151 1.5645345 0.9999983
## 2020-2012 -0.201092896 -2.512062917 2.1098771 1.0000000
## 2014-2013 0.572602740 -1.741530829 2.8867363 1.0000000
## 2015-2013 1.278082192 -1.036051377 3.5922158 0.9698586
## 2016-2013 0.659137660 -1.653414676 2.9716900 0.9999999
## 2017-2013 0.375616438 -1.938517130 2.6897500 1.0000000
## 2018-2013 0.404931507 -1.909202061 2.7190651 1.0000000
## 2019-2013 -0.330136986 -2.644270555 1.9839966 1.0000000
## 2020-2013 0.216787933 -2.095764403 2.5293403 1.0000000
## 2015-2014 0.705479452 -1.608654116 3.0196130 0.9999996
## 2016-2014 0.086534920 -2.226017416 2.3990873 1.0000000
## 2017-2014 -0.196986301 -2.511119870 2.1171473 1.0000000
## 2018-2014 -0.167671233 -2.481804801 2.1464623 1.0000000
## 2019-2014 -0.902739726 -3.216873294 1.4113938 0.9999055
## 2020-2014 -0.355814806 -2.668367142 1.9567375 1.0000000
## 2016-2015 -0.618944532 -2.931496868 1.6936078 1.0000000
## 2017-2015 -0.902465753 -3.216599322 1.4116678 0.9999060
## 2018-2015 -0.873150685 -3.187284253 1.4409829 0.9999519
## 2019-2015 -1.608219178 -3.922352746 0.7059144 0.7109692
## 2020-2015 -1.061294259 -3.373846594 1.2512581 0.9980821
## 2017-2016 -0.283521222 -2.596073557 2.0290311 1.0000000
## 2018-2016 -0.254206153 -2.566758489 2.0583462 1.0000000
## 2019-2016 -0.989274646 -3.301826982 1.3232777 0.9994449
## 2020-2016 -0.442349727 -2.753319748 1.8686203 1.0000000
## 2018-2017 0.029315068 -2.284818500 2.3434486 1.0000000
## 2019-2017 -0.705753425 -3.019886993 1.6083801 0.9999996
## 2020-2017 -0.158828505 -2.471380841 2.1537238 1.0000000
## 2019-2018 -0.735068493 -3.049202061 1.5790651 0.9999989
## 2020-2018 -0.188143574 -2.500695909 2.1244088 1.0000000
## 2020-2019 0.546924920 -1.765627416 2.8594773 1.0000000