Version information for results:

R version 4.5.0 (2025-04-11)
Platform: x86_64-apple-darwin20
Running under: macOS Sequoia 15.6.1

Matrix products: default
BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.5-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/New_York
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] viridis_0.6.5        viridisLite_0.4.2    plot3D_1.4.1         lhs_1.2.0            statmod_1.5.0       
 [6] orthopolynom_1.0-6.1 openintro_2.5.0      usdata_0.3.1         cherryblossom_0.1.0  airports_0.1.0      
[11] lubridate_1.9.4      forcats_1.0.0        stringr_1.5.1        dplyr_1.1.4          purrr_1.0.4         
[16] readr_2.1.5          tidyr_1.3.1          tibble_3.2.1         ggplot2_3.5.2        tidyverse_2.0.0     

loaded via a namespace (and not attached):
 [1] utf8_1.2.4         generics_0.1.4     tcltk_4.5.0        stringi_1.8.7      hms_1.1.3          digest_0.6.37     
 [7] magrittr_2.0.3     evaluate_1.0.4     grid_4.5.0         timechange_0.3.0   RColorBrewer_1.1-3 fastmap_1.2.0     
[13] misc3d_0.9-1       gridExtra_2.3      scales_1.4.0       cli_3.6.5          rlang_1.1.6        withr_3.0.2       
[19] yaml_2.3.10        tools_4.5.0        polynom_1.4-1      tzdb_0.5.0         vctrs_0.6.5        R6_2.6.1          
[25] lifecycle_1.0.4    pkgconfig_2.0.3    pillar_1.10.2      gtable_0.3.6       glue_1.8.0         Rcpp_1.0.14       
[31] xfun_0.52          tidyselect_1.2.1   rstudioapi_0.17.1  knitr_1.50         farver_2.1.2       htmltools_0.5.8.1 
[37] rmarkdown_2.29     labeling_0.4.3     compiler_4.5.0    