Complete exercises $q,$

$q,,11\mathrm{.}12q,$ You are going to skip $11\mathrm{.}11.$ In $11\mathrm{.}13,$ you will compare models built to address $11\mathrm{.}10,11\mathrm{.}12,$ and $11\mathrm{.}13.$

Submit your work as two attachments: $(1)$an HTML document containing all the code $+$ associated explanations $+$ outputs $+$ your interpretation of the results, organized in a systematic way with appropriate sections and subsections, and $(2)$ the $.$Rmd version of the file can be extracted, or directly as a $.$Rmd file.

Your submission should include an appropriate header that indicates the assignment number and week number, and include your name to appear prominently $($consult this week's notebook and $.$Rmd files for reference$).$ Ensure that your written responses have no issues of spelling and grammar that affect the clarity of your explanations. Also ensure that you partition the document into specific sections that map onto the specific exercise question numbers $($e$.$g$.,$ have specific sections for $11\mathrm{.}10,11,12.,$ and so on$).$

Reference requirement:

Provide references to specific sections from the textbook and$/$or the lecture notes and$/$or lecture videos for your choice of priors and the rationale associated with your interpretation of results of your analyses.

Here is That you have to solve $($Will give you rating if solve correct$)$ :

Question:

Exercise $11\mathrm{.}13($Penguins$!$ Comparing models$)$

Consider $4$ separate models of body$\_$mass$\_$g :

$\backslash$table$[[$model$,$formula$],[1,$body$\_$mass$\_$g flipper$\_$length$\_$mm$],[2,$body$\_$mass$\_$g species$],[3,\backslash$table$[[$body$\_$mass$\_$g $$ flipper$\_$length$\_$mm $+],[$species$]]],[4,\backslash$table$[[\backslash$table$[[$body$\_$mass$\_$g flipper$\_$length$\_$mm $+],[$bill$\_$length$\_$mm $+$ bill$\_$depth$\_$mm$]]]]]]$

a$.$ Simulate these four models using the function.

b$.$ Produce and compare the plots for the four models.

c$.$ Use $10-$fold cross$-$validation to assess and compare the posterior predictive quality of the four models using the

prediction$\_$summary$\_$cv$().$ NOTE: We can only predict body mass for penguins that have complete information on our model predictors. Yet two penguins have NA values for multiple of these predictors. To remove these two penguins, we select$()$ our columns of interest before removing penguins with NA values. This way, we don't throw out penguins just because they're missing information on variables we don't care about:d$.$ Evaluate and compare the ELPD posterior predictive accuracy of the four models.e$.$ In summary, which of these four models is "best?" Explain.