AN/BI588: Homework 04

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Course Outline

Course Overview

Modules

Assignments

Resources

Policies

Insurmountable Coding Problems

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What’s Your Malfunction?

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Must be submitted for Peer Commentary by 8:00 pm Wednesday, October 25th.

Peer Commentary and Final Homework DUE at 5:00 pm Wednesday, November 1st.

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Create a new GitHub repo and git-referenced Rstudio Project called “AN588_Malfunction_BUlogin”. Within that repo, create a new .Rmd file called “BUlogin_OriginalHomeworkCode_04”. Don’t forget to add your Peer Group and instructor as collaborators, and to accept their invitations to you. Making sure to push both the markdown and knitted .html files to your repository, do the following:

[1] Write a simple R function, Z.prop.test(), that can perform one- or two-sample Z-tests for proportion data, using the following guidelines:

• Your function should take the following arguments: p1 and n1 (no default) representing the estimated proportion and sample size (i.e., based on your sample data); p2 and n2 (both defaulting to NULL) that contain a second sample’s proportion and sample size data in the event of a two-sample test; p0 (no default) as the expected value for the population proportion; and alternative (default “two.sided”) and conf.level (default 0.95), to be used in the same way as in the function t.test().
• When conducting a two-sample test, it should be p1 that is tested as being smaller or larger than p2 when alternative=“less” or alternative=“greater”, the same as in the use of x and y in the function t.test().
• The function should perform a one-sample Z-test using p1, n1, and p0 if either p2 or n2 (or both) is NULL.
• The function should contain a check for the rules of thumb we have talked about (\(n * p > 5\) and \(n * (1-p) > 5\)) to ensure the validity of assuming the normal distribution in both the one- and two-sample settings. If this is violated, the function should still complete but it should also print an appropriate warning message.
• The function should return a list containing the members Z (the test statistic), P (the appropriate p value), and CI (the two-sided CI with respect to “conf.level” around p1 in the case of a one-sample test and around p2-p1 in the case of a two-sample test). For all test alternatives (“two.sided”, “greater”, “less”), calculate symmetric CIs based on quantiles of the normal distribution rather than worrying about calculating single-limit confidence bounds.

[2] The dataset from Kamilar and Cooper has in it a large number of variables related to life history and body size. For this exercise, the end aim is to fit a simple linear regression model to predict longevity (MaxLongevity_m) measured in months from species’ brain size (Brain_Size_Species_Mean) measured in grams. Do the following for both longevity~brain size and log(longevity)~log(brain size):

• Fit the regression model and, using {ggplot2}, produce a scatterplot with the fitted line superimposed upon the data. Append the the fitted model equation to your plot (HINT: use the function geom_text()).
• Identify and interpret the point estimate of the slope (\(\beta_1\)), as well as the outcome of the test associated with the hypotheses H0: \(\beta_1\) = 0; HA: \(\beta_1\) ≠ 0. Also, find a 90 percent CI for the slope (\(\beta_1\)) parameter.
• Using your model, add lines for the 90 percent confidence and prediction interval bands on the plot and add a legend to differentiate between the lines.
• Produce a point estimate and associated 90 percent PI for the longevity of a species whose brain weight is 800 gm. Do you trust the model to predict observations accurately for this value of the explanatory variable? Why or why not?
• Looking at your two models, which do you think is better? Why?

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Your Final Assignment for Homework 03

Your final assignment, due to me by 5:00 pm on November 1st, is to have in your AN588_Malfunction_BUlogin repo only the following files (aside from repo basics like an .Rproj and README file):

1. The FINAL PUSH of your Original Homework Code, including the five challenges you faced, as pushed to your repo by 5:00 pm on Wednesday, November 1st, an R Markdown file named BUlogin_OriginalHomeworkCode_04.
2. The FINAL PUSH of the Peer Commentary made on your code, an R Markdown file named Peerlogin_PeerCommentary_BUlogin_04 or PeerGroupX_PeerCommentary_BUlogin_04.
3. The FINAL PUSH of your Final Homework Code, which has taken into account any changes recommended from the Peer Commentary and notes, an R Markdown file named BUlogin_FinalHomeworkCode_04.

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Homework 04 Solutions will be posted on November 2nd.

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NOTE: If you want your homework code to look nice (beyond being very well annotated and commented), and be easy to use by others, you can check out the relatively simply example R Markdown templates in the AN588_Week_3_caschmit repo.

Please also consider consulting the following helpful guidelines on how to write effective R Markdown documents (also available at the end of Module 03), which go well beyond the simple formatting of the templates.

• An introduction to R Markdown
• R Markdown: The Definitive Guide
• R Markdown Cheatsheet
• Another R Markdown Cheatsheet
• Pimp my RMD: A Few Tips for R Markdown
• R Markdown Templates for Journal Submissions
• Using R Markdown for Class Reports
• R Markdown Theme Gallery
• Creating Pretty Documents from R Markdown