Lab 8

Leavin’ on a jet plane, confidently

Lab

Due: End of lab on Thurs, April 16

Introduction

In this lab you’ll explore the relationship between distance and air time of flights out of RDU in 2024.

And you’ll work in what’s considered a pretty unlikely situation: you have access to population data – all flights out of RDU in 2024! But we’ll ask you to pretend that you didn’t actually have access and you need to work with sample data. How? Hang in there, get the population data loaded first, then we’ll explain the next steps!

Getting started

By now you should be familiar with how to get started with a lab assignment by cloning the GitHub repo for the assignment. If you’re not sure how, refer back to an earlier lab.

Open the lab-8.qmd template Quarto file and update the authors field to add your name first (first and last) and then your teammates’ names (first and last). Render the document. Examine the rendered document and make sure your and your teammates’ names are updated in the document. Commit and push your changes with a meaningful commit message and push to GitHub.

Click to expand if you need a refresher on assignment guidelines.

Code

Code should follow the tidyverse style. Particularly,

there should be spaces before and line breaks after each + when building a ggplot,
there should also be spaces before and line breaks after each |> in a data transformation pipeline,
code should be properly indented,
there should be spaces around = signs and spaces after commas.

Additionally, all code should be visible in the PDF output, i.e., should not run off the page on the PDF. Long lines that run off the page should be split across multiple lines with line breaks.¹

Plots

Plots should have an informative title and, if needed, also a subtitle.
Axes and legends should be labeled with both the variable name and its units (if applicable).
Careful consideration should be given to aesthetic choices.

Workflow

Continuing to develop a sound workflow for reproducible data analysis is important as you complete the lab and other assignments in this course.

You should have at least 3 commits with meaningful commit messages by the end of the assignment.
Final versions of both your .qmd file and the rendered PDF should be pushed to GitHub.

Packages

In this lab we will work with the tidyverse and tidymodels packages.

library(tidyverse)
library(tidymodels)

Population data

The dataset, called rdu-flights.csv, can be found in the data folder.

Questions

Question 1 - Sample

Take a random sample of 100 flights and store it as rdu_flights_sample. Make sure that you use the same seed as your teammates.

Tip

The following code allows you to obtain a random sample of N observations from a larger dataset. Update the code below to complete Question 1.

set.seed(___)
df_sample <- df_full |>
  slice(sample(1:nrow(df_full), N))

Question 2 - Visualize

Visualize the relationship between distance (x) and air_time (y) using a scatter plot. Add a regression line to the scatter plot, but do not display the standard error ribbon around the regression line. Comment on the observed relationship.

Question 3 - Bootstrap

Compute a 95% bootstrap interval for the slope of the regression line for predicting air_time from distance. In your code, use 1,000 bootstrap samples when simulating your bootstrap distribution. Note that you should have already set a seed in your answer to Question 1; thus, you should not set a new seed.

In your narrative, provide an interpretation of the 95% confidence interval for the slope (hint: refer back to “notes 22” on the course website).

Tip

Below is a step-by-step recipe for constructing and visualizing a confidence interval. The code snippets shown are not “complete.” They include some blanks you need to fill in, and they are just intended to guide you in the right direction.

Step 1: Calculate the point estimate for the slope and the intercept of the regression line.

obs_fit <- rdu_flights_sample |>
  specify(______ ~ ______) |>
  fit()

Step 2: Simulate a bootstrap distribution of regression estimates.

boot_dist <- rdu_flights_sample |>
  specify(_____ ~ ______) |>
  generate(reps = ____, type = _______) |>
  fit()

Step 3: Calculate the bounds of the confidence interval.

conf_ints <- 
  get_confidence_interval(
    ____, 
    level = ___, 
    point_estimate = ____
  )

Question 4: Hypothesize

Set the null hypothesis:

What if there was no relationship between distance and air_time? What would the true slope of the relationship be in that case? This is your null hypothesis. You can articulate it as:

\(H_0:\) There is no relationship between distance and air time, the value of the true slope is ____, i.e., \(\beta_1\) = ____.

Fill in the blanks.

Tip

The null hypothesis always sets the true population parameter equal to a specific value.
Set the alternative hypothesis:

What if there is a relationship between distance and air_time? This is your alternative hypothesis!

\(H_A:\) There is a relationship between distance and air time, the value of the true slope is ____, i.e., \(\beta_1\) ______.

Fill in the blanks.

Tip

The alternative hypothesis always compares the true population parameter to the same specific value set in the null hypothesis. This comparison can be “not equal to”, “greater than”, or “less than” and the choice depends on the research question. In this case, our research question is whether there is some relationship between distance and air time.
Based on the 95% confidence interval you came up with in Question 3, would you expect to fail to reject or to reject the above null hypothesis at the 5% significance level? Explain your reasoning.

Wrap-up

Warning

Before you wrap up the assignment, make sure that you render, commit, and push one final time so that the final versions of both your .qmd file and the rendered PDF are pushed to GitHub and your Git pane is empty. We will be checking these to make sure you have been practicing how to commit and push changes.

Submission

By now you should also be familiar with how to submit your assignment in Gradescope.

Click to expand if you need a refresher on how to get started with a lab assignment.

Submit your PDF document to Gradescope by the end of the lab to be considered “on time”:

Go to http://www.gradescope.com and click Log in in the top right corner.
Click School Credentials \(\rightarrow\) Duke NetID and log in using your NetID credentials.
Click on your STA 199 course.
Click on the assignment, and you’ll be prompted to submit it.
Mark all the pages associated with question. All the pages of your lab should be associated with at least one question (i.e., should be “checked”).

Checklist

Make sure you have:

attempted all questions
rendered your Quarto document
committed and pushed everything to your GitHub repository such that the Git pane in RStudio is empty
uploaded your PDF to Gradescope

Grading and feedback

This lab is worth 30 points:
- 10 points for being in lab and turning in something – no partial credit for this part.
- 20 points for:
  - answering the questions correctly – there is partial credit for this part.
  - following the workflow – there is partial credit for this part.
The workflow points are for:
- committing at least three times as you work through your lab,
- having your final version of .qmd and .pdf files in your GitHub repository, and
- overall organization.
You’ll receive feedback on your lab on Gradescope within a week.

Good luck, and have fun with it!

Footnotes

Remember, haikus not novellas when writing code!↩︎