Clone the repo & start new RStudio project

• Go to the sta210-sp21 organization on GitHub . Click on the repo with the prefix lab-02-. It contains the starter documents you need to complete the lab.

• Click on the green Code button, select Use HTTPS. Click on the clipboard icon to copy the repo URL.

• Go to https://vm-manage.oit.duke.edu/containers and login with your Duke NetId and Password.

• Click to log into the Docker container STA 210 - Regression Analysis. You should now see the RStudio environment.

• Go to File ➡️ New Project ➡️ Version Control ➡️ Git.

• Copy and paste the URL of your assignment repo into the dialog box Repository URL.

• Click Create Project, and the files from your GitHub repo will be displayed the Files pane in RStudio.

Configure git

One more thing before you get started. We need to configure your git so that RStudio can communicate with GitHub. This requires two pieces of information: your GitHub username and the email address associated with your GitHub account.

Type the following lines of code in the console in RStudio filling in your name and email address.

library(usethis)
use_git_config(user.name = "GitHub username", 
               user.email="your email")

Now you’re ready to start! Open the R Markdown file (the one with extension .Rmd) to begin the assignment.

YAML

⊕The top portion of your R Markdown file (between the three dashed lines) is called YAML. It stands for “YAML Ain’t Markup Language”. It is a human friendly data serialization standard for all programming languages. All you need to know is that this area is called the YAML (we will refer to it as such) and that it contains meta information about your document.

Before we introduce the data, let’s update the name and date in the YAML.

Open the R Markdown (Rmd) file in your project, input your name for the author name and today’s date for the date, and knit the document.

Committing and pushing changes:

• Go to the Git pane in your RStudio.
• Select all of the files that appear in the Git pane.
• Click to commit. Add a short and informative commit message. - Click to Push. This will prompt a dialogue box where you first need to enter your user name, and then your password.

Make sure you push all the files from the Git pane to your assignment repo on GitHub. The Git pane should be empty after you push. If it’s not, click the box next to the remaining files, write an informative commit message, and push.

Instructions

Write all code and narrative in your R Markdown file. Throughout the assignment, you should periodically knit your R Markdown document to produce the updated PDF, commit the changes in the Git pane, and push the updated files to GitHub.

As you complete the lab…

✅ Write all narrative in complete sentences.

✅ Use an informative title and informative axis labels on all visualizations.

We want to explore whether there is a difference between the typical length of trails that allow dog walking versus those that don’t. To answer this question, we will use statistical inference to determine if the mean length differs between the two types of trails.

1. Let’s begin by examining the distribution of the trail status with a data visualization and summary statistics.

   • Create a visualization for the distribution of status, and calculate the proportion of observations in each category of status. You can use the code belwo to help you calculate the proportions.
   • Use the plot and summary statistics to describe the distribution of status.

_____ %>%
  count(_____) %>%
  mutate(proportion = n / sum(n))

2. Since the primary goal is to analyze the length of trails for trails in Durham, we will just use data for trails that existed as of November 18, 2019, the latest edit date in the data. Create a subset that only includes existing trails. You will use the subset of existing trails for exercises 3 - 7.

3. Next let’s examine the distribution of length for existing trails. Make a graph to visualize the distribution of length.

⊕See Section 7.3.1 “Visualizing Distributions” or the ggplot2 reference page for details and example code.

4. Though we can approximate the center and spread of a distribution from visualizations, it is useful to calculate summary statistics to more precisely describe distributions. Calculate the following summary statistics for length:

   • min, max
   • mean, median
   • Q1, Q3
   • IQR, standard deviation

Hint: You can use the summarise reference page for code and examples.

5. Which summary statistics are most useful for describing the distribution of length? In other words, which summary statistics most accurately reflect the center and spread of the distribution? Briefly explain.

6. Use the visualization and summary statistics to describe the distribution of length. Include a description of the shape, center, spread, and potential outliers.

7. People are more likely to take their dogs on trails that can be completed in a day, so let’s focus on trails could be feasibly completed as a day hike. Create a subset that only includes existing trails that are 10 miles or less. You will use this subset for the remainder of the lab.

8. Now that we’ve explored length, let’s look at the distribution of dogwalking.
   • What are the values of dogwalking in the dataset? To answer this question, use code to list the values of dogwalking and how often each one occurs. Note: We use code to help us answer this question, so we can produce the result in a reproducible way.
   • Consider the values of dogwalking currently in the data. What do you think a missing value of dogwalking most likely indicates?
9. Complete the code below to impute (i.e. fill in) the missing values of dogwalking with the most reasonable value. Then, display the distribution of dogwalking to check that the missing values were correctly imputed.

_____ <- _____ %>%
  mutate(dogwalking = if_else(is.na(dogwalking), ______, dogwalking))

10. Now that we’ve completed the univariate EDA (i.e. examining one variable at a time), let’s examine the relationship between the length of the trail and whether dog walking is allowed. Make a graph to visualize the relationship between length and dogwalking and calculate the appropriate summary statistics. Include informative axis labels and title on your graph.

11. Describe the relationship between length and dogwalking. In other words, describe how the distribution of length compares between trails that allow dog walking versus those that don’t. Include information from the graph and summary statistics from the previous exercise in your response.

12. Let’s use statistical inference to determine if the data provide sufficient evidence of a difference in the mean length between trails that allow dog walking and those that don’t. We’ll begin with a hypothesis test. The null and alternative hypotheses are the following:

\[\begin{align} &H_0: \mu_{yes} = \mu_{no} \\ &H_a: \mu_{yes} \neq \mu_{no}\end{align}\]

• State the null and alternative in words in the context of the data.

• Conduct the test in R. Show the code and resulting output.

• What does the test statistic mean? Write your response in the context of the data.

• State the conclusion of the test in the context of the data.

13. Let’s calculate a confidence interval to estimate the difference in the mean length between trails that allow dog-walking and those that don’t. If it isn’t displayed in Exercise 12, show the code and output to calculate the confidence interval. Then, interpret your interval in the context of the data.