Activity 38

MATH 216: Statistical Thinking

Activity 1: Think-Pair-Share

  • How does the value of \(r\) influence the interpretation of \(r^2\)?

  • Can \(r^2\) ever be negative? Why or why not?

Activity 2: Quiz

  • Given \(r = 0.8\), what is the value of \(r^2\)?

  • If \(r^2 = 0.64\), what percentage of the variability in \(y\) is explained by \(x\)?

Activity 3: Data Exploration

  1. Use the cor() function to calculate \(r\) between two variables (e.g., mpg and hp).

  2. Create a scatterplot using ggplot2 to visualize the relationship.

  3. Derive \(r^2\) manually and interpret its meaning.

Activity 4: Real Data

  • Given a dataset iris answer the following questions:

    1. Calculate \(r\) and \(r^2\) for Sepal.Length and Petal.Length.
    2. Interpret the strength and direction of the relationship.