Scatterplots and Describing a Relationship
Day 19 - Lesson 3.1
Distinguish between explanatory and response variables for quantitative data.
Make a scatterplot to display the relationship between two quantitative variables
Describe the direction, form, and strength of a relationship displayed in a scatterplot and identify unusual features.
Activity: How Many Rubber Bands Does Barbie Need?
We are going to try and teach Chapter 3 with a single question in mind:
How many rubber bands should we attach to Barbie so that she has the absolute most fun bungee jump from the balcony in the front foyer of the school?
In groups, students collect data on how far Barbie would travel using 0,1,2,3,4,5,6 and 7 rubber bands. Then they created scatterplots to see if there was a pattern (should be a very linear pattern!).
We will use the Barbie Bungee context to teach many of the Learning Targets in Chapter 3. At the end of the chapter, each group will make their predictions about the proper number of rubber bands to attach to Barbie and then we will go test them.
A BIG thank you to Fawn Nguyen for the Barbie Bungee lesson! We changed her lesson slightly to better fit the statistics curriculum. If you haven’t checked out her post yet, you need to! In fact, read her whole site. She’s awesome!
Use a variety of different Barbies. In fact, we also used Ken, Spider Man, and the Incredible Hulk. Because of the variability in weights, each group will have very unique data.
Before allowing students to collect data, show them how to connect the rubber bands together and how to connect the rubber bands to Barbie. This will cut down the time needed to collect data.
Also, clearly define for the students that they are measuring the distance from the jumping platform to the top of Barbie’s head at the lowest point of the bungee jump.
In this context, the explanatory variable is clearly the number of rubber bands and the response variable is the distance travelled. There are some contexts where this distinction is not clear, and could even be possibly argued in either direction (SAT math scores and SAT English scores). In these situations, the response variable will be the one that you are trying to predict from the explanatory variable.
When “describing a relationship” between two quantitative variables, remember what Homer Simpson orders at the bar.
D – Direction. This will be positive, negative, or none. A positive relationship means that above average values of one variable are typically associated with above average values of the other variable (or just a scatterplot that goes up and right). A negative relationship means that above average values of one variable are typically associated with below average values of the other variable (or just a scatterplot that goes down and right).
U – Unusual Features. Comment on any outliers. There may be outliers in the x-direction, the y-direction, both directions, or just a point that doesn’t follow the general trend of the rest of the data. Distinct clusters of data are also worth noting as unusual.
F – Form. For AP Statistics, this will generally be linear or nonlinear. We will stick to linear models in this chapter, but will look into nonlinear relationships in Chapter 12.
S – Strength. This is a measurement of how close the data points fit the identified form. In tomorrow’s lesson, we will use the correlation as a way to measure the strength of a linear relationship.