# Building a Better Barbie Prediction

Lesson 3 of 3

8th grade and High School Statistics / Algebra

45-60 minutes

**Description**

Help Barbie make a better prediction for her bungee jump by using a line of best fit and analyzing residuals.

**Materials**

### Introduce

In Lesson 1, students collected data relating the number of rubber bands attached to Barbie and the lowest point that Barbie's head reaches. A *scatter plot* was used to make a prediction for the number of rubber bands that would give Barbie the most thrilling jump that still keeps her safe. In Lesson 2, students discovered a method for finding a *line of best fit* and identified the *correlation coefficient *(*r)* as a measure of the strength of the linear relationship. In this lesson, students will use the equation of the* line of best fit* to create a *residual plot*. Then they will revise their *predictions *from Lesson 1.

Display the data that are at the top of the Lesson 3 Student Activity Sheet.

“During our measuring day, one of the groups forgot to record their data for 5 rubber bands. Without measuring again, how could we make a good *prediction *for this value?”

Students might suggest taking the average of the values for 4 and 6 rubber bands. Another suggestion might be to take a poll of the rest of the groups. Encourage students to think about what we did in the previous lesson. The goal is to realize that the line of best fit would be a good tool to calculate the missing value.

### Explore

The activity sheet is intended for students to complete in groups. Prompt students with ideas or questions to check for and deepen student understanding.

- “How good are the
*predictions *from the line of best fit?”
- "Why are some of the
*residuals *negative?" (SMP 2)
- "On the scatterplot, where are all of the points with a negative
*residual*?"
- "If our linear model is a good model, what should we see in the
*residual *plot?"
- "Is your
*line of best fit* a good fit for your data? How do you know?"

### Synthesize

Bring the groups back together for a class discussion. Talk through the questions on the Lesson 3 Student Activity Sheet.

Remind students that one value of the *line of best fit* is to make *predictions*.

*Predictions *made from x-values within the data set are called *interpolations*. Predictions made from x-values outside the data set are called *extrapolations *and may not be as reliable as *predictions *made using *interpolation*. Ask students, "Why do you think this is the case?" A potential response may include, "The pattern may not hold true for larger x-values, we know what the pattern is between the two x-values, but are uncertain for x-values outside. For example if you stretch rubber bands too far, they break.”

A *residual *plot shows the error in each prediction. *Residual *values close to 0 indicate the *line of best fit* will be near the actual data point. *Residual *values should also be random in nature, some positive, some negative. For example, a curved pattern of *residuals *may indicate the model is not a good fit.

The *correlation coefficient* and the* residual plot* are two ways to assess the quality of our line of best fit.

Show the students the applet from Day 2. The applet creates a residual plot.

### Teacher Reflection

- What questions did you ask students that best helped you to assess their understanding of
*residuals *and *residual plots*?
- What questions did you ask students that best helped them to move forward when they were stuck or to deepen their understanding?
- What misconceptions did your students have related to the topics addressed in this lesson and how did you address those misconceptions?

Leave your thoughts in the comments below.