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Lesson 12: How Strong Is It?

Lesson 12: How Strong Is It?

Objective:

Students will learn that the correlation coefficient is a value that measures the strength in linear associations only.

Materials:

  1. Strength of Association handout (LMR_4.14_Strength of Association)

  2. Correlation Coefficient handout (LMR_4.15_Correlation Coefficient)

    Note: Advance preparation required. This handout is the resource for the plot cutouts. DO NOT distribute as-is to students.

Vocabulary:

correlation coefficient strength of association

Essential Concepts:

Essential Concepts:

A high absolute value for correlation means a strong linear trend. A value close to 0 means a weak linear trend.

Lesson:

  1. Distribute the Strength of Association handout (LMR_4.14_Strength of Association). In teams, students will examine the scatterplots (b) through (e). Their task is to discuss the strength of the association for each plot. They will determine which plots they think show strong associations and which ones they believe show weak associations. They must explain how they made their decision. Reasons must reference the plots.

  2. As an example, demonstrate how to describe plot (a) in the Strength of Association handout. Possible description: Plot (a) shows a negative association, or decreasing trend. The association appears to be fairly strong because the points are relatively close together, forming a moderate linear pattern.

  3. Once all teams have completed the handout, assign one plot to each team for a share out. If two teams have the same plot, one team will share its explanation first and the second team can agree, disagree, or add to the first team’s description

  4. Guide students to understand that a strong association has points closer to each other and a weak association has points more scattered.

  5. Inform students that, so far, they have been labeling associations as strong, very strong, or weak. A number called the correlation coefficient measures strength of association. The correlation coefficient only applies to linear relationships, which must be checked visually with a scatterplot. Later we will learn how to calculate this number using RStudio.

    Note to teacher: Advance preparation is needed for this lesson. Each team needs one envelope with cutouts of plots A-F in LMR_4.15 (Part 1). Make envelopes according to the number of teams in the class. This process will be repeated for LMR_4.15 (Part 2).

  6. Distribute the envelopes to the teams. Students will examine the strength of association in each plot. Their task is to assign the correlation coefficient that corresponds to each plot and to explain why they assigned that correlation coefficient to that particular plot. The only piece of information they will receive is that a correlation coefficient equal to 1 has the strongest linear association and a correlation coefficient equal to 0 has the weakest association.

  7. Assign each team one plot. If there are more teams than plots, these teams will be assigned a plot in the next round. Each team will share the correlation coefficient they assigned to their plot and the explanation that goes with it.

  8. Using the Voting Cards strategy (see Instructional Strategies), the rest of the teams will show whether they approve, disapprove, or are uncertain about the teams’ assignment and/or explanation. Repeat for each plot. The correlation coefficients for each plot are:

    • Plot A: r = 1.00

    • Plot B: r = 0.72

    • Plot C: r = 0.19

    • Plot D: r = 0.48

    • Plot E: r = 0.98

    • Plot F: r = 0.00

  9. The last set of plots showed positive associations. Now students will assign the correlation coefficients for plots G-L for LMR_4.15 (Part 2).

  10. Distribute the envelopes to the teams. Students will examine the strength of association in each plot. Their task is to assign the correlation coefficient that corresponds to each plot and to explain why they assigned that correlation coefficient to that particular plot. The only piece of information they will receive is that a correlation coefficient equal to -1 has the strongest linear association and a correlation coefficient equal to 0 has the weakest association.

  11. Teams previously not assigned a plot are now assigned one. Each team will share the correlation coefficient they assigned to their plot and the explanation that goes with it.

  12. Using the Voting Cards strategy, the rest of the teams will show whether they approve, disapprove, or are uncertain about the teams’ assignment and/or explanation. Lead a class discussion whenever there is disapproval or uncertainty. Repeat for each plot. The correlation coefficients for each plot are:

    • Plot G: r = -1.00

    • Plot H: r = 0.72

    • Plot I: r = -0.19

    • Plot J: r = -0.48

    • Plot K: r = 0.98

    • Plot L: r = 0.00

  13. Journal Entry: What is a correlation coefficient, what does it do, and what does it tell us about a scatterplot?

Homework & Next Day

Students will complete the journal entry for homework if not completed in class.

LAB 4D: Interpreting Correlations

Complete Lab 4D prior to Lesson 13.