Lesson 8: What’s the Trend?

Lesson 8: What’s the Trend?

Objective:

Students will understand that the regression line is a model for a linear association (trend). They will learn to identify the direction and strength of trends.

Materials:

  1. What’s the Trend? handout (LMR_4.7_What’s the Trend)

    Note: This handout will be referenced and used in subsequent lessons.

  2. Strength of Association handout (LMR_4.8_Strength of Association)

Vocabulary:

trend, positive association, negative association, no association, shape, linear, model, strength of association

Essential Concepts:

Essential Concepts:

Associations are important because they help us make better predictions; the stronger the trend, the better the prediction we can make. “Better” in this case means that our mean squared residuals can be made smaller.

Lesson:

  1. Distribute What’s the Trend? (LMR_4.7). Students will analyze the two scatterplots on the handout. The Profits per Explosion plot shows the relationship between the number of explosions in Michael Bay’s movies and the profit earned by each movie. The Scores Over Time plot shows the relationship between M. Night Shyamalan movies made since The Sixth Sense was released in 1999 and their Internet Movie Database (IMBD) scores.

  2. In teams, students will discuss and record their responses to the following questions for each plot:

    1. What kind of plot is this? Scatterplot.

    2. What do the numbers on the x-axis represent? What do the numbers on the y-axis represent? The x-axis shows number of explosions and y-axis shows profit in millions of dollars.

    3. What is this plot telling us? Answers will vary. One example could be that if there are more explosions in a movie, then the movie will earn a greater profit.

    4. What kind of plot is this? Scatterplot.

    5. What do the numbers on the x-axis represent? What do the numbers on the y-axis represent? The x-axis shows the number of years since 1999 and the y-axis shows the movie’s IMDB score.

    6. What is this plot telling us? Answers will vary. One example could be that as M. Night Shyamalan has produced more movies, their IMDB ratings have gone down.

  3. Allow students time to discuss and record their answers to the questions.

  4. Display both plots, if possible (students may also refer to the plots in their own handout). Discuss the following questions with the whole class:

    • What is happening in each plot? What seems to be the trend? Guide students to understand that the Profits per Explosion plot shows an increasing trend, while the Scores Over Time plot shows a decreasing trend. An increasing trend is called a positive association and a decreasing trend is called a negative association.

    • What does it mean to have an increasing trend and a positive association? In Profits per Explosion, it means that as the number of explosions increase, the movie profits also increase.

    • What does it mean to have a decreasing trend and a negative association? In Scores Over Time, it means that as the years after 1999 pass, the movie IMBD ratings decrease.

  5. Quickwrite: What if we had a plot with no association? Ask students to sketch what they think a scatterplot that shows no association looks like. A correct sketch will show a scatterplot with data points that show no positive or negative association; no trend or pattern. There would be no association or a very weak one. The data would be scattered.

  6. Select a couple of sketches to share with the whole class. Discuss why the sketches show no association.

  7. Ask students to discuss their thoughts about why a line was drawn through the points of the two plots and why there are equations for each plot.

  8. Conduct a share out of their observations. Guide students to the understanding that the shape of both plots is linear. The line represents a model for the relationship between two variables. The equation shown in the plots above represents the line through the points. It provides a description of the data and the relationship between the variables.

  9. Distribute Strength of Association (LMR_4.8_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.

  10. 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.

  11. 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.

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

  13. If students run out of time, they will complete the remainder of the activity for homework.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework

Complete the Strength of Association handout (LMR_4.8_Strength of Association).