Overview

• In this in-class activity, students will use [latex]R^{2}[/latex] to evaluate how well different explanatory variables predict a response variable of interest (using linear models). Then, they will be
  asked to broaden their understanding with respect to correlation and causation.
• Students will use a mock dataset representing different predictors of student test scores in a large school district. The dataset is simulated due to privacy concerns with real student data but its results are representative of results that real school districts have found when studying these variables. The policies discussed in the activity and their results are likewise representative of policies that real school districts have implemented.
• This activity connects back to evaluating the strength of linear relationships, and prepares students for evaluating whether a linear model is appropriate for a set of bivariate data.
• [a list of tags like S2, O1, B1, V3] ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

• Develop intuition about how [latex]R^{2}[/latex] is related to the shape of a scatterplot.
• Identify variable types (explanatory and response) and plot data in a scatterplot.
• Use technology to calculate [latex]R^{2}[/latex].
• Interpret the meaning of [latex]R^{2}[/latex] in context.
• Identify possible values of [latex]R^{2}[/latex].

Intended goals for this activity

After completing this activity, students should understand that [latex]R^{2}[/latex] is a measure of prediction strength in a linear relationship, and that a high [latex]R^{2}[/latex] value does not indicated a causal relationship. They should understand that [latex]R^{2}[/latex] can be interpreted as the percentage of variation in the response variable explained by the linear relationship with an explanatory variable. They should be able to interpret [latex]R^{2}[/latex] values and determine their utility in different tasks (gauging prediction strength vs. determining a causal relationship).

Synchronous Delivery and Activity Flow

The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.

Frame the activity (3 minutes)

• Question 1 — Think-Pair-Share  S2, C4, V1, V4, O3
  • Have students read Question 1 independently then discuss their answers in pairs before sharing with the class.
  • Transition to the activity by briefly discussing the Objectives for the activity.

Activity Flow (20 minutes)

• Question 2 – 4 — Working in pairs or small groups V1, V4, O3, S2, C6
  • Pull the class together to discuss Question 2 before moving on the Questions 3 (since Question 3 may give away the responses for Question 2).
• Questions 5 and 6 — Whole Class Discussion  S4, C3, V1, O1, B2, B4
  • Question 5
    • Give students time to independently think and write their responses. Then:
      • First: Ask for a student who thinks the attendance policy is best to share their thoughts.
      • Second: Ask students if they think there is any reason to believe an attendance policy wouldn’t work. Allow for think time before asking students to answer this follow-up question.
  • Question 6
    • Have students answer this question in their pairs/groups, and then ask several groups to share their answers with the whole class. Ensure students include specific reasoning as to why attendance may not be causally related to exam scores. Complete reasoning would include examples of alternative causal mechanisms that result in a correlation between attendance and test scores.
    • To add emphasis to explanations of confounding, show and ask a student to explain the following causal graph: [link to the graph found in DC instructor guide]

Wrap-up/transition (2 minutes)

• Consider drawing various bivariate relationships on the board (positive and negative associations) and asking students which will have the lowest/highest [latex]R^{2}[/latex] values.
• Have students refer back to the Objectives for the activity and check the ones they recognize.
• Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2