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# How does this fit? CalculatingCorrelation

Lesson 8 of 10

## Objective: SWBAT compute and interpret correlation coefficients for linear relationships.

## Big Idea: Students will using statistics to understand the goodness of fit for a linear model of bivariate data.

*85 minutes*

#### Entry Ticket

*10 min*

Student will complete the **Entry Ticket: Computing and Interpreting Correlation Coefficients** where they have to compute and interpret the slope to a graph of a linear function.

This entry ticket is designed to activate student’s prior knowledge and also to help make explicit connections between the concept of slope and correlation coefficient later in the lesson.

**Academic Vocabulary:**

**Correlation**

**Correlation Coefficient**

**Line of Best Fit**

**Slope**

*Note: place academic vocabulary on word wall as a strategy to assist students in learning academic vocabulary.

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After the entry ticket, I plan to review the **PowerPoint Slides: Correlation Coefficient** presentation on computing and interpreting correlation coefficients for different scenarios.

I show the perfect positive and negative correlation to get at the idea of the correlation coefficient showing a relationship. I then transition to data that do not have perfect correlations to get at the idea that the correlation coefficient is really the slope of the line the best fits the data (and that the data does not all perfectly fit the line of best fit). During this time students are actively engaged in the note-taking process by taking **Two-Column Notes**.

We then review the concept of correlation coefficient and go through some examples together as a class. I have a number of **Turn and Talks** to provide students with ample opportunities to engage in different domains of language and maintain active engagement during the lesson. The examples and PowerPoint slides directly connect to the common core standard **MP.3** as I am asking students to develop arguments and critique the reasoning of others during the turn and talks.

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To wrap up the day's work, students work on the **Collaborative Work and/or Exit Ticket: Computing and Interpreting Correlation Coefficients **assignment to show their understanding of the day's main learning objectives.

This activity can be utilized by the teacher in a number of ways. Students can work on the Exit Ticket as a collaborative activity where they work in groups. Alternatively, the Exit Ticket can be used as a formative assessment where students complete the assignment independently.

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To conclude today's lesson I have students work in groups on their collaborative project: **Our City Statistics Project Overview**

For more information on the project assignment and expectations, see the Project: Our City Statistics Assignment Sheet**.**

I find it helpful for students to focus on identifying and interpreting the correlation coefficient for their project during this particular working group session. I like this aspect of the project as it is a nice example of how mathematics can be relevant and really help students better understand trends and patterns in their own communities.

In terms of creating scatterplots, I like to have students strategically use technology that is available to them (**MP.6). **For example, InspireData is a statistical software program that will transform a table of data into a scatterplot and calculate the line of best fit and the correlation coefficient in no time at all. Students could also use Excel to calculate the line of best fit as well as the correlation coefficient.

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Our City Statistics Project and Assessment
- LESSON 2: Correlation and Causation
- LESSON 3: Estimating Population Percentages - It is all normal
- LESSON 4: Summing it Up: Dot Plots, Histograms and Box Plots
- LESSON 5: Making Relevant Comparisons: Comparing Populations
- LESSON 6: What's the Frequency Kenneth? Summarizing Data with Frequency Tables
- LESSON 7: Cinderella's Slipper: Scatterplots, Residuals and Goodness of Fit
- LESSON 8: How does this fit? CalculatingCorrelation
- LESSON 9: What does it mean? Interpreting linear models
- LESSON 10: Outliers and Outsiders: The Impact on Data