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# Modeling with Non-Linear Data

Lesson 16 of 19

## Objective: SWBAT determine a function that best models a set of data by using technology to analyze correlation coefficients.

## Big Idea: Oh No! I dropped all of my skittles on the floor…how many have the “s” up and how many do not? This is the beginning of the study into non-linear regression.

*40 minutes*

#### Launch

*20 min*

Students are given all of their materials. For this lesson they will be working in groups of 2 or 3. Groups should be heterogeneous based on ability. Students are given a copy of the record sheet for the experiment. Students will be given a cup of at least 35 candies, the first thing they need to do is count their candies to determine the starting number for trial 0. Next, explain what is going to happen in the upcoming trials: they will be shaking the candies up in their cup and dump them onto the plate. Any candies that have the letter (either “s” or “M” facing up can be eaten. The other candies should be counted and returned to the cup, this would be the entry for trial #1. Repeat this process until all of the candies are gone or until you exceed 10 trials.

Have students do think-pair-share with their group to determine what they think the graph of this experiment will look like (this would be a great time to review the idea of positive vs. negative correlation. That questions will give all students entry to the task before they consider the actual shape of the graph). Take a couple of ideas from the class (many will say that the graph will appear linear). Then let them go and investigate. Students will be working to complete the experiment, fill in the table and then graph their results on the coordinate plane. They will need to come up with appropriate scales and labels for their graph

After students have had some time to work, bring the class back together to have them share their findings. Display some student work to show trends in the way the graph appears. After a brief discussion, students will test a quadratic, linear and exponential regression and use the correlation coefficient to determine which is the best fit equation. This is the lead in to show that not all data has to follow a linear pattern.

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#### Practice

*15 min*

After this, students have four supplementary situations that they can investigate that require them to fit either a quadratic or exponential function to the data. Through this practice, students will start to get a sense for which situations are modeled by which types of functions. Encourage students to read the situation and anticipate the relationship before looking at the table of values (MP2). This quantitative reasoning will be important moving forward as students encounter other situations where they have to determine the type of regression to be used.

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
- LESSON 6: Analyzing a Box Plot
- LESSON 7: Constructing a Histogram
- LESSON 8: Modeling with Box Plots and Histograms
- LESSON 9: Connecting Box Plots and Histograms
- LESSON 10: What's this table saying?
- LESSON 11: Creating Two-Way Tables
- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
- LESSON 13: Using a Scatterplot to Model Data
- LESSON 14: A Bivariate Relationship
- LESSON 15: Scatterplots and Non-Linear Data
- LESSON 16: Modeling with Non-Linear Data
- LESSON 17: Analyzing Residuals
- LESSON 18: Creating a Residual Plot
- LESSON 19: Got Ups? A Statistics Unit Task