## Using Regression Models (Part 2)

## Unit 4 Day 11

CED Topic(s): 2.6

##### Unit 4

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

Day 11

Day 12

Day 13

Day 14

Day 15

All Units

###### Overview

In this activity students will find or collect their own data and apply modeling techniques to interpret the data. This will give students a chance to practice noticing trends in data, choosing a regression model, interpreting a residual and a residual plot, and articulating the assumptions and limitations of a particular model.

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###### Instructions

The lesson handout walks students through the process of collecting and analyzing a data set. We suggest having students work on this project in pairs or groups of 3. While we offer some suggestions for what kind of data students may study, encourage students to pick something not listed that is interesting to them! Collecting quantitative data from their peers or actually running a little experiment can be interesting. For example, students could study the relationship between height or weight and resting heart rate or see if there is a correlation between the number of jumping jacks that can be completed in a minute (or 30 seconds) and the number of push-ups that can be completed in a minute (or 30 seconds). You may wish to give this assignment at the end of the previous day’s class so students can come to class with an idea for what relationship they want to study. You may even have them collect data at home!

Using online data sets is also a great option. Looking at how a certain quantity changes over time is a helpful context because it is likely that students will be able to look at equal intervals of the domain (time intervals) to help in their analysis. We like ourworldindata.org for finding great data sets across many different domains. Have students download the CSV file so they have easy access to the data. You may wish to have students use Stapplet instead of their graphing calculator to do their analysis if dealing with larger data sets, but be sure students do know how to utilize their graphing calculator to find each type of regression model. If using a TI-84, students should use STAT ->1:EDIT to type in their data in L1 and L2 and then STAT ->CALC to find the appropriate regression model (LinReg, QuadReg, CubicReg, QuartReg, and ExpReg are all fair game here).

Step 2 is a crucial aspect of the project and should be emphasized. Make sure students have solid reasons for why they chose their particular model. Looking at a residual plot, calculating first, second, third differences or calculating the ratio over equal intervals of the domain are all good strategies. The strategy will vary depending on what kind of data students are working with, and if equal sized intervals of the independent variable are available.

Steps 5, 6, and 7 all deal with the complexities and nuances of real-world modeling. Make sure students are spending sufficient time discussing the limitations and assumptions of their model in their groups. Asking students some thought-provoking questions here can be helpful. For example, does a certain model work well for some portions of the data set, but not for others? What aspects of this scenario are being ignored? What aspects of this scenario are oversimplified by this model? What other factors might be at play that are contributing to this trend?