Modeling a Context from Data 2

New York State Common Core Math Algebra I, Module 5, Lesson 7

Worksheets for Algebra I, Module 5, Lesson 7 (pdf)

Student Outcomes

• Students use linear, quadratic, and exponential functions to model data from tables, and choose the regression most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a regression model and then interpret the function in context. They then make predictions based on their model, and use an appropriate level of precision for reporting results and solutions.

Lesson 7: Modeling a Context from Data

Classwork

Opening Exercise

What is this data table telling us?

Example 1

Remember that in Module 2, we used a graphing display calculator (GDC) to find a linear regression model. If a linear model is not appropriate for a collection of data, it may be possible that a quadratic or exponential model will be a better fit. Your graphing calculator is capable of determining various types of regressions. Use a GDC to determine if a data set has a better fit with a quadratic or exponential function. You may need to review entering the data into the stats application of your GDC.
When you are ready to begin, return to the data presented in the Opening Exercise. Use your graphing calculator to determine the function that best fits the data. Then, answer some questions your teacher will ask about the data.

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Exercises

1. Use the following data table to construct a regression model, and then answer the questions.
   a. What function type appears to be the best fit for this data? Explain how you know.
   b. A student chooses a quadratic regression to model this data. Is he right or wrong? Why or why not?
   c. Will the moisture content for this product ever reach 0%? Why or why not?
   d. Based on this model, what would you expect the moisture content to be of a chicken breast fried for 50 minutes?
2. Use the following data table to construct a regression model, then answer the questions based on your model.
   a. What trends do you see in this collection of data?
   b. How do you interpret this trend?
   c. If the trend continues, what would we expect the percentage of people in the U.S. who report no leisure-time physical activity to be in 2020?

Lesson Summary

• Using data plots and other visual displays of data, the function type that appears to be the best fit for the data can be determined. Using the correlation coefficient, the measure of the strength and the direction of a linear relationship can be determined.
• A graphing calculator can be used if the data sets are imperfect. To find a regression equation, the same steps will be performed as for a linear regression.

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