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Linear Models in a Data Context

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Examples, solutions, and videos to help Grade 8 students learn how to recognize and justify that a linear model can be used to fit data.

New York State Common Core Math Grade 8, Module 6, Lesson 11

Download Worksheets for Grade 8, Module 6, Lesson 11

Lesson 11 Student Outcomes

• Students recognize and justify that a linear model can be used to fit data.
• Students interpret the slope of a linear model to answer questions or to solve a problem.

Lesson 11 Summary
In the real world, it is rare that two numerical variables are exactly linearly related. If the data are roughly linearly related, then a line can be drawn through the data. This line can then be used to make predictions and to answer questions. For now, the line is informally drawn, but in later grades you will see more formal methods for determining a best-fitting line.

Lesson 11 Classwork

Exercise 1
Old Faithful is a geyser in Yellowstone National Park. The following table offers some rough estimates of the length of an eruption (in minutes) and the amount of water (in gallons) in that eruption.
a. Chang wants to predict the amount of water in an eruption based on the length of the eruption. What should he use as the dependent variable? Why?
b. Which of the following two scatter plots should Chang use to build his prediction model? Explain.
c. Suppose that Chang believes the variables to be linearly related. Use the first and last data points in the table to create a linear prediction model.
d. A friend of Chang’s told him that Old Faithful produces about 3,000 gallons of water for every minute that it erupts. Does the linear model from part (c) support what Chang’s friend said? Explain.
e. Using the linear model from part (c), does it make sense to interpret the -intercept in the context of this problem? Explain.

Exercise 2
The following table gives the times of the gold, silver, and bronze medal winners for the men’s 100 meter race (in seconds) for the past 10 Olympic Games.
a. If you wanted to describe how mean times change over the years, which variable would you use as the independent variable, and which would you use as the dependent variable?
b. Draw a scatter plot to determine if the relationship between mean time and year appears to be linear. Comment on any trend or pattern that you see in the scatter plot.
c. One reasonable line goes through the 1992 and 2004 data. Find the equation of that line.
d. Before he saw these data, Chang guessed that the mean time of the three Olympic medal winners decreased by about 0.05 seconds from one Olympic Games to the next. Does the prediction model you found in part (c) support his guess? Explain.
e. If the trend continues, what mean race time would you predict for the gold, silver, and bronze medal winners in the 2016 Olympic Games? Explain how you got this prediction.
f. The data point (1980, 10.3) appears to have an unusually high value for the mean race time (10.3) Using your library or the Internet, see if you can find a possible explanation for why that might have happened.

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