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• “Why is creating a linear model useful?” (A linear model allows us to make predictions for the data in a range near the given data. It also helps to describe the relationship between the two variables quantitatively.)
• “What are some situations where you have encountered a scatter plot or a line of best t previously? What is the meaning of the slope and vertical intercept of the line of best t in this context?” (In science class we graphed the relationship between the temperature and the time it took for a reaction to take place. The slope represents how much the reaction time changes, on average, for each unit increase in temperature. The vertical intercept represents the reaction time when the temperature is 0.)
4.4 Roar of the Crowd
Cool Down: 5 minutes
Student Task Statement
The scatter plot shows the maximum noise level when di erent numbers of people are in stadium. The linear model is given by the equation
where represents maximum noise
level and represents the number of people, in thousands, in the stadium.
1. The slope of the linear model is 1.5. What does this mean in terms of the maximum noise level and the number of people?
2. A sports announcer states that there are 65,000 fans in the stadium. Estimate the maximum noise level. Is this estimate reasonable? Explain your reasoning.
3. What is the -intercept of the linear model given? What does it mean in the context of the problem? Is this reasonable? Explain your reasoning.
Student Response
1. Sample response: For every additional thousand people in the stadium, the noise level increases by about 1.5 decibels.
Unit 3 Lesson 4: Linear Models 59