3.1.5 Using an Equation for a Fit Line
3.1.5 • Using an Equation for a Fit Line
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The scatter plot shows the maximum noise level when different numbers of people are in a 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.
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?
Compare your answer:
For every additional thousand people in the stadium, the noise level increases by about 1.5 decibels.
A sports announcer states that there are 65,000 fans in the stadium. Estimate the maximum noise level. Be prepared to show your reasoning.
Compare your answer:
120.2 decibels
Is your estimate for the previous question reasonable?
Compare your answer: Your answer may vary, but here is a sample.
It is a reasonable value since the data seem to fit a linear model well, so it is probably near this value.
What is the -intercept of the linear model given? Be prepared to show your reasoning.
Compare your answer:
The 𝑦-intercept is (0, 22.7).
What does the value of the -intercept mean in the context of the problem?
Compare your answer:
The point (0, 22.7) means a stadium with no people in it will have a maximum noise level of 22.7 decibels.
Is this value for the -intercept reasonable?
Compare your answer: Your answer may vary, but here are some samples.
- This is actually reasonable since a whisper is about 20 decibels.
- This is not reasonable since it should be silent with no people in the stadium.
- This is not reasonable because the point is so far from the data that it is unlikely that the linear model will be accurate.