Question

a piano teacher tracks the number of audience members for a recital to plan the best size auditorium to reserve for future recitals. the model \\(\hat{y} = 2.8x + 7.6\\) explains the relationship between \\(x\\), the number of students performing, and \\(\hat{y}\\), the predicted number of audience members. identify and interpret the slope.\
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\\(\bigcirc\\) the slope is 7.6. for every additional audience member, there is a predicted increase of 7.6 performers\
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\\(\bigcirc\\) the slope is 7.6. for every additional performer, there is a predicted increase of 7.6 audience members\
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\\(\bigcirc\\) the slope is 2.8. for every additional performer, there is a predicted increase of 2.8 audience members\
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\\(\bigcirc\\) the slope is 2.8. for every additional audience member, there is a predicted increase of 2.8 performers

Explanation:

The linear regression model is in the form \(\hat{y}=mx + b\), where \(m\) is the slope. In the given model \(\hat{y}=2.8x + 7.6\), \(x\) represents the number of students performing and \(\hat{y}\) represents the predicted number of audience members. The slope \(m = 2.8\) means that for each unit increase in \(x\) (each additional performer), \(\hat{y}\) (the number of audience members) is predicted to increase by \(2.8\).

Answer:

C. The slope is \(2.8\). For every additional performer, there is a predicted increase of \(2.8\) audience members.