Asked by Dusty Dawson on Jun 21, 2024

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Sarah is a server at a restaurant and has been keeping track of the tips she receives.The smallest bill she received a tip for was $24.44,and the largest bill was $89.75.She used linear regression to model tips received (y)as a function of the restaurant bill (x).Using her data,she wrote a linear regression equation of y = 0.22x-0.27.Sarah would really like to get a $50 tip.Based on her linear regression equation,what would the restaurant bill have to be to lead to a $50 tip? Would this calculation be considered interpolation or extrapolation?

Linear Regression

A statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Interpolation

To predict corresponding variables within the domain.

Extrapolation

To predict corresponding variables outside of the domain.

  • Understand and apply the concept of linear regression to model real-world phenomena.
  • Determine when a calculation falls within the realm of interpolation or extrapolation.
  • Apply statistical methods to make predictions based on given models.
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Amanda EnglishJun 27, 2024
Final Answer :
To get a tip of $50.00,the restaurant bill would have to be $228.50.Since $228.50 is not in the domain of the data Sarah collected,it would be considered extrapolation.
To get a tip of $50.00,the restaurant bill would have to be $228.50.Since $228.50 is not in the domain of the data Sarah collected,it would be considered extrapolation. ​   ​