Asked by Dusty Dawson on Jun 21, 2024
Verified
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.
Verified Answer
AE
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.
Learning Objectives
- 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.