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Will there ever be a case where two different lines will serve as the best fit for the data? But if we try to extrapolate a cost when x = 50, x = 50, that is in 50 years, the model would not apply because we could not account for factors fifty years in the future.
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For example, predicting a cost function for a period of two years may involve examining the data where the input is the time in years and the output is the cost.
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When our model no longer applies after a certain point, it is sometimes called model breakdown. Predicting a value outside of the domain and range has its limitations. There is a difference between making predictions inside the domain and range of values for which we have data and outside that domain and range. Extrapolation would occur if we used our model to predict temperature when the values for chirps are less than 18.5 or greater than 44. We can see that interpolation would occur if we used our model to predict temperature when the values for chirps are between 18.5 and 44. The process of extrapolation is used when we predict a value outside the domain and range of the data.įigure 4 compares the two processes for the cricket-chirp data addressed in Example 2. We use a process known as interpolation when we predict a value inside the domain and range of the data. While the data for most examples does not fall perfectly on the line, the equation is our best guess as to how the relationship will behave outside of the values for which we have data. Recognizing Interpolation or Extrapolation This linear equation can then be used to approximate answers to various questions we might ask about the trend.