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Example 3 from Algebra and Trigonometry, 4.3 Fitting Linear Models to Data
Understanding Interpolation and Extrapolation
Use the cricket data from Table 1 to answer the following questions:
- ⓐWould predicting the temperature when crickets are chirping 30 times in 15 seconds be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.
- ⓑWould predicting the number of chirps crickets will make at 40 degrees be interpolation or extrapolation? Make the prediction, and discuss whether it is reasonable.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
- ⓐThe number of chirps in the data provided varied from 18.5 to 44. A prediction at 30 chirps per 15 seconds is inside the domain of our data, so would be interpolation. Using our model:
Based on the data we have, this value seems reasonable.
- ⓑThe temperature values varied from 52 to 80.5. Predicting the number of chirps at 40 degrees is extrapolation because 40 is outside the range of our data. Using our model:
We can compare the regions of interpolation and extrapolation using Figure 5.
Figure 5- ⓐThe number of chirps in the data provided varied from 18.5 to 44. A prediction at 30 chirps per 15 seconds is inside the domain of our data, so would be interpolation. Using our model:
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
According to the data from Table 1, what temperature can we predict it is if we counted 20 chirps in 15 seconds?
How did it go?