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Solutions to Exercises in Chapter 6

15 June, 2015 - 12:54
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Solution to Example 6.11, Problem 2

The x values in the data are between 65 and 75. 90 is outside of the domain of the observed x values in the data (independent variable), so you cannot reliably predict the final exam score for this student. (Even though it is possible to enter x into the equation and calculate a y value, you should not do so!)

To really understand how unreliable the prediction can be outside of the observed x values in the data, make the substitution x = 90 into the equation.

\hat{y}= -173.51 + 4.83 (90) = 261.19

The final exam score is predicted to be 261.19. The largest the final exam score can be is 200.

Note: The process of predicting inside of the observed x values in the data is called interpolation. The process of predicting outside of the observed x values in the data is called extrapolation.