Question 1196685: For a set of data: x = (0,1,2,3,4,5,6) and y=(36, 28, 25, 24, 23, 21, 19), is it wise to use a linear regression to extrapolate data for x = 50?
Proposed Solution:
Since the coefficient of determination is 0.8582, the linear model is a reasonably good fit for the data, so extrapolation for any x-value is acceptable.
What is wrong with the proposed solution?
A. As the extrapolation value gets farther away from the known data points,
the accuracy diminishes. An x-value of x = 50 is far too distant from the
known data to obtain accurate results.
B. It is possible that other models (non-linear models) would have a
coefficient of determination closer to 1.0, and therefore be a better model
to make predictions from.
C. The coefficient of determination is a measure used to gauge the relative
effectiveness of different data models, not as an indication of the accuracy
of distant extrapolation.
D. Choices A, B, and C are all valid of the incorrectness of the proposed
solution.
E. The proposed solution is correct
Answer by ikleyn(52879)   (Show Source):
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