For a set of dа ta: 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? 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 this solution?

Question

Nash Armstrong

Mathematics

8 August, 10:49

For a set of dа ta: 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? 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 this solution?

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Karissa Jennings · Answer 1

The problem with this solution is that a regression model is not recommended to extrapolate because we do not know if the linear relation that we calculated for a specific range of x values still holds outside this range.

Step-by-step explanation:

We have a linear regression model, with a range of the independent variable "x" that goes from 0 to 6.

The regression model finds a good fit (r=0.8582).

As it has a good fit, it is proposed to use this model to extrapolate and calculate the value of y for x=50.

It is not recommended to extrapolate a regression model unless we are really sure that the model is still valid within the range within we are extrapolating.

This means that if we have no proof that y has a linear relation in a range of x that includes x, the extrapolation has no validity and can lead to serious errors.

A linear regression model is only suitable for interpolation or extrapolating within the range we are sure that the relation between y and x is linear within a certain acceptable error.