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? 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?

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.

fichoh fichoh · Answer 2 · 2021-10-28T10:20:51+02:00

Extrapolation describes a prediction technique whereby a regression model is used to obtain the predicted value, y for a certain value of x which is beyond the set of x - values used in creating the model.

For the dataset where the range of x - values used to create the regression model is : (0, 1, 2, 3, 4, 5, 6) ; using the model to extrapolate the value of y when x = 50 is not recommended.

When the value of x for the data to be extrapolated falls far beyond the range of x ; then the strength of the coefficient of determination decreases and may not be valid.

Therefore, since the difference between the maximum value of x in the dataset and the value of x to be extrapolated is very large, then the extrapolated value would be very unreliable.

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