High School

For this data set, the least squares regression line is [tex] y = -1.11x + 68.17 [/tex], where [tex] x [/tex] represents the weight of the cars in hundreds of pounds and [tex] y [/tex] represents the mpg rating. A car weighing 5000 pounds is predicted to have a 67 mpg rating. Which one of the following is a reason the prediction is not accurate?

A. There is a calculation error.
B. There are no cars in the data set that weighed 5000 pounds.
C. This is considered an extrapolation.

Answer :

Answer:

Option c) this is considered an extrapolation, correctly identifies this as the reason the prediction is not accurate.

Explanation:

The reason the prediction is not accurate is because this is considered an extrapolation.

Extrapolation involves making predictions or estimations beyond the range of known data. In this case, the given least squares regression line is based on the data set, but it is being used to predict the mpg rating for a car weighing 5000 pounds. However, the regression line is only valid for the range of weights present in the data set. If there are no cars in the data set that weighed 5000 pounds, then using the regression line to predict the mpg rating for a car weighing 5000 pounds would be extrapolating beyond the known data range.

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