Question

When we use a least-squares line to predict y values for x values beyond the range of x values found in the data, are we extrapolating or interpolating? Are there any concerns about such predictions?

Answer 1

The prediction involves extrapolation, when the x-values are beyond the range. In extrapolation, the pattern of data change outside the range of x, may result in unrealistic forecast values.

The predictions where the values of $\hat{y}$ are predicted for the values of x that are beyond the observed values in the data set, are called extrapolation.

Since extrapolation involves the values of x that are far away from the range of the observed data set, the pattern of data changes outside the range of x. In this case, the least-squares line may produce impractical values for $\hat{y}$ , which is dangerous.