Q.Why should predictions made using a regression equation be treated cautiously when the given value of the independent variable lies far outside the range of the original data?

A regression line is fitted only to the pattern shown by the observed data, so extending it far beyond that range assumes the same relationship keeps holding, which may not be true. …

A regression equation like $Y=a+b_{yx}X$ is derived purely from the pattern in the observed pairs of $(X,Y)$ values used to fit it. Within that observed range, the equation reflects a genuine, tested relationship. Beyond that range, however, the equation is simply being extended on the assumption that the same straight-line relationship continues — an assumption the data itself never actually tested.

In real business and economic situations this assumption frequently fails. For example, a firm's regression of sales ($Y$) on advertising expenditure ($X$) fitted over a moderate range of past spending levels may show sales rising steadily with more advertising. But at a very large advertising spend, the market may already be saturated and additional advertising may add little extra sales (the true relationship flattens); at a very low or zero spend, sales may not fall to the negative value the straight line would predict, since a baseline of sales normally continues from repeat/loyal customers regardless of advertising. …

Treating any regression-based prediction as an exact, guaranteed value regardless of how far the independent variable's value is from the observed data; failing to mention the observed-range …