Statistics for Business: Decision Making and Analysis, 3rd Edition

... cost of 1-carat diamonds. That’s another extrapolation. All of these diamonds weigh less than half of a carat; none differ in weight by a carat. It is more sensible to interpret the slope in the context of the data. For example, the difference in estimated cost between diamonds that differ in weight by 1/10th of a carat is 1/10th of the slope:

$$b_1/10=\$2,697/10\approx \$270$$

Similarly, the difference in estimated cost is $27 per point (a point is 1/100th of a carat). Notice that only the difference in weight matters because fixed costs affect both prices by the same amount.

Caution

It is tempting, but incorrect, to describe the slope as “the change in Y caused by changing X.”

For instance, we might say “The estimated cost of diamonds increases $27 for each ...