How can linear regression be applied in business settings?
They are applied daily, and mostly incorrectly, in any kind of trend line you want (sales, income, production...).
A linear regression is used in business as a means to forecast a possible trend from a set of historical data. Over-reliance on the projections with little understanding of the uncertainties in the calculated regressions often lead to decision errors regardless of the data accuracy.
As the investment community is fond (or required) of telling people "past performance does NOT indicate future results"!! Use it at your own (understood!) risk.