log(sales) = beta_0 + beta_1 * GDP
The usual process of transforming a variable such as price into log(price) to measure an approximate percentage change means that if you include an independent variable in your regression that is measured in units (e.g. GDP $) then you interpret it as:
- A one unit increase in GDP increases sales on average by (BETA_1 * 100) percent, holding all else constant.
This is because the beta coefficient on GDP is measuring changes in deminal percentages (0 - 1). What happens if your independent variable is not log transformed but already in percentages, except it ranges from 0 - 100?
sales_% = beta_0 + beta_1 * GDP
Would this mean we now interpret the beta coefficient as a proportional increase in sales_%? For example, if beta_1 = 10, then:
- A one unit increase in GDP increases sales on average by 10 percent, holding all else constant.