Suppose you estimate the sample regression function $$\log ( \text { Solar } \widehat {Syst}em \text { Sales} ) = 108,632.47 - 3.78 \cdot \log ( \text { Solar System Tax Rate } )$$
You should conclude that a
A)$1 increase in the solar system tax rate is associated with 3.78 fewer solar system sales.
B)1 percent increase in the solar system tax rate is associated with a 3.78 percent decrease in solar system sales.
C)1 percent increase in the solar system tax rate is associated with 3.78 fewer solar system sales.
D)$1 increase in the solar system tax rate is associated with a 3.78 percent decrease in solar system sales.

Question

Quizplus · Accepted Answer

The coefficient of the logarithm of the tax rate is -3.78, which means that a one percent increase in the tax rate is associated with a 3.78 percent decrease in sales (since a one percent increase in the tax rate corresponds to a log increase of 0.01 * log(tax rate) and the estimated coefficient is -3.78). Therefore, B is the correct choice.