I am reading a research paper which models a regression model where the returns are regressed on the number of ad exposures.
the equation looks something like this:
$Returns = beta_1*nExp + beta_2*nExp^2$
nExp: The number of times the user looks at the ad. Returns: The revenue from the user
The result is that: $beta_1$ is positive (and statistically significant), which means that the ad exposures has a $+ve$ relation with the revenue.
However, $beta_2$ is negative. And the research paper says:
term for the square of the number of exposures, which has a negative coefficient suggesting diminishing returns to ad exposure.
What does it really mean? What does it mean when the term's coefficient is $+ve$ but the coefficient of it's squared term in the equation is $-ve$?