Consider a multiple regression model used to forecast the monthly sales of a retail store based on several independent variables, including advertising expenses ($X_1$), number of promotions ($X_2$), and average customer income ($X_3$). The regression equation estimated is:
$$ ext{Sales} = 50 + 3.5X_1 + 2.0X_2 + 1.5X_3 + ext{error}$$
In this model, the coefficients indicate the expected change in sales for a one-unit change in each independent variable, holding all other variables constant.
After performing the regression analysis, the following statistics were calculated: Standard errors for the coefficients were 0.5, 0.6, and 0.8 for $X_1$, $X_2$, and $X_3$, respectively. The R-squared value for the model is 0.85, indicating that 85% of the variability in sales can be explained by the model.
Based on this information, what can we conclude about the coefficient of $X_2$?