**Step 1: Introduction/Overview of the Question** The question provides a regression equation and asks for the partial effect of the variable \( B \) on the variable \( F \). This means we need to find how a change in \( B \) affects \( F \), holding all other variables constant. This is done by finding the partial derivative of \( F \) with respect to \( B \). --- **Step 2: Calculation—Finding the Partial Derivative** Given regression equation: \[ F = -3.36 - 0.002B + 0.17S + 0.011B \times A \] To find the partial effect of \( B \) on \( F \), take the partial derivative: \[ \frac{\partial F}{\partial B} = \frac{\partial}{\partial B} \left( -3.36 - 0.002B + 0.17S + 0.011B \times A \right) \] - The derivative of \(-3.36\) with respect to \( B \) is 0. - The derivative of \(-0.002B\) with respect to \( B \) is \(-0.002\). - The derivative of \(0.17S\) with respect to \( B \) is 0 (since \( S \) is not a function of \( B \)). - The derivative of \(0.011B \times A\) with respect to \( B \) is \(0.011A\). So, \[ \frac{\partial F}{\partial B} = -0.002 + 0.011A \] --- **Step 3: Matching with the Given Choices** From the calculation, the partial effect is: \[ -0.002 + 0.011A \] Now, compare this with the given options: - a) \(-0.002 + 0.011A\) - b) \(-0.002B + 0.011A\) - c) \(-0.002B + 0.011B \times A\) - d) \(-0.002 + 0.011B \times A\) The correct match is option **a**. --- **Final Answer:** **a) \(-0.002 + 0.011A\)**