Financial Risk Manager Part 1

Explanation

Choice C is correct. If independent variable $X_1$ increases by 1 unit, we would expect $Y$ to increase by 0.25 units, holding $X_2$ constant. This is the correct interpretation of the coefficient of $X_1$ in the given multiple regression model. In multiple regression models, each slope coefficient represents the estimated change in the dependent variable for a one-unit change in that independent variable, holding the other independent variables constant. This is also known as the partial effect of the independent variable on the dependent variable. Therefore, if $X_1$ increases by 1 unit, we would expect $Y$ to increase by 0.25 units, assuming that $X_2$ remains constant.

Choice A is incorrect. While it is true that an increase in $X_1$ by 1 unit would lead to an increase in $Y$ by 0.25 units, this statement does not take into account the effect of the other independent variable, $X_2$. In a multiple regression model, the change in the dependent variable due to a unit change in one independent variable is calculated while holding all other variables constant.

Choice B is incorrect. The ratio of coefficients ($0.25/0.14$) does not represent any meaningful relationship between $Y$ and $X_1$. Each coefficient represents the expected change in $Y$ for a unit change in its corresponding independent variable, holding all other variables constant.

Choice D is incorrect. The sum of coefficients ($0.25 + 0.14$) does not represent any meaningful relationship between $Y$ and either of the independent variables ($X_1, X_2$). Each coefficient represents the expected change in $Y$ for a unit change in its corresponding independent variable, holding all other variables constant.