A study on school student performance finds that the average study hours per week is $\bar{x} = 12$ hours with a standard deviation of $s_x = 3$ hours. The average exam score is $\bar{y} = 75$ points with a standard deviation of $s_y = 10$ points. The correlation coefficient between study hours and exam score is $r = 0.60$. Find the regression equation to predict exam score $\hat{y}$ from study hours $x$, and calculate the predicted score for a student who studies $15$ hours.