To find the \( \hat{y} \) value using the line of best fit, you can substitute the value of \( x = 7 \) into the equation of the line:
\[ \hat{y} = 5.6x + 53.7 \]
Substituting \( x = 7 \):
\[ \hat{y} = 5.6(7) + 53.7 \]
Calculating \( 5.6 \times 7 \):
\[ 5.6 \times 7 = 39.2 \]
Now add \( 53.7 \) to \( 39.2 \):
\[ \hat{y} = 39.2 + 53.7 = 92.9 \]
Thus, the \( \hat{y} \) value is
\[ \boxed{92.9} \]