To find the predicted \( y \) value (\( \hat{y} \)) for the given \( x \) value using the line of best fit equation \( \hat{y} = 5.6x + 53.7 \), we'll substitute \( x = 7 \) into the equation.
\[ \hat{y} = 5.6(7) + 53.7 \]
Calculating \( 5.6(7) \):
\[ 5.6 \times 7 = 39.2 \]
Now, add 53.7:
\[ \hat{y} = 39.2 + 53.7 = 92.9 \]
Thus, the \( \hat{y} \) value is approximately \( 92.9 \).
The \( \hat{y} \) value is \( 92.9 \).