To find the predicted y-value (\( \hat{y} \)) for the given z-value in the equation of the line of best fit \( \hat{y} = 5.6z + 53.7 \), we can substitute \( z = 7 \) into the equation:
\[ \hat{y} = 5.6(7) + 53.7 \]
Calculating this step-by-step:
- \( 5.6 \times 7 = 39.2 \)
- \( 39.2 + 53.7 = 92.9 \)
So, the predicted y-value is:
\[ \hat{y} = 92.9 \]
Thus, the y value is 92.9.