To find the value of \( \hat{y} \) (the predicted weight) given the age of 8 years, we can use the line of best fit equation:
\[ \hat{y} = 5.5x + 16 \]
Here, \( x \) is the age, which is 8 in this case:
\[ \hat{y} = 5.5(8) + 16 \]
Now we calculate:
\[ \hat{y} = 44 + 16 = 60 \]
So, the value for \( \hat{y} \) is 60.