To find the value of \( \hat{y} \) given the age (x) of 8, you will use the line of best fit equation provided:
\[ \hat{y} = 5.5x + 16 \]
Substituting \( x = 8 \):
\[ \hat{y} = 5.5(8) + 16 \]
Calculating \( 5.5 \times 8 \):
\[ 5.5 \times 8 = 44 \]
Now add 16:
\[ \hat{y} = 44 + 16 = 60 \]
So the value for \( \hat{y} \) when age is 8 is 60.