To find the value of the line of best fit provided in your equation \( y = 5.5x + 16 \) for an age of 8, we can substitute \( x = 8 \) into the equation.
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Substitute \( x = 8 \): \[ y = 5.5(8) + 16 \]
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Calculate \( 5.5 \times 8 \): \[ 5.5 \times 8 = 44 \]
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Now add 16: \[ y = 44 + 16 = 60 \]
The predicted value of \( y \) (the line of best fit) when \( x = 8 \) is 60.
To find the residual, which is the difference between the actual value given in the table (61) and the predicted value (60), you can use the formula:
\[ \text{Residual} = \text{Actual Value} - \text{Predicted Value} \]
- Substitute the actual value: \[ \text{Residual} = 61 - 60 = 1 \]
So, the value of the line of best fit for an age of 8 is 60, and the residual is 1.