To find the residual of the data point (2, 15.27), we first need to determine the predicted \( y \) value for \( x = 2 \) based on the line that is drawn through the points. The residual is calculated as follows:
\[ \text{Residual} = \text{Actual } y - \text{Predicted } y \]
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Determine Predicted Value: Since we don't have the exact equation of the line, let's assume you have it or can estimate it from your data.
- Let’s say the equation of the line is \( y = mx + b \) where \( m \) is the slope and \( b \) is the y-intercept.
- For example, if the equation is something like \( y = 2x + 11.27 \), you would substitute \( x = 2 \):
\[ \text{Predicted } y = 2(2) + 11.27 = 4 + 11.27 = 15.27 \]
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Calculate the Residual:
- Actual \( y = 15.27 \)
- Predicted \( y = 15.27 \)
\[ \text{Residual} = 15.27 - 15.27 = 0 \]
Now, if the prediction was different based on the actual equation of the line, you would substitute the correct predicted values into the residual formula.
- Rounding: Ensure that your final answer is rounded to the nearest thousandth.
Without the exact equation of the line from your data, I cannot calculate the residual accurately. However, if you have that equation, just replace the predicted \( y \) with the output of that line at \( x = 2 \) and perform the subtraction to find your residual.
Please provide the equation of the line or the predicted \( y \) at \( x = 2 \) for an exact calculation if needed.