For an activity in class, a team of students was given the line of best fit, y=−0.9x+18. If one of the actual data points is (1,16.88), what is the residual of the data point? Round the answer to the nearest hundredths.(1 point)

Question

The residual of the data point (1,16.88) is
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Answer 1

To calculate the residual of the data point (1, 16.88) using the line of best fit \( y = -0.9x + 18 \), we first need to find the predicted value of \( y \) when \( x = 1 \).

1. Substitute \( x = 1 \) into the equation of the line: \[ y = -0.9(1) + 18 \] \[ y = -0.9 + 18 = 17.1 \]

2. The predicted value of \( y \) when \( x = 1 \) is \( 17.1 \).

3. The residual is calculated as the actual value minus the predicted value: \[ \text{Residual} = \text{Actual Value} - \text{Predicted Value} \] \[ \text{Residual} = 16.88 - 17.1 \] \[ \text{Residual} = -0.22 \]

So, the residual of the data point (1, 16.88) is \(\boxed{-0.22}\).