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

1 answer

The residual of a data point is calculated as the difference between the actual value and the predicted value given by the line of best fit.

  1. Given data:

    • The line of best fit: \( y = -0.9x + 18 \)
    • The actual data point: \( (1, 16.88) \)
  2. Calculate the predicted value when \( x = 1 \): \[ y_{\text{predicted}} = -0.9(1) + 18 = -0.9 + 18 = 17.1 \]

  3. Find the residual: \[ \text{Residual} = \text{Actual value} - \text{Predicted value} = 16.88 - 17.1 \] \[ \text{Residual} = -0.22 \]

  4. Round the answer to the nearest hundredths: \[ \text{Residual} = -0.22 \]

Thus, the residual of the data point (1, 16.88) is -0.22.