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)

1 answer

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

  1. Plug \( x = 1 \) into the equation to find the predicted y-value:

\[ y = -0.9(1) + 18 \] \[ y = -0.9 + 18 \] \[ y = 17.1 \]

  1. The actual y-value from the data point is 16.88.

  2. The residual is calculated as:

\[ \text{Residual} = \text{Actual} - \text{Predicted} \] \[ \text{Residual} = 16.88 - 17.1 \] \[ \text{Residual} = -0.22 \]

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

Rounding to the nearest hundredths, the final answer is:

\[ \boxed{-0.22} \]