Question

For an activity in class, a team of students was given the line of best fit, y = - 0.9x + 18.11 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 __

Answer 1

To find the residual of the data point (1, 16.88), we first need to calculate the predicted value of \( y \) using the given line of best fit, which is:

\[
y = -0.9x + 18.11
\]

Plugging in \( x = 1 \):

\[
y = -0.9(1) + 18.11
\]
\[
y = -0.9 + 18.11
\]
\[
y = 17.21
\]

Now, the residual is calculated by taking the actual value of \( y \) and subtracting the predicted value of \( y \):

\[
\text{Residual} = \text{Actual } y - \text{Predicted } y
\]
\[
\text{Residual} = 16.88 - 17.21
\]
\[
\text{Residual} = -0.33
\]

So, the residual of the data point (1, 16.88) is \(\boxed{-0.33}\).