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 answer

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

\[ y = -0.9x + 18 \]

Now, substitute \( x = 1 \) into the equation:

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

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

Next, the residual is calculated as the difference between the actual value and the predicted value:

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

Thus, the residual of the data point (1, 16.88) is:

\[ \boxed{-0.22} \]