Question

For an activity in class, a team of students was given the line of best fit, y=−0.9x+18
𝑦
=
−
0.9
𝑥
+
18
. If one of the actual data points is (1,16.88)
(
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)
(
1
,
16.88
)
is .

Answer 1

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

Substituting \( x = 1 \) into the equation:

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

Next, we find the residual, which is the difference between the actual \( y \) value from the data point and the predicted \( y \) value:

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

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