Question

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)
i

Answer 1

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

1. Substitute \(x = 1\) into the equation:
\[
y = -0.9(1) + 18
\]
\[
y = -0.9 + 18
\]
\[
y = 17.1
\]

2. The predicted \(y\) value for \(x = 1\) is \(17.1\).

3. Now, calculate the residual, which is the difference between the actual \(y\) value and the predicted \(y\) value:
\[
\text{Residual} = \text{Actual} - \text{Predicted}
\]
\[
\text{Residual} = 16.88 - 17.1
\]
\[
\text{Residual} = -0.22
\]

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