Question

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

Answer 1

To calculate the residual of a data point, you need to find the difference between the actual y-value and the predicted y-value (which is obtained from the line of best fit) for the corresponding x-value.

Given the line of best fit:

\[ y = -0.9x + 18 \]

For the actual data point \( (1, 16.88) \):
- The x-value is \( 1 \).
- The actual y-value is \( 16.88 \).

Now, let's calculate the predicted y-value by substituting \( x = 1 \) into the line of best fit equation:

\[
y_{\text{predicted}} = -0.9(1) + 18
\]
\[
y_{\text{predicted}} = -0.9 + 18
\]
\[
y_{\text{predicted}} = 17.1
\]

Now, we can calculate the residual:

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

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