Question

A team of students were following different stocks for a project. They plotted stock prices and found that one of the stocks had the following trend line:

y=−0.23x+9.9
. If the actual data point for day four is (4,8.63)
what is the residual of the data point for day four? Round the answer to the nearest hundredths.

(1 point)
The residual of the data point (4,8.63)
is

Answer 1

To find the residual of the data point (4, 8.63) using the trend line \( y = -0.23x + 9.9 \), we first need to calculate the predicted value of \( y \) for \( x = 4 \).

1. Substitute \( x = 4 \) into the trend line equation:

\[
y = -0.23(4) + 9.9
\]

2. Calculate the value:
\[
y = -0.92 + 9.9 = 8.98
\]

Now we have the predicted value \( \hat{y} = 8.98 \).

3. The residual is calculated as the difference between the actual value and the predicted value:
\[
\text{Residual} = \text{Actual value} - \text{Predicted value}
\]
\[
\text{Residual} = 8.63 - 8.98
\]
\[
\text{Residual} = -0.35
\]

Thus, the residual of the data point (4, 8.63) is \(-0.35\).

Final answer rounded to the nearest hundredths is:
\[
\text{The residual of the data point (4, 8.63) is } -0.35
\]