Question

A team of students collected data on the growth of a plant. They plotted the height of the plant every day and found the line of best fit y=0.23x+9.9
𝑦
=
0.23
𝑥
+
9.9
for the growth of the plant. If the actual data point for day six is (6,7.82)
(
6
,
7.82
)
, what is the residual of the data point for day six? Round the answer to the nearest hundredths.(1 point)
The residual of the data point (6,7.82)
(
6
,
7.82
)
is .

Answer 1

To find the residual for the data point (6, 7.82), we first need to calculate the predicted value of \( y \) using the line of best fit equation \( y = 0.23x + 9.9 \).

Substituting \( x = 6 \) into the equation:

\[
y = 0.23(6) + 9.9
\]
\[
y = 1.38 + 9.9
\]
\[
y = 11.28
\]

The predicted value for day six is 11.28.

Next, we calculate the residual, which is the difference between the actual data point \( y \) value (7.82) and the predicted \( y \) value (11.28):

\[
\text{Residual} = \text{Actual value} - \text{Predicted value}
\]
\[
\text{Residual} = 7.82 - 11.28
\]
\[
\text{Residual} = -3.46
\]

The residual of the data point (6, 7.82) is \(-3.46\).