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
for the growth of the plant. If the actual data point for day six is (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)
is
for the growth of the plant. If the actual data point for day six is (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)
is
Answers
GPT-4o mini
To find the residual for the data point (6, 7.82), we first need to calculate the predicted value of the height of the plant using the line of best fit equation \( y = 0.23x + 9.9 \).
1. Substitute \( x = 6 \) into the equation:
\[
y = 0.23(6) + 9.9
\]
\[
y = 1.38 + 9.9
\]
\[
y = 11.28
\]
2. Now, we have the predicted height at day 6, which is \( 11.28 \). The actual height at day 6 is \( 7.82 \).
3. The residual is calculated as the actual value minus the predicted value:
\[
\text{Residual} = \text{Actual} - \text{Predicted}
\]
\[
\text{Residual} = 7.82 - 11.28
\]
\[
\text{Residual} = -3.46
\]
So the residual of the data point (6, 7.82) is \(-3.46\).
1. Substitute \( x = 6 \) into the equation:
\[
y = 0.23(6) + 9.9
\]
\[
y = 1.38 + 9.9
\]
\[
y = 11.28
\]
2. Now, we have the predicted height at day 6, which is \( 11.28 \). The actual height at day 6 is \( 7.82 \).
3. The residual is calculated as the actual value minus the predicted value:
\[
\text{Residual} = \text{Actual} - \text{Predicted}
\]
\[
\text{Residual} = 7.82 - 11.28
\]
\[
\text{Residual} = -3.46
\]
So the residual of the data point (6, 7.82) is \(-3.46\).