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 .
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 \( y \) using the line of best fit equation \( y = 0.23x + 9.9 \).
1. Substitute \( x = 6 \) into the equation:
\[
y = 0.23(6) + 9.9
\]
2. Calculate \( 0.23 \times 6 \):
\[
0.23 \times 6 = 1.38
\]
3. Now add this to 9.9:
\[
y = 1.38 + 9.9 = 11.28
\]
The predicted value of \( y \) for day six is \( 11.28 \).
4. To find the residual, subtract the actual value from the predicted value:
\[
\text{Residual} = \text{Actual value} - \text{Predicted value}
\]
\[
\text{Residual} = 7.82 - 11.28
\]
5. Performing the subtraction:
\[
\text{Residual} = 7.82 - 11.28 = -3.46
\]
Therefore, the residual of the data point (6, 7.82) is \(-3.46\).
So, the final answer is:
\(\text{The residual of the data point (6, 7.82) is } -3.46.\)
1. Substitute \( x = 6 \) into the equation:
\[
y = 0.23(6) + 9.9
\]
2. Calculate \( 0.23 \times 6 \):
\[
0.23 \times 6 = 1.38
\]
3. Now add this to 9.9:
\[
y = 1.38 + 9.9 = 11.28
\]
The predicted value of \( y \) for day six is \( 11.28 \).
4. To find the residual, subtract the actual value from the predicted value:
\[
\text{Residual} = \text{Actual value} - \text{Predicted value}
\]
\[
\text{Residual} = 7.82 - 11.28
\]
5. Performing the subtraction:
\[
\text{Residual} = 7.82 - 11.28 = -3.46
\]
Therefore, the residual of the data point (6, 7.82) is \(-3.46\).
So, the final answer is:
\(\text{The residual of the data point (6, 7.82) is } -3.46.\)