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

Question

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

Answer 1

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

1. Substitute \(x = 6\) into the equation:

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

\[ y = 1.38 + 9.9 = 11.28 \]

2. The predicted height for day 6 is 11.28.

3. The actual height given is 7.82.

4. The residual is calculated as follows:

\[ \text{Residual} = \text{Actual Value} - \text{Predicted Value} \]

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

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