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), you first need to calculate the predicted height of the plant on day 6 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 \( 0.23(6) \):

\[ 0.23 \times 6 = 1.38 \]

3. Add this result to 9.9:

\[ y = 1.38 + 9.9 = 11.28 \]

The predicted height of the plant on day 6 is 11.28.

4. Now, calculate the residual by finding the difference between the actual height and the predicted height:

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

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

Thus, the answer is:

-3.46.