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 for the data point (6, 7.82), you'll first need to determine the expected height of the plant on day six using the line of best fit \( y = 0.23x + 9.9 \).

1. Substitute \( x = 6 \) into the equation: \[ y = 0.23(6) + 9.9 \] \[ y = 1.38 + 9.9 = 11.28 \]

2. Now, find the residual by subtracting the actual height (7.82) from the expected height (11.28): \[ \text{Residual} = \text{Actual height} - \text{Expected height} \] \[ \text{Residual} = 7.82 - 11.28 = -3.46 \]

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