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
=
0.23
+
9.9
for the growth of the plant. If the actual data point for day six is (6,7.82)
(
6
,
7.82
)
, what is the residual of the data point for day six? Round the answer to the nearest hundredths.
To find the residual for the data point (6,7.82), we first need to calculate the predicted height of the plant on day six using the equation of the line of best fit.
Plug in x=6 into the equation y=0.23x+9.9:
y = 0.23(6) + 9.9
y = 1.38 + 9.9
y = 11.28
The predicted height of the plant on day six is 11.28.
Now, we can calculate the residual by subtracting the actual height of the plant on day six from the predicted height:
Residual = Actual Height - Predicted Height
Residual = 7.82 - 11.28
Residual = -3.46
Therefore, the residual for the data point on day six is -3.46 (rounded to the nearest hundredths).