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.

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 of the plant for day six 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 the value:

\[ y = 1.38 + 9.9 = 11.28 \]

So, the predicted height of the plant on day six is 11.28.

3. The actual height of the plant on day six is 7.82.

4. The residual is calculated as the actual value minus the predicted value:

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

5. Calculate the residual:

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

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