To find the residual of the data point for day six, we first need to calculate the predicted height of the plant on day six using the equation of the line of best fit, which is:
\[ y = 0.23x + 9.9 \]
Substituting \( x = 6 \) into the equation, we can find the predicted height \( y \):
\[ y = 0.23(6) + 9.9 \] \[ y = 1.38 + 9.9 \] \[ y = 11.28 \]
The actual data point for day six is (6, 7.82).
Now, we calculate the residual, which is the difference between the actual value and the predicted value:
\[ \text{Residual} = \text{Actual} - \text{Predicted} \] \[ \text{Residual} = 7.82 - 11.28 \] \[ \text{Residual} = -3.46 \]
Thus, the residual for the data point for day six is \(-3.46\).
So, rounded to the nearest hundredths, the answer is \(-3.46\).