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A team of students collected data on the growth of a plant the plot the they plotted the height of the plant every day and found a line of best fit y = 0.23x + 9.9 for the growth of the plant if the actual data point for day 6 is 6, 7.82 what is the residual of the data point for day six round your answer to the nearest hundredths

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To calculate the residual for the data point on day 6, you first need to find the predicted height of the plant using the given line of best fit equation \( y = 0.23x + 9.9 \).

  1. Calculate the predicted height (y) for day 6 (x = 6): \[ y = 0.23(6) + 9.9 \] \[ y = 1.38 + 9.9 = 11.28 \]

  2. Identify the actual data point for day 6:
    The actual height of the plant on day 6 is given as \( 7.82 \).

  3. Calculate the residual:
    The residual is calculated as the actual value minus the predicted value: \[ \text{Residual} = \text{Actual} - \text{Predicted} \] \[ \text{Residual} = 7.82 - 11.28 = -3.46 \]

So, the residual for the data point on day 6, rounded to the nearest hundredths, is \(-3.46\).