In the context of residuals analysis, what does a residual value of $-0.8$ indicate about a data point relative to the line of best fit?

• A. The observed value is $0.8$ units above the value predicted by the line of best fit.
• B. The observed value is $0.8$ units below the value predicted by the line of best fit.
• C. The data point lies exactly on the line of best fit.
• D. The predicted value is $0.8$ units below the observed value.

Answer: (B)

Verified step by step guidance

1. Recall that a residual is calculated as the difference between the observed value and the predicted value from the line of best fit: \(\text{Residual} = \text{Observed} - \text{Predicted}\).
2. Given a residual value of \(-0.8\), substitute into the formula: \(-0.8 = \text{Observed} - \text{Predicted}\).
3. Rearrange the equation to express the observed value in terms of the predicted value: \(\text{Observed} = \text{Predicted} - 0.8\).
4. Interpret this result: since the observed value is the predicted value minus 0.8, the observed value is 0.8 units less than the predicted value.
5. Therefore, a residual of \(-0.8\) indicates that the data point lies 0.8 units below the line of best fit.