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Multiple Choice
In the context of residuals analysis, what does a residual value of indicate about a data point relative to the line of best fit?
A
The observed value is units above the value predicted by the line of best fit.
B
The observed value is 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 units below the observed value.
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1
Recall that a residual is calculated as the difference between the observed value and the predicted value from the line of best fit: \(\text{Residual} = \text{Observed} - \text{Predicted}\).
Given a residual value of \(-0.8\), substitute into the formula: \(-0.8 = \text{Observed} - \text{Predicted}\).
Rearrange the equation to express the observed value in terms of the predicted value: \(\text{Observed} = \text{Predicted} - 0.8\).
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.
Therefore, a residual of \(-0.8\) indicates that the data point lies 0.8 units below the line of best fit.