Problem

Using \(\text{residual}~=~\text{observed}~-~\text{predicted}\), interpret a test-score prediction of \(80~\text{points}\) with residual \(+5~\text{points}\). Give the residual equation, observed score, prediction direction, and error magnitude.

Big Picture

What this problem is really about

Use the residual equation to connect prediction, observation, and error in one consistent direction. Reconstruct the observation by adding the residual to the prediction, then translate a positive result as underprediction and a negative result as overprediction, keeping the output units attached.

Answer choices

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Preview only

equation=observed−80=−5; observed=75 points; direction=model overpredicted; magnitude=prediction was5 points above observed

equation=observed−80=0; observed=80 points; direction=neither under nor over; magnitude=prediction is treated as exact

equation=observed−80=−5; observed=75 points; direction=model overpredicted; magnitude=observed is5 points lower than predicted

equation=observed-80=5; observed=85 points; direction=model underpredicted; magnitude=prediction was5 points below observed

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Using \(\text{residual}~=~\text{observed}~-~\text{predicted}\), interpret a test-score prediction of \(80~\text{points}\) with residual \(+5~\text{points}\). Give the residual equation, observed score, prediction direction, and error magnitude.

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