For a regression model, the actual value of y is 52 and the predicted value is ŷ = 47. Find the residual and interpret its sign.

Step 1: Recall the residual formula.

Residual = observed value - predicted value

In symbols:
e = y - ŷ

Step 2: Identify the values.

Observed value:
y = 52

Predicted value:
ŷ = 47

Step 3: Calculate the residual.

e = 52 - 47
e = 5

Step 4: Interpret the sign.

The residual is positive because the observed value is greater than the predicted value.

A residual of 5 means the model underpredicted the actual value by 5 units.

Therefore, the residual is 5, and the positive sign indicates that the actual value is 5 units above the model's prediction.