Check your understanding of this module before moving on.
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Checkpoint quiz 3 questions
A quick check on this module's key ideas before you move on
Question 01
Why does least-squares regression minimize squared error rather than raw signed error?
B is correct. Without squaring, a model that over-predicts on one point and under-predicts on another by the same amount would look like it has zero error. Squaring also makes large errors cost disproportionately more, which discourages leaving any single point far off.
Question 02
In the worked example, a residual of 4 contributes how much to the sum of squared errors compared to a residual of 1?
B is correct. Squared error scales with the square of the residual: 4² = 16 versus 1² = 1, so the residual of 4 contributes 16 times as much.
Question 03
What does a curved (for example, U-shaped) pattern in the residuals suggest?
B is correct. A random scatter of residuals around zero suggests a good fit. A systematic curve in the residuals means the model is missing real structure in the data, namely a non-linear relationship.