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QuizMultiple Choice

Statistics as a Problem-Solving Process and the Role of Questioning — Test

Question 1 • Statistical Reasoning

The equation hat y is equal to 17 point 4 plus 0 point 5 x is called the least-squares regression line because it

Answer
A
makes the strongest association between weight and height.
B
minimizes the sum of the squared distances from the actual y -value to the predicted y -value.
C
maximizes the sum of the squared distances from the actual y -value to the predicted y -value.
D
is least able to make accurate predictions for the data.

Explanation

A least-squares regression line is chosen to minimize the total squared residuals. A residual is the difference between an actual y-value and the y-value predicted by the line, so the line minimizes the sum of those differences squared. Therefore, the correct choice is D, “minimizes the sum of the squared distances from the actual y-value to the predicted y-value.”

AI-written and checked against the verified answer.

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