5
QuizMultiple Choice

Calculating the Least-Squares Regression Line — Quiz

Question 5 • Statistical Reasoning

The equation hat y is equal to 54 point 1 6 plus 0 point 8 7 x is called the least-squares regression line because it

Answer
A
makes the sum of the squared residuals as large as possible.
B
is least able to make accurate predictions for the data.
C
causes the relationship between English scores and math scores to be strongest.
D
makes the sum of the squared residuals as small as possible.

Explanation

A least-squares regression line is chosen to minimize the sum of the squared residuals. A residual is the difference between an observed value and the value predicted by the line, and squaring prevents positive and negative differences from canceling. Therefore, choice D, “makes the sum of the squared residuals as small as possible,” is correct.

AI-written and checked against the verified answer.

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