Calculating the Least-Squares Regression Line

Question 9 • CA-Statistics and Probability A

Let x represent the points allowed and ŷ represent the predicted wins. Which correctly states the equation for the least-squares regression line and the interpretation of its y-intercept?

Answer

ŷ = 0.02 ‒ 14.92x; A team that allows 0.02 points is predicted to have about 0 wins.

ŷ = 0.02 ‒ 14.92x; A team that allows 0 points is predicted to have about 0.02 wins.

ŷ = 14.92 ‒ 0.02x; A team that allows 15 points is predicted to have about 0 wins.

ŷ = 14.92 ‒ 0.02x; A team that allows 0 points is predicted to have about 15 wins.

Explanation

The least-squares line is ŷ = 14.92 − 0.02x, so its y-intercept is 14.92. The y-intercept gives the predicted number of wins when points allowed is 0. Thus, a team that allows 0 points is predicted to have about 15 wins, as stated in choice D.

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