Making Predictions from a Least-Squares Regression Line — Quiz
Question 9 • Statistical Reasoning
A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a game and how well that game is rated among board game players. Information was collected on several board games and was used to obtain the regression equation widehat y is equal to 27 point 2 7 3 x plus 18 point 1 8 2 , where x represents time it takes to play (in hours) and widehat y is the predicted rating of that game (in points). Which statement best describes the meaning of the y - intercept of the regression line?
Answer
A
When the time to play is 0 hours, the predicted rating is 27 point 2 7 3 . This interpretation is not meaningful since a game cannot have a playtime of 0 hours.
B
When the time to play is 0 hours, the predicted rating is 18 point 1 8 2 . This interpretation is not meaningful since a game cannot have a playtime of 0 hours.
C
When the rating of a game is 0 points, the predicted time to play is 18 point 1 8 2 hours.
D
When the rating of a game is 0 points, the predicted time to play is 0 hours.
Explanation
The y-intercept is 18.182, so the regression line predicts a rating of 18.182 points when playtime is 0 hours (x = 0). This interpretation is not meaningful in context because a board game cannot have a playtime of 0 hours. Choice C states this correctly.
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