Making Predictions from a Least-Squares Regression Line — Quiz
Question 2 • 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 the 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 slope of the regression line?
Answer
A
For each increase in hours of play by 1 , the predicted rating of the game increases by 27 point 2 7 3 points.
B
For each increase in rating by 1 point, the predicted hours of play increase by 18 point 1 8 2 .
C
For each increase in rating by 1 point, the predicted hours of play increase by 27 point 2 7 3 .
D
For each increase in hours of play by 1 , the predicted rating of the game increases by 18 point 1 8 2 points.
Explanation
The slope is 27.273, which tells how much the predicted rating changes for each 1-hour increase in play time. Since x measures hours and y measures rating points, the predicted rating increases by 27.273 points per additional hour. This matches choice C.
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