AnswersStatistical ReasoningMaking Predictions from a Least-Squares Regression Line

Making Predictions from a Least-Squares Regression Line — Quiz Answers

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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?

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.
3

A statistics teacher was interested in the relationship between the number of days students waited to start a project and the score that project received (out of 100 points). Information was collected on several students and was used to obtain the regression equation widehat y is equal to negative 3 point 6 4 x plus 96 point 5 , where x represents the number of procrastination days and widehat y is the predicted grade. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in number of procrastination days by 1 , the predicted grade decreases by 3 point 6 4 points.
B
For each increase in number of procrastination days by 1 , the predicted grade decreases by 96 point 5 points.
C
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 96 point 5 days.
D
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 3 point 6 4 days.
5

A movie production company was interested in the relationship between the budget to make a movie and how well that movie was received by the public. The company collected information on several movies and used it to obtain the regression equation widehat y is equal to 0 point 1 4 5 x plus 0 point 1 3 6 , where x represents the budget of the movie (in millions of dollars) and widehat y is the predicted score of that movie (in points from 0 to 1 ). Which statement best describes the meaning of the y - intercept of the regression line?

A
When the score of a movie is 0 points, the predicted budget is 0 dollars .
B
When the budget of a movie is 0 dollars , the predicted rating is 0 point 1 3 6 points. This interpretation is not meaningful, because a movie cannot have a budget of 0 dollars .
C
When the score of a movie is 0 points, the predicted budget is 0 point 1 3 6 dollars million.
D
When the budget of a movie is 0 dollars , the predicted rating is 0 point 1 4 5 points. This interpretation is not meaningful, because a movie cannot have a budget of 0 dollars .
8

A movie production company was interested in the relationship between a movie’s budget and how well that movie was received by the public. Information was collected on several movies and was used to obtain the regression equation widehat y is equal to 0 point 1 4 5 x plus 0 point 1 3 6 , where x represents the budget of the movie (in millions of dollars) and widehat y is the predicted score of that movie (in points from 0 to 1 ). Which statement best describes the meaning of the slope of the regression line?

A
For each increase in score by 1 point, the predicted budget increases by 0 point 1 3 6 dollars million.
B
For each increase in budget by 1 dollars million, the predicted score increases by 0 point 1 4 5 points.
C
For each increase in score by 1 point, the predicted budget increases by 0 point 1 4 5 dollars million.
D
For each increase in budget by 1 dollars million, the predicted score increases by 0 point 1 3 6 points.
9

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?

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.
10

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation widehat y is equal to 2 x minus 106 , where x represents the club speed and widehat y is the predicted distance. Which statement best describes the meaning of the slope of the regression line?

A
For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards.
B
For each increase in distance by 1 yard, the predicted club speed decreases by 106 ft/sec.
C
For each increase in distance by 1 yard, the predicted club speed increases by 2 ft/sec.
D
For each increase in club speed by 1 ft/sec, the predicted distance decreases by 106 yards.

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