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Making Predictions from a Least-Squares Regression Line 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 ŷ = 27.273x + 18.182, where x represents the time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). Which statement best describes the meaning of the slope of the regression line?

For each increase in rating by 1 point, the predicted hours of play increase by 18.182.

For each increase in rating by 1 point, the predicted hours of play increase by 27.273.

For each increase in hours of play by 1, the predicted rating of the game increases by 18.182 points.

For each increase in hours of play by 1, the predicted rating of the game increases by 27.273 points.

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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 ŷ = 27.273x + 18.182, where x represents time it takes to play (in hours) and ŷ is the predicted rating of that game (in points). Which statement best describes the meaning of the y-intercept of the regression line?

When the rating of a game is 0 points, the predicted time to play is 0 hours.

When the rating of a game is 0 points, the predicted time to play is 18.182 hours.

When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game cannot have a playtime of 0 hours.

When the time to play is 0 hours, the predicted rating is 27.273. This interpretation is not meaningful since a game cannot have a playtime of 0 hours.

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 ŷ = –3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. Which statement best describes the meaning of the y-intercept of the regression line?

When the grade is 0, the predicted number of procrastination days is 0.

When the grade is 0, the predicted number of procrastination days is 96.5.

When the number of procrastination days is 0, the predicted grade is 3.64 points.

When the number of procrastination days is 0, the predicted grade is 96.5 points.

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 ŷ = 0.145x + 0.136, where x represents the budget of the movie (in millions of dollars) and ŷ 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?

For each increase in score by 1 point, the predicted budget increases by $0.136 million.

For each increase in score by 1 point, the predicted budget increases by $0.145 million.

For each increase in budget by $1 million, the predicted score increases by 0.136 points.

For each increase in budget by $1 million, the predicted score increases by 0.145 points.

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 ŷ = 2x - 106, where x represents the club speed and ŷ is the predicted distance. Which statement best describes the meaning of the slope of the regression line?

For each increase in distance by 1 yard, the predicted club speed increases by 2 ft/sec.

For each increase in distance by 1 yard, the predicted club speed decreases by 106 ft/sec.

For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards.

For each increase in club speed by 1 ft/sec, the predicted distance decreases by 106 yards.

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 ŷ = –3.64x + 96.5, where x represents the number of procrastination days and ŷ is the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?

24.59

71.02

92.86

96.5

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. Information was collected on several movies and was used to obtain the regression equation ŷ = 0.145x + 0.136, where x represents the budget of a movie (in millions of dollars) and ŷ is the predicted score of that movie (in points from 0 to 1). What is the predicted score of a movie that has a $250,000 budget?

0.03625 points

0.17225 points

0.7862 points

1 point

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Making Predictions from a Least-Squares Regression Line Answers

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