Making Predictions from a Least-Squares Regression Line Answers

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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 2 days?

A
25.96
B
85.58
C
89.22
D
103.78
4

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?

A
0.03625 points
B
0.17225 points
C
0.7862 points
D
1 point
5

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. What is the predicted distance of a ball that is hit with a club speed of 168 ft/sec?

A
106 yards
B
137 yards
C
230 yards
D
336 yards
6

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?

A
For each increase in rating by 1 point, the predicted hours of play increase by 18.182.
B
For each increase in rating by 1 point, the predicted hours of play increase by 27.273.
C
For each increase in hours of play by 1, the predicted rating of the game increases by 18.182 points.
D
For each increase in hours of play by 1, the predicted rating of the game increases by 27.273 points.
7

Market researchers were interested in the relationship between the price of bobbleheads and the demand of bobbleheads. Information was collected from a survey and was used to obtain the regression equation ŷ = –0.277x + 50.455, where x represents the price of a bobblehead (measured in dollars) and ŷ is the predicted demand of bobbleheads (in units). Which statement best describes the meaning of the slope of the regression line?

A
For each increase in demand by 1 unit, the predicted price decreases by $0.227.
B
For each increase in demand by 1 unit, the predicted price decreases by $50.455.
C
For each increase in price by $1, the predicted demand decreases by 0.227 units.
D
For each increase in price by $1, the predicted demand decreases by 50.455 units.
8

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?

A
24.59
B
71.02
C
92.86
D
96.5
9

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 slope of the regression line?

A
For each increase in number of procrastination days by 1, the predicted grade decreases by 3.64 points.
B
For each increase in number of procrastination days by 1, the predicted grade decreases by 96.5 points.
C
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 96.5 days.
D
For each increase in grade by 1 point, the predicted number of procrastination days decreases by 3.64 days.
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 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?

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

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