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Practice

3.3.5 Practice

3.3.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

Using the following information, find the residual for each of the coordinate pairs, ( x , y ) in 1 - 6.

A line of best fit for a data set is y = 1.1 x + 3.4 .

  1. ( 5 , 8.8 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. ( 2.5 , 5.95 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. ( 0 , 3.72 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. ( 1.5 , 5.05 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. ( − 3 , 0 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. ( − 5 , − 4.86 )
  1. -2.76
  2. 0
  3. 0.32
  4. -0.2
  5. -0.1
  1. In the scatter plot below, the length of fish and the age of the fish are shown. The residual for the fish that is 2 years old and 100 mm long is 8.06 mm.
    A SCATTER PLOT THAT SHOWS AGE OF FISH IN YEARS ON THE X-AXIS AND LENGTH OF FISH IN MILLIMETERS ON THE Y-AXIS. A LINE OF BEST FIT IS DRAWN, AND THE POINT (2, 100) IS LABELED.
    What does this residual mean?
  1. The actual fish at 2 years old is about 8 mm shorter than the linear model estimates.
  2. The actual fish at 2 years old is about 8 mm longer than the linear model estimates.

Use the following information to answer questions 8 – 11.

Four athletes on a track team are comparing their personal bests in the 100-meter and 200-meter events. A table of their best times is shown below. 

Athlete 100 m time (seconds) 200 m time (seconds)

1

12.95

26.68

2

13.81

29.48

3

14.66

28.11

4

14.88

30.93

The line of best fit has an equation of y = 1.5115 x + 7.526 , where x represents the 100-meter time and y represents the 200-meter time.

  1. What is the residual for athlete number 1?
  1. − 1.08
  2. − 0.91
  3. 0.91
  4. 1.08
  5. 0.42
  6. − 0.42
  7. − 1.57
  8. 1.57
  1. What is the residual for athlete number 2?
  1. − 1.08
  2. − 0.91
  3. 0.91
  4. 1.08
  5. 0.42
  6. − 0.42
  7. − 1.57
  8. 1.57
  1. What is the residual for athlete number 3?
  1. − 1.08
  2. − 0.91
  3. 0.91
  4. 1.08
  5. 0.42
  6. − 0.42
  7. − 1.57
  8. 1.57
  1. What is the residual for athlete number 4?
  1. − 1.08
  2. − 0.91
  3. 0.91
  4. 1.08
  5. 0.42
  6. − 0.42
  7. − 1.57
  8. 1.57
  1. The curb weight of a car is the weight of the car without luggage or passengers. The scatter plot below shows the curb weight, in pounds, of 5 cars and their fuel efficiency, in miles per gallon. 

    Will the residual for 25.33 be a positive or negative value?
    A SCATTER PLOT WITH CURB WEIGHT IN HUNDREDS OF POUNDS ON THE X-AXIS AND FUEL EFFICIENCY IN MILES PER GALLON ON THE Y-AXIS. A LINE OF BEST FIT IS DRAWN. FOUR POINTS ARE ABOVE THE LINE AND ONE POINT IS BELOW.
  1. positive
  2. negative