Practice: Curve of Best Fit

Practice: Curve of Best Fit

Name: ____________________________

Directions: For each of the following sets of data: a. Identify whether the data is best modeled by a linear or quadratic function b. Find the regression equation and the value of r2 . c. Interpret your results based on your equation and r 2 d. Answer the question

1. The table below shows the life expectancy of males and females based on the year of their birth.

Year

1970

1975

1980

1985

1990

1995

2000

Men

68.7

70.3

71.7

72.9

73.7

74.7

76.5

Women 77.0

78.6

79.4

80.1

80.6

80.8

81.3

Men

Women

a.

b.

c.

d. If the trend continues, in what year will men have the life expectancy of women in 1985?

If the trend continues, what would the life expectancy of women be in 2020?

2. Amery recorded the distance and height of a basketball when shooting a free throw. The data is shown in the table below.

Distance

0

Height

4

2

6

9

12

13

15

8.4

12.1

14.2

13.2

10.5

9.8

a.

b.

c. d. Using the model, what is the approximate maximum height of the basketball? If the free throw line

is 15 feet from the basket, which is 10 feet from the ground, did the ball go in?

Practice: Curve of Best Fit

3. A pumpkin tossing contest is held each year in Morton, Illinois, where people compete to see whose catapult will send pumpkins the farthest. One catapult launches pumpkins 25 feet above the ground at a speed of 125 feet per second. The table shows the horizontal distance travelled at different angles.

Angle (degrees)

20

30

40

50

60

70

Distance (feet)

372

462

509

501

437

323

a.

b.

c.

d.

At what angle would the pumpkin be thrown the farthest?

4. The table below shows the number of tickets sold each year at a chain of movie theaters.

Year 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 Tickets

sold 1368 1392 1411 1420 1446 1472 1471 1511 1538 1533 (millions)

a.

b.

c. d. Predict the number of tickets sold in 2014.

Practice: Curve of Best Fit

5. The table shows how wind affects a runner's performance in the 200 meter dash. Positive wind speeds correspond to tailwinds and negative wind speeds correspond to headwinds. The change in t in the finishing time is the difference between the runner's time when the wind speed is s and the runner's time when there is no wind.

Wind speed (m/sec), s -6

-4

-2

0

2

4

6

Change in finishing time (sec), t (millions)

2.28

1.42

0.67

0

-0.57 -1.05 -1.42

a. b. c. d. What is the expected change in finishing time when there is a headwind of 12 m/sec?

6. The table shows the lengths and corresponding ideal weights of sand sharks.

Length Weight

60

62

64

66

68

70

72

105 114 124 131 139 149 158

a. b. c. d. How long would a sand shark be if it is at its ideal weight of 165?

Practice: Curve of Best Fit

7. The following chart gives information on 10 high school students. The data shows how many hours per week each student watched and what their GPA is.

Student

1 2 3 4 5 6 7 8 9 10

Hours per week watching TV 41 22 32 35 16 26 39 24 11 5

GPA

2.5 3.5 3.0 2.8 3.7 3.4 2.9 3.6 3.8 3.9

a.

b.

c. d. What is the expected GPA of a student that watches 50 hours of TV a week?

8. The table shows the population of a town from 1996 to 2004.

Year, t (since 1996) Population, p (in thousands)

0 1 2 3 4 5 6 7 8 22.8 25.0 26.5 27.1 27.8 28.1 27.9 26.9 26.1

a. b. c. d. If the trend continues, in what year will the population of the town be the same as it was in 1996?

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