Question

In: Statistics and Probability

Use Excel to graph the following data sets (these graphsdo not need to be adjustable)...

Use Excel to graph the following data sets (these graphs do not need to be adjustable) and then find the equation of the linear regression line and its R2 Value. Use the equation to answer any questions.

A. The data shows the results of a study that compared the daily average number of cigarettes an individual smoked per day to his or her death.

Daily average # of cigarettes

12

15

22

30

35

38

42

46

55

60

Average age at death

75

72

69

66

64

62

61

58

56

51

If a person smokes no cigarettes, what is the expected age at the time of death?

B. Population density is a measure of how crowded a population is. In the United States, the number of people per square mile is given. Use a base year of 0 for 1900 in your equation.

Year

1900

1910

1920

1930

1940

1950

1960

1970

1980

1990

2000

Density (people/mi2)

21.5

26.0

29.9

34.7

37.2

42.6

50.6

57.5

64.0

70.3

74.9

Predict the population density of the United States in 2020.

Solutions

Expert Solution

A. The scatter plot, regression equation and R2 value are shown below:

The regression equation is y (avg age at death) = -0.4573 * x + 79.634, x being the daily avg # cigarettes

If a person doesn't smoke, x = 0

Expected avg age at death, y = -0.4537 x 0 + 79.634 = 79.634 years.

B. Following is the table of revised years basis base year of 1990:

Year Revised year Population Density
1900 0 21.5
1910 10 26
1920 20 29.9
1930 30 34.7
1940 40 37.2
1950 50 42.6
1960 60 50.6
1970 70 57.5
1980 80 64
1990 90 70.3
2000 100 74.9

Below is the scatter plot along with regression equation and R2 value:

The regression equation for population density, y = 0.5505*x + 18.768

where y is the population density and x is the revised year.

For the year 2020, revised year, x = 2020 - 1900 = 120

expected population density in the year 2020, y = 0.5505*120 + 18.768 = 66.06 + 18.768 = 84.828 (people/mi)


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