Below is the life expectancy for an individual born in the United States in certain years

| August 30, 2017

Question
Below is the life expectancy for an individual born in the United States in certain years. (Source: National Center for Health Statistics)

Year of Birth

Life Expectancy

1930

59.7

1940

62.9

1950

70.2

1965

69.7

1973

71.4

1982

74.5

1987

75

1992

75.7

Using the table above, answer the following:

a. Decide which variable should be the independent variable and which should be the dependent variable.

b. Draw a scatter plot of the ordered pairs.

c. Calculate the least squares line. Put the equation in the form of:

^y= a + bx

d. Find the correlation coefficient. Is it significant?

e. Find the estimated life expectancy for an individual born in 1950 and for one born in 1982.

f. Why aren’t the answers to part (e) the values on the above chart that correspond to those years?

g. Use the two points in (e) to plot the least squares line on your graph from (b).

h. Based on the above data, is there a linear relationship between the year of birth and life expectancy?

i. Are there any outliers in the above data?

j. Using the least squares line, find the estimated life expectancy for an individual born in 1850

Does the least squares line give an accurate estimate for that year? Explain why or why not.

k. What is the slope of the least squares (best-fit) line? Interpret the slope.

In 1990 the number of driver deaths per 100,000 for the different age groups was as follows (Source: The National Highway Traffic Safety Administration’s National Center for Statistics and Analysis):

Age

Number of Driver Deaths per 100,000

15-24

28

25-39

15

40-69

10

70-79

15

80+

25

Complete the following using the table above:

a. For each age group, pick the midpoint of the interval for the x value. (For the 80+ group, use 85.)

b. Using ages as the independent variable and Number of driver deaths per 100,000 as the dependent variable, make a scatter plot of the data.

c. Calculate the least squares (best-fit) line. Put the equation in the form of: ^y= a + bx

d. Find the correlation coefficient. Is it significant?

e. Pick two ages and find the estimated fatality rates.

f. Use the two points in (e) to plot the least squares line on your graph from (b).

g. Based on the above data, is there a linear relationship between age of a driver and driver fatality rate?

h. What is the slope of the least squares (best-fit) line? Interpret the slope.

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