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
2010
78.7
Decide which variable should be the independent variable and which should be the dependent variable.
Draw a scatter plot of the ordered pairs.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
Find the estimated life expectancy for an individual born in 1950 and for one born in 1982.
Why aren’t the answers to part (e) the values on the above chart that correspond to those years?
Use the two points in (e) to plot the least squares line on your graph from (b).
Based on the above data, is there a linear relationship between the year of birth and life expectancy?
Are there any outliers in the above data?
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.
What is the slope of the least squares (best-fit) line? Interpret the slope.
The percent of female wage and salary workers who are paid hourly rates is given below for the years 1979 - 1992. (Source:
Bureau of Labor Statistics, U.S. Dept. of Labor )
Year
Percent of workers paid hourly rates
1979
61.2
1980
60.7
1981
61.3
1982
61.3
1983
61.8
1984
61.7
1985
61.8
1986
62.0
1987
62.7
1990
62.8
1992
62.9
Using “year” as the independent variable and “percent” as the dependent variable, make a scatter plot of the data.
Does it appear from inspection that there is a relationship between the variables? Why or why not?
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
Find the estimated percents for 1991 and 1988.
Use the two points in (e) to plot the least squares line on your graph from (b).
Based on the above data, is there a linear relationship between the year and the percent of female wage and salary earners who are paid hourly rates?
Are there any outliers in the above data?
What is the estimated percent for the year 2050? Does the least squares line give an accurate estimate for that year? Explain why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
Yes
0.9448; Yes
62.8233; 62.3265
yes; (1987, 62.7)
72.5937; No
slope = 0.1656. As the year increases by one, the percent of workers paid hourly rates tends to increase by 0.1656.
The maximum discount value of the Entertainment® card for the “Fine Dining” section, Edition 10, for various pages is given below.
Page number
Maximum value ($)
4
16
14
19
25
15
32
17
43
19
57
15
72
16
85
15
90
17
Decide which variable should be the independent variable and which should be the dependent variable.
Draw a scatter plot of the ordered pairs.
Calculate the least squares line. Put the equation in the form of:
Find the correlation coefficient. Is it significant?
Find the estimated maximum values for the restaurants on page 10 and on page 70.
Use the two points in (e) to plot the least squares line on your graph from (b).
Does it appear that the restaurants giving the maximum value are placed in the beginning of the “Fine Dining” section? How did you arrive at your answer?
Suppose that there were 200 pages of restaurants. What do you estimate to be the maximum value for a restaurant listed on page 200?
Is the least squares line valid for page 200? Why or why not?
What is the slope of the least squares (best-fit) line? Interpret the slope.
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Source:
OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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