Concept explainers
The following table gives the life expectancy at birth of females born in the United States in various years from 1970 to 2010.
Source: National Center for Health Statistics.
Year of Birth | Life Expectancy (years) |
1970 | 74.7 |
1975 | 76.6 |
1980 | 77.4 |
1985 | 78.2 |
1990 | 78.8 |
1995 | 78.9 |
2000 | 79.3 |
2005 | 80.1 |
2010 | 81.0 |
Find an equation for the least squares line for these data, using year of birth as the independent variable.
Answer to Problem 1EA
Solution:
Explanation of Solution
Given: Consider the data provided in the table.
Year of birth | Life expectancy |
---|---|
1970 | 74.7 |
1975 | 76.6 |
1980 | 77.4 |
1985 | 78.2 |
1990 | 78.8 |
1995 | 78.9 |
2000 | 79.3 |
2005 | 80.1 |
2010 | 81.0 |
Explanation:
Let the data points be
Here, the value of slope is calculated by
and the intercept is calculated by
Now, compute the least squares line for the provided data.
Let
The required data is shown in the table:
70 | 74.7 | 5229 | 4900 | 5580.09 |
75 | 76.6 | 5745 | 5625 | 5867.56 |
80 | 77.4 | 6192 | 6400 | 5990.76 |
85 | 78.2 | 6647 | 7225 | 6115.24 |
90 | 78.8 | 7092 | 8100 | 6209.44 |
95 | 78.9 | 7495.5 | 9025 | 6225.21 |
100 | 79.3 | 7930 | 10,000 | 6288.49 |
105 | 80.1 | 8410.5 | 11,025 | 6416.01 |
110 | 81 | 8910 | 12,100 | 6561 |
Now, substitute these values to determine the value of slope and intercept.
Compute the slope
Compute the intercept
Now, the least squares line is
Conclusion: The equation of the least squares line is
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Chapter 1 Solutions
Finite Mathematics (11th Edition)
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning