Concept explainers
Life Expectancy The average life expectancy in the United States has been rising steadily over the past few decades, as shown in the table.
- (a) Make a scatter plot of the data.
- (b) Find and graph the regression line.
- (c) Use the linear model you found in part (b) to predict the life expectancy in the year 2006.
- (d) Search live Internet or your campus library to find the actual 2006 average life expectancy. Compare to your answer in part (c).
Year | Life expectancy |
1920 | 54.1 |
1930 | 59.7 |
1940 | 62.9 |
1950 | 68.2 |
1960 | 69.7 |
1970 | 70.8 |
1980 | 73.7 |
1990 | 75.4 |
2000 | 76.9 |
(a)
To graph: The scatter plot of the data.
Explanation of Solution
Graph:
Consider the Year as the x coordinates and average life expectancy as the y coordinates.
Let x = Year – 1920.
The scatter plots of the given data are shown below in Figure 1.
In Figure 1, all the points are plotted on the graph.
The year 1920 is corresponds to 0 and 2000 is corresponds to 80.
(b)
To find: The regression line that represents the given data and draws the graph of the same.
Answer to Problem 9P
The regression line that represents the given data is
Explanation of Solution
By the use of online calculator, the regression line for the given data obtained is
Therefore, the regression line that represents the given data is
The graph that represents the equation
From Figure 2, the graph for the linear equation
(c)
To find: The estimate life expectancy in the year 2006.
Answer to Problem 9P
The estimate life expectancy in the year 2006 is 80.4.
Explanation of Solution
Consider the year 2006.
From part (b), it is obtained that the linear equation that represents the given data is
Substitute x = 2006 − 1920 in the above equation to compute the life expectancy in the year 2006.
Thus, the estimate life expectancy in the year 2006 is 80.4 years.
(d)
To Compare: The estimate value with the actual value.
Explanation of Solution
By the use of internet, the actual life expectancy in United states in the year 2006 is 77.69 years.
From part (c), it is obtained that the estimate life expectancy in the year 2006 is 80.4 years.
It is observed that the actual life expectancy is less than the average life expectancy estimated by the use of linear model
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning