To graph: The scatter plot of the data.
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.
To find: The regression line that represents the given data and draws the graph of the same.
The regression line that represents the given data is .
By the use of online calculator, the regression line for the given data obtained is , where average life expectancy is the y-intercept and year is the x-intercept.
Therefore, the regression line that represents the given data is .
The graph that represents the equation is shown below in Figure 1.
From Figure 2, the graph for the linear equation is a straight line.
To find: The estimate life expectancy in the year 2006.
The estimate life expectancy in the year 2006 is 80.4.
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.
To Compare: The estimate value with the actual value.
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 .
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