Concept explainers
To find:
An equation for the least squares line for given data.
Answer to Problem 1EA
Solution:
The equation for the least squares line is
Explanation of Solution
Given:
The data is given by,
Year of Birth | Life Expectancy (years) |
Table
Approach:
The general equation for least square line is as follows.
Here,
And
Calculation:
Consider
The total number of data is
So,
Construct the new table for find the value for
Totals |
Table
Then,
Now calculate for
Therefore, the equation for the least squares line is
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Chapter 1 Solutions
Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)
- Cigarette Smokers The following table gives a recent estimate in millions of the smoking status among persons 25 years of the age and over their highest level of education. Source: National health interview survey. Education Current smoker Former smoker Non smoker Total Less than a high school diploma 7.90 6.66 14.12 28.68 High school diploma or GED 14.38 13.09 25.70 53.17 Some collage 12.41 13.55 28.65 54.61 Bachelors degree or higher 4.97 12.87 38.34 56.18 Total 39.66 46.17 106.81 192.64 a. Find the probability that a person is a current smoker. b. Find a probability that a person has less than a high school diploma. c. Find a probability that a person is a current smoker and has less than a high school diploma. d. Find the probability that a person is a current smoker, given that the person has less than a high school diploma. e. Are the events current smoker and less than a high school diploma independent events?arrow_forwardOil ProductionThe following table shows the amount of crude oil in billions of barrels produced in the United States in recent years. Source: U.S. Energy Information Administration. Year Crude Oil Produced 2002 2.097 2003 2.060 2004 1.989 2005 1.893 2006 1.857 2007 1.853 2008 1.830 2009 1.954 2010 2.000 2011 2.063 2012 2.377 In this exercise we are interested in the total amount of crude oil produced over the 10-year period from mid-2002 to mid-2012, using the data for the 11 years above. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation. Approximate the amount of crude oil produced over the 10-year period 2002-2012 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a. This is also equivalent to a formula known as the trapezoidal rule, discussed in the next chapter. If your calculator has a cubic regression feature, find the best-fitting cubic function for these data, letting t=0 correspond to 2000. Then integrate this equation over the interval [2.12] to estimate the amount of crude oil produced over this time period. Compare with your answer to part a.arrow_forward
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