Concept explainers
Polynomial Models Use a graphing calculator to do the following cubic and quartic regression problems. (See Examples 5 and 6.)
Gross National Income The following table shows the gross national income (GNI) in dollars per capita for middle- and upper- income countries for selected years. (Data from: Organization for Economic Cooperation and Development.)
Year | 2000 | 2002 | 2004 | 2006 | 2008 | 2010 | 2012 | 2014 |
GNI | 1768 | 1842 | 2335 | 3148 | 4403 | 5472 | 6949 | 7901 |
a. Plot the data with
b. Use cubic regression to find a third-order polynomial function
c. Graph
d. What does the model predict for the GNI in the year 2017?
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Check out a sample textbook solutionChapter 3 Solutions
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- Torontos Jewish Population The table gives the population of Torontos Jewish community at various times. Source: The Mathematics Teacher. Plot the population on the y-axis against the year on the x-axis. Let x represents the years since 1900. Do the data appear to lie along a straight line? Plot the natural logarithm of the population against the year. Does the graph appear to be more linear than the graph in part a? Find an equation for the least squares line for the data plotted in part b. If your graphing calculator has an exponential regression feature, find the exponential function that best fits the given data according to the least squares method. Take the natural logarithm of the equation found in part d, and verify that the result is same as the equation found in part c. In Section 11.1 on Solutions of Elementary and Separable Differential Equations, we will see another type of function that is a better fit to these data.arrow_forwardLife Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forwardA regression was run to determine whether there is arelationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). Theresults of the regression are given below. Use this topredict the age of a tree with diameter 10 inches. y=ax+ba=6.301b=1.044r=0.970arrow_forward
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