The table shows the total gross domestic products y (in billions of dollars) of the United States for the years 2009 through 2015.

(a) Find the least squares regression line y = at + b for the data, where t represents the year with t = 9 corresponding to 2009, by solving the system

for a and b. Use the regression feature of a graphing utility to confirm the result.
(b) Use the linear model to create a table of estimated values of y. Compare the estimated values with the actual data.
(c) Use the linear model to estimate the gross domestic product for 2016.
(d) Is the linear model valid for long-term predictions of gross domestic products? Explain.

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Year GDP, y 14,414.6 2009 2010 14,798.5 2011 15,379.2 2012 16,027.2 2013 16,498.1 2014 17,183.5 2015 17,803.4 Spreadsheet at LarsonPrecalculus.com 1b + (84b + 1036a = 1,361,309.3 112,104.5 84a