Problem 4.

You read that alternative and nuclear energy use in the US, as a percentage of total energy use, was 10.7696% in 2000, 10.6167% in 2003, 10.6212% in 2005, 11.1976% in 2008, 11.7183% in 2010, 11.9923% in 2011, and 12.0645% in 2012. Let x be the number of years after 2000, and let y be alternative and nuclear energy use in the US, as a percentage of total energy use, so the data points are (0, 10.7696), (3, 10.6167), (5, 10.6212), (8, 11.1976), (10, 11.7183), (11, 11.9923), and (12, 12.0645). (a) For a linear model of the form y = c1 + c2x which is a best fit for this data in the sense of least squares, use MATLAB to find the normal equations for c1 and c2. (b) Find the coefficients of the least-squares line y = c1 +c2x for the data points.

(c) Estimate alternative and nuclear energy use in the US, as a percentage of total energy use, for 2017. You may assume the trends of 2000 to 2012 continue.