2. . The total cost of a federal government program in millions of dollars is shown in uie table below. (Notice that the year 2010 data is missing.) 2015 2016 1159 1267 1367 | 1436 1505 1562 year 2005 2006 | 2007 2008 | 2009 2011 | 2012 2013 2014 | $ in mil. 731 782 833 886 956 (a) Determine and plot the degree 10 Lagrange polynomial through the data. Use it to estimate the 2010 cost and compare to the actual value of $1,049 (in mil.).

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Chapter2: Second-order Linear Odes
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Please answer part a, b and c

2.
The total cost of a federal government program in millions of dollars is shown
in ume table below. (Notice that the year 2010 data is missing.)
2005 2006 | 2007 2008 2009 | 2011 2012 2013 2014 | 2015 2016
1159 1267 1367 1436 1505 1562
year
$ in mil.
731
782
833
886
956
(a) Determine and plot the degree 10 Lagrange polynomial through the data. Use it
to estimate the 2010 cost and compare to the actual value of $1,049 (in mil.).
(b) Determine and plot a clamped cubic spline for the data (using the appropriate
slopes at 2005 and 2016). Use it to estimate the 2010 cost and compare to the
actual value of $1,049 (in mil.)
1
(c) Perform a least-squares analysis and estimate the 2010 cost and compare to the
actual value of $1,049 (in mil). (Choose an appropriate least squares linear or
polynomial model.)
Transcribed Image Text:2. The total cost of a federal government program in millions of dollars is shown in ume table below. (Notice that the year 2010 data is missing.) 2005 2006 | 2007 2008 2009 | 2011 2012 2013 2014 | 2015 2016 1159 1267 1367 1436 1505 1562 year $ in mil. 731 782 833 886 956 (a) Determine and plot the degree 10 Lagrange polynomial through the data. Use it to estimate the 2010 cost and compare to the actual value of $1,049 (in mil.). (b) Determine and plot a clamped cubic spline for the data (using the appropriate slopes at 2005 and 2016). Use it to estimate the 2010 cost and compare to the actual value of $1,049 (in mil.) 1 (c) Perform a least-squares analysis and estimate the 2010 cost and compare to the actual value of $1,049 (in mil). (Choose an appropriate least squares linear or polynomial model.)
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