3. Bureau of Meteorology has the mean annual temperatures tn in Melbourne as follows n 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 tn 16.6 16.0 17.1 16.3 16.8 16.5 16.5 16.4 16.9 17.0 Your need to nd the real number a: such that function T301) 2 x(n 2014) + 17 provides the best approximation of the given data. (a) Show that the residual sum of squares R(3:) between the data points and TI is a poly nomial of degree 2. Write expressions for its coefcients, using sigma notation. (b) Prove that R has a unique stationary point. Explain why it is the global minimum. (c) Find the value of a: = as\" (to the third decimal place) that minimises R(:c). (d) Compare T342018) with the real value 132313 : 17.0. What conclusions can you draw