The table lists the closing Dow Jones Industrial Averages (DJIA) at the first day the market is open for the months from March 2013 to June 2014. Entry Month Year DJIA 0 March 2013 14090 1 April 2013 14573 2 May 2013 14701 3 June 2013 15254 4 July 2013 14975 5 August 2013 15628 6 September 2013 14834 7 October 2013 15193 8 November 2013 15616 9 December 2013 16009 10 January 2014 16441 11 February 2014 15373 12 March 2014 16168 13 April 2014 16533 14 May 2014 16559 15 June 2014 16744 a. Construct the trigonometric discrete least squares polynomial of degree 4 for the above data. b. Approximate the closing averages on April 8, 2013, and April 8, 2014, using the polynomial constructed in part (a). c. The closing on the given days in part (b) were 14613 and 16256. Overall, how good do you think this polynomial can predict closing averages? d. Approximate the closing for June 17, 2014. The actual closing was 16808. Was this prediction of any use?

Intro to Multivariable Calculus Lecture 4 Thursday, September 1, 2019:37 AM MATH 2204 Notes Page 1 MATH 2204 Notes Page 2 MATH 2204 Notes Page 3