Some statisticians have done (semi-serious) studies to connect Super Bowl scores to the performance of the Dow Jones Industrial Average (DJIA). (For example, see summers, P.M.: The Super Bowl Theory: Fourth and Long, College Mathematics Journal 31.) Below is a table showing the total points scored in recent Super Bowls and the % change in the DJIA for a sample of six years?

a. Compute the sample covariance for Super Bowl points and % change in the DJIA.
b. Compute the sample correlation coefficient here. (The sample standard deviation, s x, of the Total Points data is 8.65; the sample standard deviation, s y, for the DJIA data is 19.34.)

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% Change in DJIA for Total Winner Points th Year* Year 2005 2006 2007 2008 2009 2010 Patriots 46 31 46 31 Steelers 16.3 Colts 6.4 Giants Steelers 18.8 11.1 Saints S0 33.8 48