In response to the Great Recession, Federal Reserve leaders continue to keep the short run target interest rate near zero. While the Fed controls short-term interest rates, long-term interest rates essentially depend on supply/demand dynamics, as well as longer-term interest rate expectations. Consider the following annualized rates for 3-month Treasury yields and 10-year Treasury yields.

a. Construct and interpret a scatter plot of a 10-year treasury yield against a 3-month yield.
b. Calculate and interpret the sample correlation coefficient. Use α = 0.05 to test if the population correlation coefficient is significantly different from zero.
c. Estimate and interpret a sample regression equation using the 10-year yield as the response variable and the 3-month yield as the explanatory variable.

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Year 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 3-Month Yield (%) 3.47 1.63 1.03 1.40 3.21 4.85 4.47 1.39 0.15 0.14 10-Year Yield (%) 5.02 4.61 4.02 4.27 4.29 4.79 4.63 3.67 3.26 3.21