The level at which commercial lending institutions set mortgage interest rates has a significant effect on the volume of buying, selling, and construction of residential and commercial real estate. The data in the table are the annual average mortgage interest rates for conventional, fixed-rate, 30-year loans for the period 1990-2015.

a. Fit the simple regression model
E(Yt) = β0 + β1t
where t is the number of years since 1990 (i.e., t = 0, 1, c, 25).
b. Forecast the average mortgage interest rate in 2016. Find a 95% prediction interval for this forecast.

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Interest Rate (%) Interest Rate (%) Year Year 5.86 5.93 6.47 9.97 1990 1991 1992 2004 2005 2006 2007 11.14 8.27 1993 1994 1995 1996 1997 1998 7.17 8.28 7.86 7.76 7.57 6.92 6.40 6.23 2008 2009 2010 2011 2012 5.38 4.86 4.45 3.66 7.46 8.08 7.01 6.56 5.89 2013 2014 2015 1999 2000 2001 2002 2003 3.98 4.17 3.85