Mortgage interest rates. 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 1992–2019. Year Interest Rate (%) Year Interest Rate (%) 1992 8.27 2006 6.47 1993 7.17 2007 6.40 1994 8.28 2008 6.23 1995 7.86 2009 5.38 1996 7.76 2010 4.86 1997 7.57 2011 4.45 1998 6.92 2012 3.66 1999 7.46 2013 3.98 2000 8.08 2014 4.17 2001 7.01 2015 3.85 2002 6.56 2016 3.65 2003 5.89 2017 3.99 2004 5.86 2018 3.54 2005 5.93 2019 3.78 Source: US Census Bureau.

a. Fit the simple regression model E1Yt2 = b0 + b1t where t is the number of years since 1992 (i.e., t = 0, 1,

c, 27).

b. Forecast the average mortgage interest rate in 2020. Find a 95% prediction interval for this forecast