Question

6. ​Recently, fixed mortgage rates have been at historical lows due to the housing slowdown. The data table linked below shows the​ 30-year fixed average mortgage rate for the month of December every year between 1987 and 2010.

Year   Rate_(%)
1987   11.09
1988   11.04
1989   10.17
1990   9.93
1991   8.57
1992   8.3
1993   7.25
1994   9.04
1995   7.21
1996   7.06
1997   7.07
1998   6.84
1999   7.65
2000   7.74
2001   7.07
2002   6.84
2003   6.94
2004   6.79
2005   7.02
2006   6.82
2007   6.63
2008   5.88
2009   5.64
2010   5.4

b. Forecast the average December mortgage rate in 2011 using a trend projection ​(Round to two decimal places as​ needed.)

c. Calculate the MAD for this forecast. ​(Round to two decimal places as​ needed.)

d. Determine the Durbin–Watson statistic (Round to two decimal places as​ needed.)

e. Identify the critical values. ​(Round to two decimal places as​ needed.)

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	47964	183.99	1150	56.4	-224.23
mean	1998.50	7.67	SSxx	SSyy	SSxy

sample size ,   n =   24          
here, x̅ = Σx / n=   1998.50   ,     ȳ = Σy/n =   7.67  
                  
SSxx =    Σ(x-x̅)² =    1150.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   -224.2          
                  
estimated slope , ß1 = SSxy/SSxx =   -224.2   /   1150.000   =   -0.1950
                  
intercept,   ß0 = y̅-ß1* x̄ =   397.3303          
                  
so, regression line is   Ŷ =   397.3303   +   -0.1950   *x
...............

Predicted Y at X=   2011   is                  
Ŷ =   397.33030   +   -0.194978   *   2011   =   5.2290

.................

MAD = 0.5835

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