Question

In: Statistics and Probability

The general fund budget (in billions of dollars) for a U.S. state for 1988 (period 1)...

The general fund budget (in billions of dollars) for a U.S. state for 1988 (period 1) to 2011 (period 24) follows.

Year Period Budget
($ billions)
1988 1 3.03
1989 2 3.29
1990 3 3.56
1991 4 4.31
1992 5 4.46
1993 6 4.61
1994 7 4.65
1995 8 5.15
1996 9 5.34
1997 10 5.66
1998 11 6.11
1999 12 6.20
2000 13 6.58
2001 14 6.75
2002 15 6.56
2003 16 6.88
2004 17 7.08
2005 18 7.65
2006 19 8.38
2007 20 8.57
2008 21 8.76
2009 22 8.43
2010 23 8.33
2011 24 8.76

(b)Develop a linear trend equation for this time series to forecast the budget (in billions of dollars). (Round your numerical values to three decimal places.)

Tt = ____?______

(c)What is the forecast (in billions of dollars) for period 25? (Round your answer to two decimal places.)

$___?_____ billion

Solutions

Expert Solution

b.

        X - Mx         Y - My        (X - Mx)2 (X - Mx)(Y - My)
-11.5 -3.1825 132.25 36.5988
-10.5 -2.9225 110.25 30.6863
-9.5 -2.6525 90.25 25.1988
-8.5 -1.9025 72.25 16.1713
-7.5 -1.7525 56.25 13.1438
-6.5 -1.6025 42.25 10.4163
-5.5 -1.5625 30.25 8.5937
-4.5 -1.0625 20.25 4.7813
-3.5 -0.8725 12.25 3.0538
-2.5 -0.5525 6.25 1.3813
-1.5 -0.1025 2.25 0.1537
-0.5 -0.0125 0.25 0.0062
0.5 0.3675 0.25 0.1838
1.5 0.5375 2.25 0.8063
2.5 0.3475 6.25 0.8688
3.5 0.6675 12.25 2.3363
4.5 0.8675 20.25 3.9038
5.5 1.4375 30.25 7.9063
6.5 2.1675 42.25 14.0888
7.5 2.3575 56.25 17.6813
8.5 2.5475 72.25 21.6538
9.5 2.2175 90.25 21.0663
10.5 2.1175 110.25 22.2338
11.5 2.5475 132.25 29.2963
SS: 1150 SP: 292.21

Sum of X = 300
Sum of Y = 149.1
Mean X = 12.5
Mean Y = 6.2125
Sum of squares (SSX) = 1150
Sum of products (SP) = 292.21

Regression Equation = ŷ = bX + a

b = SP/SSX = 292.21/1150 = 0.254

a = MY - bMX = 6.21 - (0.25*12.5) = 3.036

ŷ = 0.254X + 3.036

c. For x=25, ŷ = (0.254*25) + 3.036=9.39


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