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.)
$___?_____ billion
Solutions
Expert Solution
b.
| X - Mx | Y - My | (X - Mx)2 | (X - Mx)(Y - My) |
| -11.5 | -3.1825 | 132.25 | 36.5988 |
| -10.5 | -2.9225 | 110.25 | 30.6863 |
| -9.5 | -2.6525 | 90.25 | 25.1988 |
| -8.5 | -1.9025 | 72.25 | 16.1713 |
| -7.5 | -1.7525 | 56.25 | 13.1438 |
| -6.5 | -1.6025 | 42.25 | 10.4163 |
| -5.5 | -1.5625 | 30.25 | 8.5937 |
| -4.5 | -1.0625 | 20.25 | 4.7813 |
| -3.5 | -0.8725 | 12.25 | 3.0538 |
| -2.5 | -0.5525 | 6.25 | 1.3813 |
| -1.5 | -0.1025 | 2.25 | 0.1537 |
| -0.5 | -0.0125 | 0.25 | 0.0062 |
| 0.5 | 0.3675 | 0.25 | 0.1838 |
| 1.5 | 0.5375 | 2.25 | 0.8063 |
| 2.5 | 0.3475 | 6.25 | 0.8688 |
| 3.5 | 0.6675 | 12.25 | 2.3363 |
| 4.5 | 0.8675 | 20.25 | 3.9038 |
| 5.5 | 1.4375 | 30.25 | 7.9063 |
| 6.5 | 2.1675 | 42.25 | 14.0888 |
| 7.5 | 2.3575 | 56.25 | 17.6813 |
| 8.5 | 2.5475 | 72.25 | 21.6538 |
| 9.5 | 2.2175 | 90.25 | 21.0663 |
| 10.5 | 2.1175 | 110.25 | 22.2338 |
| 11.5 | 2.5475 | 132.25 | 29.2963 |
| SS: 1150 | SP: 292.21 |
Sum of X = 300
Sum of Y = 149.1
Mean X = 12.5
Mean Y = 6.2125
Sum of squares (SSX) = 1150
Sum of products (SP) = 292.21
Regression Equation = ŷ = bX + a
b = SP/SSX = 292.21/1150 = 0.254
a = MY - bMX = 6.21 - (0.25*12.5) = 3.036
ŷ = 0.254X + 3.036
c. For x=25, ŷ = (0.254*25) + 3.036=9.39
orchestra answered 3 years agoRelated Solutions
The general fund budget (in billions of dollars) for a U.S. state for 1988 (period 1)...
The general fund budget (in billions of dollars) for a U.S.
state for 1988 (period 1) to 2011 (period 24) follows.
Year
Period
Budget
($ billions)
1988
1
3.03
1989
2
3.29
1990
3
3.56
1991
4
4.41
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
6.01
1999
12
6.20
2000
13
6.48
2001
14
6.75
2002
15
6.66
2003
16
6.78
2004
17
7.08
2005
18
7.65...
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
4.41
1992
5
4.36
1993
6
4.51
1994
7
4.65
1995
8
5.15
1996
9
5.34
1997
10
5.66
1998
11
6.01
1999
12
6.30
2000
13
6.58
2001
14
6.75
2002
15
6.56
2003
16
6.78
2004
17
6.98
2005
18
7.65...
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
4.41
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
6.01
1999
12
6.20
2000
13
6.48
2001
14
6.75
2002
15
6.56
2003
16
6.78
2004
17
7.08
2005
18
7.65...
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