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 4.41
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
2006 19 8.48
2007 20 8.57
2008 21 8.76
2009 22 8.53
2010 23 8.23
2011 24 8.76

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

A certain company produces and sells frozen pizzas to public schools throughout the eastern United States. Using a very aggressive marketing strategy, they have been able to increase their annual revenue by approximately $10 million over the past 10 years. But increased competition has slowed their growth rate in the past few years. The annual revenue, in millions of dollars, for the previous 10 years is shown.

Year Revenue
1 8.43
2 10.74
3 13.08
4 14.11
5 16.41
6 17.21
7 18.47
8 18.55
9 18.40
10 18.43

(b) Using Minitab or Excel, develop a quadratic trend equation that can be used to forecast revenue (in millions of dollars). (Round your numerical values to three decimal places.)

Tt =

(c) Using the trend equation developed in part (b), forecast revenue (in millions of dollars) in year 11. (Round your answer to two decimal places.)

$  million

Solutions

Expert Solution

Question 1: We input the data set in Excel and use the "Regression" option under Data > Data Analysis to answer the given questions. The screenshot of the output and the data set is given below.

Develop a linear trend equation for this time series to forecast the budget -> Tt = 3.040 + 0.254 t. Here, t = Period, Tt = Budget.
(c) Forecast -> 3.040 + (0.254 * 25) = $9.39 billion.


Question 2: We input the data set in Excel and use the "Regression" option under Data > Data Analysis to answer the given questions. The screenshot of the output and the data set is given below.

Develop a quadratic trend equation that can be used to forecast revenue -> Tt = 552.050 + 297.072 t + (-16.822) t2. Here, t = Year, Tt = Revenue.
(c) Forecast -> 552.050 + (297.072 * 11) + (-16.822 * 121) = $1784.38 million.

orchestra answered 2 years ago
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