Question

In: Statistics and Probability

The annual revenues collected in each of the past ten years for the Orange County Solid...

The annual revenues collected in each of the past ten years for the Orange County Solid Waste Division are provided below. If the revenue total for 2014 is $42,843,901, which revenue projection method (SMA, TMA, or regression) is the most accurate in this case? Use APE to justify your answer. Use the last three years of revenues for moving averages and all years for regression

Year

Revenue

2005

33,120,989

2006

36,979,392

2007

36,390,302

2008

35,678,632

2009

37,986,901

2010

39,697,702

2011

37,639,287

2012

39,479,675

2013

40,099,709

Solutions

Expert Solution

SOLUTION:

[Moving average of the given last 3 years = (37739287 + 39479674 + 40199709)/3 = 39139556

Estimated regression equation is: y2014 = 33934691.44 + (710496.73 x 10) = 41039659.

Clearly, 41039659 is closer to 2014 actual of 43844901]

Back-up Theory

The linear regression model Y = β0 + β1X + ε, ………………………………………..(1)

where ε is the error term, which is assumed to be Normally distributed with mean 0 and variance σ2.

Estimated Regression of Y on X is given by: Y = β0cap + β1capX, …………………….(2)

where β1cap = Sxy/Sxx = r.√(Syy/Sxx) = r.(SDy/SDx) and β0cap = Ybar – β1cap.Xbar..…………………………….…..(3)

Mean X = Xbar = (1/n) Σ(i = 1 to n)xi ………………………………………….……….….(4)

Mean Y = Ybar = (1/n) Σ(i = 1 to n)yi ………………………………………….……….….(5)

Sxx = Σ(i = 1 to n)(xi – Xbar)2 ………………………………………………..…………....(6)

Syy = Σ(i = 1 to n)(yi – Ybar)2 ……………………………………………..………………(7)

Sxy = Σ(i = 1 to n){(xi – Xbar)(yi – Ybar)} ……………………………………………….(8)

Now to work out the solution,

Take the given first year as x = 1, next year as x = 2, and so on, last year as x = 9 and revenue as y.

n

9

Xbar

5.00

ybar

37487175.1111

Sxx

60

Syy

4.07794E+13

Sxy

42629804

β1cap

710496.7333

β0cap

33934691.44

Estimated regression equation is: ycap = 33934691.44 + 710496.73x.


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