Question

The following table shows a company's annual revenue (in billions of dollars) for 2009 to 2014.

Year	Period (t)	Revenue ($ billions)
2009	1	23.6
2010	2	29.2
2011	3	37.8
2012	4	50.3
2013	5	59.8
2014	6	66.6

a)

What type of pattern exists in the data?

The time series plot shows an upward curvilinear trend.

The time series plot shows a downward curvilinear trend.     

The time series plot shows a downward linear trend.

The time series plot shows an upward linear trend.

(b)

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

T_t = ____

(c)

What is the average revenue increase per year (in billions of dollars) that this company has been realizing? (Round your answer to three decimal places.)

$ ____ billion

(d)

Compute an estimate of this company's revenue (in billions of dollars) for 2015. (Round your answer to two decimal places.)

$ ____ billion

Answer 1

X	Y	XY	X²	Y²
1	23.6	23.6	1	556.96
2	29.2	58.4	4	852.64
3	37.8	113.4	9	1428.84
4	50.3	201.2	16	2530.09
5	59.8	299	25	3576.04
6	66.6	399.6	36	4435.56
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
21	267.3	1095.2	91	13380.13

Sample size, n =	6
x̅ = Ʃx/n = 21/6 =	3.5
y̅ = Ʃy/n = 267.3/6 =	44.55
SSxx = Ʃx² - (Ʃx)²/n = 91 - (21)²/6 =	17.5
SSyy = Ʃy² - (Ʃy)²/n = 13380.13 - (267.3)²/6 =	1471.915
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 1095.2 - (21)(267.3)/6 =	159.65

a)

The time series plot shows an upward linear trend.

b)

Slope, b = SSxy/SSxx = 159.65/17.5 =    9.122857143

y-intercept, a = y̅ -b* x̅ = 44.55 - (9.12286)*3.5 =    12.62

Regression equation :   

ŷ = 12.62 + (9.123) x  

c)

average revenue increase per year = 9.123 billion

d)

Predicted value of y at x =    7

ŷ = 12.62 + (9.1229) * 7 = 76.48 billion