Question

1 8 of 24 (20 complete) Score: 0 of 3 pts Problem 4.16 Sales of Volkswagen's popular Beetle have grown steadily at auto dealerships in Nevada during the past 5 years (see table below) Year Sales 450 510 516 575 595 a) Forecasted sales for year 6 using the trend projection (linear regression) method are sales (round your response to one decimal place).

Answer 1

a)

	Year(x)	Sales (y)	xy	x2
	1	450	450	1
	2	510	1020	4
	3	516	1548	9
	4	575	2300	16
	5	595	2975	25
Total	15	2646	8293	55

x-bar = Sum(x)/n = 15/5 = 3
y-bar = Sum(y)/n = 2646/5 = 529.2

b = (Sum(xy) – n*x-bar*y-bar)/(Sum(x2) – n*x-bar*x-bar) = (8293-5*3*529.2)/(55–5*3*3)
   = 355/10 = 35.5

a = y-bar –b*x-bar
= 529.2-35.5*3 = 422.7

Regression equation is y = a + bx,
we get following regression equation by substituting values of a and b
Regression equation is y =422.7 + 35.5x

for x = 6, Sales = 422.7 + 35.5*6 = 635.7

Forecasted sales for year 6 using the trend projection method are 635.7 sales