Question

Given the following​ data, use​ least-squares regression to derive a trend​ equation:                                                                                      Period 1 2 3 4 5 6 Demand 6 8 5 8 7 13 The​ least-squares regression equation that shows the best relationship between demand and period is ​(round your responses to two decimal​ places):

y = ? + ?x

where y = demand and x = period

Answer 1

Period(X) Demand (Y). XY X^2(Square of X)

1 6 6 1

2 8 16 4

3 5 15 9

4 8 32 16

5 7 35 25

6 13 78 36

X = 1+2+3+4+5+6 = 21

Y = 6+8+5+8+7+13 = 47

XY = 6+16+15+32+35+78 = 182

X^2 = 1+4+9+16+25+36 = 91

n = Number of periods = 6

X-bar = X / n = 21/6 = 3.5

Y-bar = Y/n = 47/6 = 7.83

b = ( XY - nX-bar .Y-bar ) / ( X^2 - n. Square of X-bar)

= [182 - (6)(3.5)(7.83) ] / [91 - (6)(3.5)(3.5)]

= (182 - 164.43) / (91 - 73.5)

= 17.57 / 17.5

= 1.00

a = Y-bar - b(X-bar) = 7.83 - 1.00(3.5) = 7.83 - 3.5 = 4.33

Y = a + bx => Y = 4.33 + 1.00x

So the regression equation is Y = 4.33 + 1.00x