Page 165 - Microsoft Word - 00 BA3 IW Prelims STUDENT.docx

Inter-relationships between variables

Question 6

Least-squares regression

Calculate the line of best fit formula using least-squares regression on the
following data.

Advertising spend ($000) Sales value ($000)
10 1,500
12 2,000
15 2,200

18 2,700
19 2,700
21 2,720

n = 6
2
x y xy x
10 1,500 15,000 100
12 2,000 24,000 144
15 2,200 33,000 225
18 2,700 48,600 324
19 2,700 51,300 361
21 2,720 57,120 441
95 13,820 229,020 1,595
∑ ∑ ∑
b =

∑ ∑
2
b = (6 × 229,020 – 95 × 13,820)/(6 × 1,595 – 95 )

b = 61,220/545

b = 112.33

a = y – bx

a = 13,820/6 – 112.3 × 95/6

a = 525.25

y = 525.25 + 112.33x

159