Question

ASSIGNMENT ON STATISTICS As a marketing analyst for Mutual life Assurance Plc. You gather the following data on advertising and sales Advertising ($)’00 Sales (Units)’000 1 1 2 1 3 2 4 2 5 4 i. Find the least square lines relating sales and advertising ii. Interpret your answer in (i) above.

Answer 1

x y x^2 xy

1 1 1 1

2 1 4 2

3 2 9 6

4 2 16 8

5 4 25 20

Sum 15 10 55 37

(i)

$b=\frac{n\sum_{i=1}^nx_iy_i-\sum_{i=1}^nx_i\sum_{i=1}^ny_i}{n\sum_{i=1}^nx_i^2-(\sum_{i=1}^nx_i)^2}=\frac{5*37-15*10}{5*55-15^2}=0.7$

$a=\frac{\sum_{i=1}^ny_i-b\sum_{i=1}^nx_i}{n}=\frac{10-0.7*15}{5}=-0.1$

The least square line: $y=a+bx=-0.1+0.7x$

(ii)

When Advertising increases by $100, the Sales increases by $700.