Question

The following are the monthly figures of advertising expenditure and sales of a company. It is found that advertising expenditure has impact on sales generally after 2 months. Allowing for this time lag, calculate the coefficient of correlation :

Month	Advertising expenditure (in thousand )	Sales (in units)
January	50	1200
February	60	1500
March	70	1600
April	90	2000
May	120	2200
June	150	2500
July	140	2400
August	160	2600
September	170	2800
October	100	2000
November	200	3100
December	250	3900

Answer 1

Let X be the random variable denoting the advertising expenditure and Y be the random variable denoting the sales (in units). Since, advertising expenditure has impact on sales after 2 months, we expect the expenditure in January to be correlated with March sales, the expenditure in February to be correlated with April sales and so on.

Hence, the day points are: (50, 1600), (60, 2000), (70, 2200), (90, 2500), (120, 2400), (150, 2600), (140, 2800), (160, 2000), (170, 3100) and (100, 3900).

We have, E(X) = 111, SSx = 16890, E(Y) = 2510, SSy = 3829000, SSxy = 99900

The correlation co-efficient, r = = 0.3928 (Ans).