QTB – Nov 2015 – L1 – SB – Q5b – Statistics

Calculate Pearson’s correlation coefficient between company expenditure and income over eight years and interpret the result.

Question

An auditing firm is carrying out an analytical review of the financial transactions of its client, XYZ Manufacturing Company Limited. In order to ascertain the relationship that exists between the company’s annual expenditure and annual income, the following information was extracted from the company’s record for eight different years:

Years	1	2	3	4	5	6	7	8
Expenditure (x)	30	25	40	35	50	30	55	20
Income (y)	42	45	55	50	60	40	70	35

You are required to:

i. Calculate the Pearson’s product-moment correlation coefficient between $x$ and $y$ . (9 Marks)

ii. Comment on the result in (i). (1 Mark)

(Total: 10 Marks)

Answer

(ii) Comment on the Result:

The value $r = 0.962$ indicates a strong positive correlation between the company’s annual expenditure and annual income. This suggests that as expenditure increases, income also tends to increase in a proportional manner.