Question

Tim is a marketing executive at a large retail company and is interested in investigating the association between product sales and advertising expenditure. Tim collects data from a random sample of 15 products, and records the annual sales (in $) and advertising expenditure (in $) for each product. Tim calculates the coefficient of correlation between these two numerical variables to be 0.80. So increased advertising expenditure is strongly associated with increased sales. A week later, Tim is informed by the advertising team that the advertising expenditure of two of the products was incorrectly recorded. After correcting the two values, Tim runs his calculations again. The covariance between sales and advertising expenditure has decreased by 14%. The standard deviation of advertising expenditure has decreased by 10%. What is the revised coefficient of correlation between sales and advertising expenditure after correction of the two erroneous values?

Answer 1

Let X= Advertising expenditure (in $)

Y=annual sales (in $)

Let

• be the original coefficient of correlation
• cov(X,Y) be the old correlation coefficient
• be the old sample standard deviation of Advertising expenditure (in $)
• be the sample standard deviation of  annual sales

We can write

After the correction, we find that the covariance between sales and advertising expenditure has decreased by 14%.

The revised covariance is

The standard deviation of advertising expenditure has decreased by 10%.

the revised standard deviation of X is

The revised correlation coefficient is

ans: the revised coefficient of correlation between sales and advertising expenditure after correction of the two erroneous values is 0.7644