Question

The director of marketing at vangaurd corporation belives that sales of the company bright side laundry detergent CSS are related to vanguards own advertising expenditure(A), as well as the combined adverstising expenditure of it's three biggest rival detergents( R) The marketing director collects 36 weekly observations on S, A, R to estimate the following regression euvation: S = a+b.A+C.r, where S,A and R are measured in dollars per week. Vanguards marketing director is comfortable using parameters estimates that are statistically significant at the 10% level or better.

a. What sign does the marketing director expect a,b and c to have?

b. Which new variable is introduced in to this will cause multi-collinearity? Name and define the variable?

c. State the reason for multi collinearity?

d. Will the forecast of sales in this case follow a times series or a seasonal trend provide reason

Answer 1

a. What sign does the marketing director expect a,b and c to have?

--- The coefficient of own advertising expenditure (A) is expected to have a positive sign, whereas the coefficient of the combined adverstising expenditure of it's three biggest rival detergents( R) is expected to have a negative sign. On the other hand, the intercept "a" is expected to have a positive sign, which is the baseline sales without any advertising activity. Expected signs of coefficients: a (+), b (+) and c(-).

b. Which new variable is introduced in to this will cause multi-collinearity? Name and define the variable?

--- If we consider the sales of the competitors also in the model along with the combined advertising expenditure (R), it will have multicollinearity.

c. State the reason for multi collinearity?

--- Since, the sales and advertising expenditure of the competitors will be highly correlated with themselves, multicollinearity problem will be there.

d. Will the forecast of sales in this case follow a times series or a seasonal trend provide reason

--- Only 36 weeks of data is considered here which does not cover even a year. Hence, seasonal trend is not expected. However, there could be a time series trend.