Question 3 [24]
As the marketing and sales director of Bricor Ltd, you recently assumed the role of
project leader of a team appointed by the CEO to research the key variables that determine the demand for the company’s product and to formulate a demand equation for the company’s product. The team also included sales representatives, two representatives from the advertising agency responsible for Bricor Ltd’s advertising, the accountant and a statistician. After conducting intensive research, the project team concluded that the following demand equation is a very good approximation of the demand curve for the product:
Q = 40 – 80P + 25Ps + 50Y
(30) (15.8) (15)
Ṝ2 = 0.56
n = 60
Where:
P = Price of product per unit of cement bricks in rand (A unit = 1 000 bricks.)
Ps = Price of a substitute product per unit of clay bricks in rand (A unit = 1 000 bricks.)
Y = Income per capita per annum measured in thousands of rands
Ṝ2 = Adjusted multiple coefficient of determination
n = Sample size
The standard error of each coefficient (SEC) is listed in brackets below each coefficient.
Other information:
T-values for the variables at the 5% level of significance:
- tp = 2.7
- tps = 1.6
- ty = 3.3
Required
3.1. You are currently presenting the findings of the project team to the executive committee of the company. Explain to the committee members what the signs and magnitudes of each of the three (3) variables of the equation mean in business terms for the company. (12)
3.2. The members of the meeting are very impressed with your analysis, but the production manager, still being a bit sceptical, then asks you what the statistical significance of the results is. Make use of your understanding of the “rule of 2”, the t-test and R2 values provided to explain the statistical significance of the results. Make sure that you also include the coefficient of determination in your reply. (12)
