Homebase (PTY) Ltd is the manufacturer of a robot vacuum cleaner, iRobot-H. It makes use of built-in cameras and sensors to find its way around a home without fuss. It has different cleaning modes and advanced features such as the ability to produce maps of where it has cleaned and for how long. It really takes the drudge out of vacuum-cleaning homes.

The company sells this product through 55 independent retail stores across the country. Homebase's marketing research team developed the demand equation below for iRobot-H, based on its average retail sales over the last 24 months. From this equation the expected sales for the next 12 months can be estimated.

Q = 6,200 - 40P + 25Pc + 6.2Y + 0.3A + 0.20S

(2.002) (17.5) (6.2) (2.5) (0.09) (0.21) - Standard deviation (SEC) of each parameter

R² = 0.55 n = 55 F = 4.88

The following are the independent variables and their current values:

• Q = Quantity sold per month (sales)
• P (in Rand) = Price of iRobot-H = $2,900
• Pc (in Rand) = Price of leading competitor's product = $3,500
• Y (in Rand) = Average per capita income in the country = $25,000
• A (in Rand) = Homebase's monthly advertising expenditure = $20,000
• S (in units) = Number of robot vacuum cleaners sold across the country = 7,000
• F ( critical value) = 3.38 at 5% level of significance

Required:

1. Calculate the number of iRobot-H vacuum cleaners that Homebase (PTY) Ltd is expected to sell over the next 12 months.
2. Calculate the elasticities for the price of iRobot-H (P), the product of the leading competitor (Pc), average income (Y) and advertising income (A).
3. What is the meaning of the variables -40P, +6.2Y and 0.20S?
4. What is the meaning of the equation R² = 0.55?
5. Determine the t-values for P, Pc and Y, and discuss their significance.