Regression Analysis

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You work for a consulting firm as a market analyst. Your firm been hired by two Burger King restaurants in a suburban Atlanta market area to study the demand for its basis hamburger meal package referred as a "Combo 1" on its menu. The two restaurants face competition from five other hamburger restaurants and three others serving "drive-through" fast food.

The owner of the Burger King restaurants provided you with the data shown in Table below. Q is the total of Combo 1 meals sold at both locations during each week in 2006. P is the price charged for Combo 1 meal at the two locations. (Prices are identical at the two Burger King restaurants.)

Every week the Burger King owner advertises special price offers at its two restaurants exclusively in daily newspaper advertisements. A is the dollar amount spent on ads for each week in 2006. The owner could not provide your firm with data on prices charged by other competing restaurants in 2006. For the one-year time period of the study, household income and population in the suburb did not change enough to warrant inclusion in the demand analysis.

a. Using statistical software (i.e.: Excel), run a regression to derive the industry demand equation for Combo 1 meals. Estimate the parameters of the empirical demand function specified in a linear functional form for the demand of Combo 1 meals. Write your estimated industry demand equation for Combo 1 meals.
b. Evaluate your regression results by examining the signs of the relevant parameters such as p-values, t-statistics, and R2.
c. Discuss how the estimation of demand might be improved.
d. Using your estimated demand equation, calculate an own-price elasticity and advertising elasticity. Compute the elasticity values at the sample means of the data in Table 2. Discuss, in quantitative terms, the meaning of each elasticity.
e. If the owner plans to charge a price of $ 4.15 for a Combo1 meal and spend $ 18,000 per week on advertising, how many Combo 1 meals do you predict will be sold each week?
f. If the owner spends $ 18,000 per week on advertising, write the equation for the inverse demand function. Then, calculate the demand price for 50,000 Combo 1 meals.