Demand Estimation - Soft Drinks - Case Study Example

Q is the quantity demanded (average cans consumed per year); the dependent variable
P, I, and T represent price, income, and mean temperature respectively, and are the exogenous variables.
α, β1, β2, and β3 are estimators of the parameters and ε is the error term.
Using MS Excel the regression results are as shown in the table below.
Therefore the estimated model becomes:
Q= 514.27-242.97P+1.36I+ 2.93T
Interpret each coefficient of the independent variable in the soft drink demand estimated function in question 1. (20%)

α = 514.27
It implies that holding all factors affecting consumption constant, approximately 514 cans will be consumed on average.
β1 = -242.97, which means that a unit increase in the 6-pack’s price, reduces the number of cans consumed by 242.97 and vice versa, ceteris paribus.
β2 = 1.36, holding price and mean temperature constant, an unit ($1000) increase in per capita income increases average consumption by 1.36 cans and vice versa.
β1 = 2.93, a rise in average temperature by 1F, increases the soft drink consumption by 2.93 cans, holding income and price constant.

Given your answer to question 1, please comment on whether the regression estimated function is a good fit or not.
It’s not a good Tom fit, R2 is a bit low.
What is the interpretation of the coefficient of determination (R-square)?

R2 = 0.6980, the implication is that, the independent variables; price, income, and mean temperature only explain 69.80% of the changes that occur to the regressand, leaving 30.20% to be explained by variables not included in the model.
Moreover, when adjusted for degrees of freedom, the regressors only explain 67.74% of the changes in quantity demanded (adjusted R squared = 0.6774)
May we use the estimated function to predict future demand? Explain why. (20%)

The model is statistically significant and thus useful in determining future demand. Note that, significant F = 1.6455* 10-11 (approximately equal to zero). The implication is that the model is relevant with the estimators statistically different from zero (i.e. β1 ≠ β2≠ β3≠0)
How many cans/capita/year of soft drink should be for a state in which 6-pack price=$1.95, Income/Capita=$23,500, and Mean Temp= 68°F? (20%)
Using the estimated demand function;
Q= 514.27-242.97P+1.36I+ 2.93T
Q= 514.27-242.97*1.95+1.36*23.5+ 2.93*68
= 271.67
≈ 271 cans

Now omit the price and temperature from the regression equation. Should a marketing plan for soft drinks be designed that relocates most canned drink machines into low-income neighborhoods? Why or why not? (20%)
If income is the only exogenous variable, i.e Q = α +β1I + ε
And the estimated demand function becomes; Q = 254 – 5.96I
However, given that the R2 is 0.11 ( very low), the independent variable only explains 11% of the changes in the dependent variable leaving a very high percentage ( 89%) to be explained by other factors, hence not a good model. Read More