Question

1. Liza is a manager of a leading soft drink manufacturing firm. Liza uses 10 months data and estimates the following demand equation:

Q = 10 – .5P + 1.5Y + .25P_R

       (.10)   (.03)   (.045)   (.50)

where P is the price of the soft drink manufactured by Liza's firm, Y refers to household per capita income (in thousands of dollars), and P_R is the price of a rival soft drink manufacturing firm. The p-values are given in the parentheses. The R² = 0.71 (p-value = .034).

1. Which of the explanatory variables have significant effects on the demand for soft drink manufactured by Liza's firm (and how do you know)?

2. Interpret the coefficient on two of the variables and comment on if it makes economic sense.

3. Comment on how well this regression estimates demand, include both statistical and economic reasons.

Answer 1

Q = 10 – .5P + 1.5Y + .25P_R

       (.10)   (.03)   (.045)   (.50)

evaluating the significance at 5% significance level

P value for P = 0.03

since the p value is less than 0.05 , we can say that price is a significant explanatory variable.

P value for Y = 0.045 and is less than 0.05 , we can say that income  is a significant explanatory variable.

P value for PR = 0.50 and is more than 0.05 , we can say that income  is a insignificant explanatory variable.

coefficient estimate for P = -0.5.

yes this makes economic sense as the sign of coefficient is negative which is consistent with demand theory of inverse relation between price and demand . According to this , $1 increase in price will cause the demand to fall by 0.5

coefficient estimate for Y = 1.5

yes this makes economic sense as the sign of coefficient is positive which is consistent with direct   relation between income  and demand. According to this , $1 increase in income will cause the demand to increase by 1.5

the value of R2 = 0.71 .this means that 71% of variation in demand for soft drink are explained by these 3 variables and the model is statistically significant as P value < 0.05 . Given the industry standards the above model provides a good estimate of demand for soft drink through these variables. Also according to economic theory the signs of variable are correct and consistent with economic theory .