Liza is a manager of a leading soft drink manufacturing firm. Liza uses 10 month

Question

Liza is a manager of a leading soft drink manufacturing firm. Liza uses 10 months data and estimates the following demand equation: Q=10-0.25P+1.5Y+0.5Pr. (2) (0.50) (0.75) (0.17) where P is the price of the soft drink manufactured by Liza's firm, Y refers to household per capita income, and Pr is the price of a rival soft drink manufacturing firm. The standard errors of the coefficients are given in the parenttheses. Which of the explanatory variables have significant effects on the demand for soft drink manufactured by Liza's firm? Explain. (hint: t-score are calculated t=(a-0)/se), (at 95% confidence level, the relevant t-statistic for 6 degrees of freedom is 1.94)

Explanation / Answer

The demand equation is,

Q=10-0.25P+1.5Y+0.5Pr

For each of the explanatory variables, we need to test the hypothesis that the coefficient of the exaplanatory variable is not 0. For that we need to calculate the t-score and compare the t-score with the critical value of t (1.94) at 95% confidence level and for 6 degrees of freedom. If the observed t-score is less than -1.94 or greater than 1.94, we reject the null hypothesis (that is the coefficient of the explanatory variable is not 0) and conclude that the explanatory variables has significant effects. If the observed t-score is in between -1.94 and 1.94, we fail to reject the null hypothesis (that is the coefficient of the explanatory variable is 0) and conclude that the explanatory variables has no significant effects.

For P,

coefficient a = -0.25

Standard error, se = 0.5

t=(a-0)/se) = (-0.25-0)/0.5 = -0.5

As, t-score lies in between -1.94 and 1.94, we fail to reject the null hypothesis (that is the coefficient of the explanatory variable is 0) and conclude that the explanatory variables has no significant effects.

For Y,

coefficient a = 1.5

Standard error, se = 0.75

t=(a-0)/se) = (1.5-0)/0.75 = 2

As, t-score is greater than 1.94, we reject the null hypothesis (that is the coefficient of the explanatory variable is not 0) and conclude that the explanatory variables has significant effects.

For Pr,

coefficient a = 0.5

Standard error, se = 0.17

t=(a-0)/se) = (0.5-0)/0.17 = 2.94

As, t-score is greater than 1.94, we reject the null hypothesis (that is the coefficient of the explanatory variable is not 0) and conclude that the explanatory variables has significant effects.

Thus, Y and Pr have significant effects on the demand for soft drink manufactured by Liza's firm.

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