Question

Rebel Sole is a rapidly expanding shoe company. The following is the demand estimate for its popular shoes. The estimate was done using 40 observations.

Q = 10 – 10 P + 4 A + 0.42 I + 0.25 P_y

       (3)   (1.8)    (0.7)   (0.1)     (0.1)

F = 93, s = 6, R^₂ = 93%

Q is quantity sold (in thousands), P is shoe price, A is advertising expenditure (in thousands), the numbers in parentheses are standard errors, I is disposable income per capita (thousands of dollars), and P_y is the price of related goods.

1. Evaluate the model based on F, R².
2. Test the significance of P_y.
3. If P = $5, A = $30,000, I = 50,000, and P_y = $6, calculate advertising elasticity.
4. Given the information in c. above, calculate the 95% confidence interval for Q.

Answer 1

(a)

F = 93

All independent variables have a jointly significant effect on Q.

R² = 93%

Represents that price, advertising, disposable income and price of related goods cause 93% variability in Q.

(b)

Z = 0.25 / 0.1 = 2.5

Z is 1.96 for 5% of level significance, which is less than 2.5.

Explanation: Py is significant.

(c)

Q = 10 -10P + 4A + 0.42I + 0.25Py

Q = 10 – 10(5) + 4(30) + 0.42(50) + 0.25(6)= 10- 50 + 120 + 21 +1.5

= 102.5

Advertising Elasticity = 4 x 30 / 102.5 = 1.17

(d)

Q.= 0.1 ± 1.96 (3) = 0.1 ± 5.88

Lower Limit= - 5.78

Upper Limit = 5.98