Question

Just the Fax, Inc. (JTF) hired a consultant to estimate the demand for its line of telecommunications devices in 35 different market areas for one month. The available data set includes observations on the number of thousands of units sold by JTF per month (QX), the price per unit charged by JTF (PX), the average unit price of competing brands (PZ), monthly advertising expenditures by JTF (A), and average gross sales (in thousands of dollars) of businesses in the market area (I). The consultant provided the results below without the estimated coefficients. He, however, provided the standard errors (in parenthesis), t-stats (in square brackets), and R square. JTF has hired you as a second consultant to produce the estimated coefficients, and to determine whether they are statistically significant.

QX = b0 + b1PX + b2PZ + b3A + b4I

(250) (1.4) (0.8) (0.5) (0.4)

[1.5] [-2.5] [1.5] [3.0] [2.5]

R2 = 0.80

a) If the critical t value at 30 degree of freedom and at 5% significance level is 2.04, which of the coefficients are statistically significant?

b) If b3 equals 1.5, explain how a change in advertising affects sales:

Answer 1

Part a) Coefficients are statistically significant if the calculated t-stats value is more than the critical t value for a given degree of freedom and significance level.

The critical t value at 30 degree of freedom and 5% significance level is 2.04.

The coefficients of price per unit charged by JTF (PX), monthly advertising expenditures by JTF (A), and average gross sales (in thousands of dollars) of businesses in the market area (I) are more than 2.04. So, these coefficients are statistically significant.

Part b) It is given that the value of b3 = 1.5. A is monthly advertising expenditures by JTF. The value of b3 shows that for one unit change in the monthly advertising expenditure, number of units sold by JTF per month (QX) increases by 1,500.