Question

Use the following to answer the question on the basis of the following regression equation. (Standard errors in parentheses, n = 200.) Q = -6,500 - 100PA + 50PB + .3I + .2A; R2 =.12 (2,500) (50) (30) (.1) (.08) where Q is the quantity demanded of good A; PA = $10, price of good A; PB = $8, price of good B; I = $12,000, per capita income; and A = $20,000, monthly advertising expenditures. Which of the variables does not pass the t-test at the .05 level of significance? (Hint: You can use the “rule of 2” to approximate.)

Answer 1

Use the relationship of coefficient of the parameter with its standard error to find the required t-statistic

• t-statistic for Intercept = |-6500/2500| > 2
• t-statistic for PA = |-100/50| = 2
• t-statistic for PB = |50/30| < 2
• t-statistic for I = |0.3/0.1| > 2
• t-statistic for A |0.2/0.08| > 2

As per the rule of thumb, if the absolute value of the t-statistic is greater than or equal to 2, then the corresponding parameter estimate is statistically different from zero. Here PB is not greater than zero, Hence PB does not pass the t-test at the .05 level of significance