Problem bank

Problem 233 of 333MediumStatisticsP233

Reading a coefficient next to an interaction

  1. A colleague fits r=β0+β1s+β2V+β3 sV+εr = \beta_0 + \beta_1 s + \beta_2 V + \beta_3\, sV + \varepsilon, where ss is a trading signal and VV is the VIX level (between about 12 and 40 in the sample, mean 20). The estimates are β^1=−0.3\hat\beta_1 = -0.3 and β^3=0.05\hat\beta_3 = 0.05. They conclude that the signal has a negative effect on returns. Are they right? What would the coefficient on ss be if VV were centered at 20?