If the Decision to Include Average Tenure at the Company

Multiple Choice

If the decision to include average tenure at the company as a control variable in an attempt to estimate if West coast store locations are outperforming store locations in the rest of the country (i.e., the regression, StoreProfits_i = β₀ + β₁West Coast_i + β₂Avg.Tenure_i + U_i) , which of the following conditions need to be true in order for the estimate of β₁ to be the same regardless of whether Avg. Tenure is used as a control or not?

A) The p-value on average tenure is low.
B) The p-value on average tenure is above 0.10
C) Average tenure and West Coast are uncorrelated.
D) The semi-partial correlation of Store Profits on West Coast holding Avg. Tenure fixed is zero.