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.

Question

Quizplus · Accepted Answer

If the variables of interest (West Coast) and the potential control variable (Avg. Tenure) are uncorrelated, then the estimate of β₁ will be the same regardless of whether Avg. Tenure is used as a control or not. This is because the effect of West Coast on Store Profits is not confounded by Avg. Tenure in this case. The p-value on average tenure or the semi-partial correlation of Store Profits on West Coast holding Avg. Tenure fixed do not necessarily have an impact on the estimate of β₁.

If the Decision to Include Average Tenure at the Company