In determining the causal effect of Price on Sales, if advertising spend is a good control variable, how will the correlation of the error terms from the regression, Sales_i = β₀ + β₁Price_i + U_i, and Sales_i = α₀ + α₁Price_i + α₂Advertising_i + V_i and price be related? A) Cor(U_i, V_i) = 0 B) Cor(U_i, Price_i) = 0, Cor(Price_i, V_i) = 0 C) Cor(U_i, Price_i) ≠ 0, Cor(Price_i, V_i) = 0 D) Cor(U_i, Price_i) = 0, Cor(Price_i, V_i) ≠ 0

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Including advertising spend as a control variable in the regression model aims to isolate the effect of price on sales by accounting for advertising's influence. If advertising is a good control, it means that any correlation between price and the error term in the model without advertising (U) should be due to omitted variable bias, which is reduced when advertising is included. Therefore, before controlling for advertising, the error term (U) may be correlated with price because advertising affects both sales and is correlated with price. After including advertising in the model, the new error term (V) should not be correlated with price if advertising adequately controls for the omitted variable, leading to the conclusion that Cor(U, Price) ≠ 0 and Cor(Price, V) = 0.

In Determining the Causal Effect of Price on Sales, If