Multiple Regression Analysis: Model Assumptions

Company XYZ is analyzing the relationship between its advertising expenses and sales revenue using a multiple regression model. The analysts developed the following regression equation:

$$ Sales_t = \beta_0 + \beta_1 \times Advertising_t + \beta_2 \times Price_t + \epsilon_t $$

where:

• $$ Sales_t $$ = Sales revenue at time t
• $$ Advertising_t $$ = Advertising expenses at time t
• $$ Price_t $$ = Price of the product at time t
• $$ \beta_0, \beta_1, \beta_2 $$ = coefficients to be estimated
• $$ \epsilon_t $$ = error term

The analysts know that for their model assumptions to hold, some critical conditions must be satisfied. After estimating the model, they found that the residuals displayed a clear pattern when plotted against the fitted values, indicating potential issues with the model assumptions. Which of the following statements best describes the violation of the model assumptions based on their observations?