Question I .- Kraft Promotion Analysis Linear Regression (8 points) Kraft is considering running a promotion of a 20% discount along with a feature ad. However, a potential concern for the management is a signicant drop in sales the week following the promotion. In the industry jargon this is often referred to as \"Trough\". If the trough following the promotion is large enough, the promotion may be rendered ineffective. Your objective is to develop a sales response model and evaluate the effectiveness of the promotion using historical data. a. Please create the following variables using the existing variables. 1) % Discount = (Shelf Price Price Paid) / (Shelf Price) 2) Feature Dummy = 1 when product is advertised, 0 otherwise 3) Trough = Lag (% Discount) this variable takes the value of previous week % Discount. It is used to capture the impact of promotion in previous week on sales in the current week. b. Estimate the following regression model. Please show the parameter estimates Regression MODEL: Units Sold = a + b * ShelfPrice + c * %Discount + d * Feature Dummy + e * Trough c. How would you interpret each parameter, a, b, c, d and e? Which variable is the most important? d. Please assess the model fit and perform residual diagnostics