|il'tuestion 2 {4D marks] A consultant specifies a multiplicative model for monthly saies of a brand with just three independent variables: monthly price {Pricey}, monthly advertising spend (Adv!) and a December dummy {Decembenj to capture the {positive} lChristmas effect: {'1} Safes: = DPriceflo'ufz y''m'rgu: Questions: {a} {5 iTIEFKSi Please show that til is the price elasticity through a mathematical derivation. {h} {5 marks} Please show that y is the multiplier for December through a mathematical derivation or through a numerical example. {c} {E merits} Please explain how model {1} includes interaction effects between variables through a mathematical derivation or through a numerical example. {d} {E marks} In some of the months. advertising spend is zero. Please explain whether this is a prohiem for model {'1} and if it is, what you can do to solve it. {e} {5 marks} The model {i} only includes current-month advertising effects. Please explain how you can change this to capture carryover advertising effects from previous months. {f} {1D marks} To estimate model {1} as a linear regression model1 a certain mathematical transformation needs to he applied. Please explain which transformation and show what the model looks like after the transformation