Please explain each answer. Thanks! LOGISTIC REGRESSION An independent film dist

Question

Please explain each answer. Thanks!

LOGISTIC REGRESSION An independent film distribution company has built a logistic regression model to predict the possibility that a movie will be a "hit" - that is, earn more than $5 million dollars in revenues. The model uses only the film's genre (either drama, comedy or action) and the amount spent in marketing the film as explanatory variables. The probability that a film will be a hit is calculated using the standard logistic regression formula exp(w(x)) P -1 + exp(w) where x is a vector of independent variables and is a linear function of the independent variables. The specific independent variables and corresponding coefficient values for the movie prediction model are Variable (x) Description Parameter (B) INTERCEPT COMEDY DRAMA ACTION BUDGET Constant term COMEDY 1 if the film is a comedy. COMEDY O otherwise DRAMA 1 if the film is a comedy. DRAMA 0 otherwise ACTION 1 if the film is an action film. ACTION0 otherwise Marketing budget in millions of$ 15 Question 1: According to the model, given the same marketing budget is a comedy or an action movie more likely to be a hit? Explain Question 2: The company is considering acquiring the rights to a new Australian action film, The Melbourne Identity and promoting it with a marketing budget of $1.5 million. According to their model, what is the probability that it will be a hit? a. 0.26 b. 1.05 C. 0.74 d. 0.50

Explanation / Answer

1) Action will be a hit as the parameter for action is 0.2 and probability is higher.

For action w(x) = 0.1 + 0.2 = 0.3

P = e^0.3/1+e^0.3 = 0.57

For comedy w(x) = 0.1

P = e^0.1/1+e^0.1 = 0.52

2) Budget = 1.5, action movies

w(x ) = 1.5 * 0.5 + 0.2 = 0.95

P = e^0.95/1+e^0.95 = 0.74

C option

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