The owner of a movie theater in a small town decided to experiment with charging

Question

The owner of a movie theater in a small town decided to experiment with charging lower prices on week days, when ticket sales tended to be low. He has daily time series data on ticket sales that include information about the day of the week, the month of the year, and the national ticket sales that week for the movie he was showing. The data cover three years. During the first two years he charged the same price every day of the week, and raised that price half way through the second year. During the last year he ran his experiment, giving a 25% discount on Mondays through Thursdays. He wants to use regression analysis to determine whether his weekday discount raised ticket sales enough to raise his revenues. He first estimates the following population model: log(sales)t = 0 + 1log(price)t + 2log(natsales)t + ut where sales is the number of tickets sold, price is the price of an adult ticket, and natsales is the number of tickets sold for the movie nationally during the week of the observation.

a. Notice that this is a static model. Is there a good reason to add lagged values of either of the independent variables? Explain.

Explanation / Answer

Predictions by Regression: After we have statistically checked the goodness of-fit of the model and the residuals conditions are satisfied, we are ready to use the model for prediction with confidence. Confidence interval provides a useful way of assessing the quality of prediction. In prediction by regression often one or more of the following constructions are of interest:

Confidence Interval Estimate for a Future Value: A confidence interval of interest can be used to evaluate the accuracy of a single (future) value of y corresponding to a chosen value of X (say, X0). This JavaScript provides confidence interval for an estimated value Y corresponding to X0 with a desirable confidence level 1 - a.

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