Answer Happy

Problem 1 (25 points) A researcher has data on the number of tickets sold per theater screen in a large number of theaters over a certain weekend. The data includes 4 different cities, with a total 15 theaters, and 95 screens. One observation is one screen. There were 6 different movies shown in that weekend, labeled 1 through. 6. The dependent variable is tickets sold (variable TICKETS). The researcher regresses this on a number of independent variables, with results as shown below. REGRESSION CHARACTERISTICS Observations 95 Dependent Variable: TICKETS Independent Variable Constant Price D1 D2 D3 D4 D5 Senior Independent Variable Definition Explained (ESS) Residuals (SSR) Total (TSS) The price of each ticket Dummy variable, 1 if the movie shown on that screen is movie 1, -0 otherwise. Dummy for movie 2 (definition analogous to dummy 1 above). Dummy for movie 3 (definition analogous to dummy 1 above). Dummy for movie 4 (definition analogous to dummy 1 above). Dummy for movie 5 (definition analogous to dummy 1 above), Dummy for whether the theater offers. discounts to seniors Sum of Squares 4467.89 5671.02 10138.91 Coefficient. 1203.5 -23.84 -3.92 -3.89 -5.27 -6,98 -1.38 13.23 Standard: Error 40.1 12.86 1.03 2.11 2.36 3.01 0.75 4.38 1 2
a. Calculate the R² of the regression (not the R²1). b. Why is the variable D6 (dummy for movie 6, analogous to the dummies above) not included in the regression? What would happen if it were included? For this question, suppose that the dummies for movies are dropped. An omitted variable in this regression is the average critic review for each of the movies (AvgRev). Do you think this variable may cause omitted variable bias? Why? Assume that theater policies on pricing and senior discount do not change with the critic reviews. (NOTE: the dummies were dropped to avoid collinearity. The variable AvgRev is collinear with the dummies for the movies. This, however, is irrelevant for this question, so you can ignore the "dummies were dropped" part.) (HINT: consider the two conditions necessary for omitted variable bias to happen. Are they likely to occur here?) d. For this question suppose that the researcher included dummies for movies (D1 through D5, excluding D6), and also dummies for the city where the screen is situated (DumCity1 through DumCity3, excluding DumCity4). Would this cause any multicollinearity? Explain intuitively (without formulas). e. Suppose that you run the regression Y₁ = Bo + B₁X₁ + B₂X2 + u₁. The formula for the variance of the OLS estimator is as follows, where the notation is the same as the textbook. 1 03. - 1 (1 - 2², = ) 0 Which element of this formula represents the fact that variation in the independent variable leads to precise estimates? Briefly justify your answer.