2. (15 pts} Extend the regression model above to include a dummy variable indicating whether or not the game took place on a weekend. The new PHF to be analyzed is K = 330 +.81X1i +52X21: +51: where K- is the attendance of each home game, X 11- is the temperature at the start of each home game in degrees, and X3,- is a dummy variable which equals 1 when the game took place on a weekend (1} otherwise). Estimate the above PHF using the sample provided. (a) Determine ill, and 52 and interpret them (mind the units of the variables and remember that this is a multiple regression model with a dummy variable). (b) What is the predicted di'erence between the attendance at a baseball game on an 81} degree day during the week or the weekend? (:3) Extend the model again to include an interaction between temperature and the weekend dummy variable, K: = :30 + )3an + 32X21+ 133X3+ Ea where X3;- is the interaction term. Construct this variable in your data, and estimate the PRF. Is the interaction term {333:} signicantly different from 0? Provide the p-value for this test and explain your