A computer game company is preparing to launch a new simulation game to the market, Econotopia. You start the game with 300 reputation points and, earn/lose reputation points for your management performance in the end. In line with one of the most essential principles in game development, the project team seeks to keep the effort-reward balance, the more effort the players put the higher reward they should get. The early access codes are distributed to 500 players and after two weeks, they have collected the data from the users terminals where Yi= the reputation points earned and Xi= the number of hours devoted to the game. After plotting the data, the data analyst also runs the simple regression model Yi = 80-81Xi + zi Points Earned 1000 12m 800 400 Number of Hours a) Assume that the intercept of the regression model is statistically insignificant at 95% confidence level. In what interval would you expect that the t-value of intercept to fall? Hi b) A colleague who knows little about econometrics argues that the errors are smaller for short time played while it is larger as the time played gets longer. Name the problem formally. Explain the potential drawbacks. c) The data analyst proposes that the robust standard errors to solve the problem (in part (c)) and conducts a simulation to support his argument. For a given data generating process, he/she shows that the fraction of false rejections in significance tests under constant variance assumptions is 0.075. When he/she performs the same simulation with robust standard errors, the fraction of false rejections drops down to 0.05. Would you believe that the robust standard errors really solve the problem? d) The data analyst shows the bottom panel of the regression table. Table 1: OLS Results (Bottom Panel) R Adjusted R 0.44 0.44 Residual Std. Error F Statistic 180.68 (df-498) 393.88 (di = 1: 498) Considering the critical value of the F-distribution given a 95% confidence level and (df-1; 498) is 3.86, comment on the overall significance of the regression model.