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1. (10 pts) You are an analyst at MLB.com who was asked to determine how the temperature during a home game influences attendance. You select

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1. (10 pts) You are an analyst at MLB.com who was asked to determine how the temperature during a home game influences attendance. You select a sample of 60 observations of home- game attendance and the day's temperature from around the league, and attempt to estimate the following PRF where ? is the attendence of each home game and X, is the temperature at the start of each home game in degrees. Estimate the above PRF using the sample provided (a) Determine by and by, and interpret them (mind the units of the variables). (b) Determine the coefficient of determination A , and interpret it. (c) Using only your regression output, can you say there is a statistically significant rele- tionship between temperature and attendance at baseball games? Explain your answer. (d) Predict the attendance at a baseball game on an 80 degree day. (DO NOT provide a confidence interval around this point estimate). (e) Is there evidence that one additional degree in temperature results in less then 100 additional attendees at the 95%% confidence level? Provide the null and alternative hy- potheses, the p-value associated with this test, and your conclusion. 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 PRF to be analyzed is where Y is the attendance of each home game, Xy, is the temperature at the start of each home game in degrees, and ky; is a dummy variable which equals 1 when the game took place on a weekend (0 otherwise). Estimate the above PRF using the sample provided. (a) Determine by, and by 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 difference between the attendance at a baseball game on an 80 degree day during the week or the weekend? (c) Extend the model again to include an interaction between temperature and the weekend dummy variable, where Xy, is the interaction term. Construct this variable in your dets, and estimate the PRF. Is the interaction term (8,) significantly different from 01 Provide the p-value for this test and explain your

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