question archive 1)You are an analyst at MLB
1)You are an analyst at MLB
Subject:MathPrice: Bought3
1)You are an analyst at MLB.com who was asked to determine how the
temperature during a home game ináuences attendance. You select a sample of 50 observations of homegame attendance and the dayís temperature from around the league, and attempt to estimate the following PRF
Yi = 0 + 1Xi + "i
where Yi is the attendance of each home game and Xi is the
temperature at the start of each home game in degrees. Estimate the above PRF
using the sample provided.
(a) Determine b0 and b1, and interpret them (mind the units of the variables).
(b) Determine the coe¢ cient of determination R2 , and interpret it.
(c) Using only your regression output, can you say there is a statistically signiÖcant relationship 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 conÖdence interval around this point estimate).
(e) Is there evidence that one additional degree in temperature results in less than 100 additional attendees at the 95% conÖdence level? Provide the null and alternative hypotheses, the p-value associated with this test, and your conclusion.
2. 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
Yi = 0 + 1X1i + 2X2i + "i
where Yi is the attendance of each home game, X1i is the temperature at the start of each home game in degrees, and X2i 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 b1, and b2 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,
Yi = 0 + 1X1i + 2X2i + 3X3i + "i
where X3i is the interaction term. Construct this variable in your data, and estimate the PRF. Is the interaction term (
3 ) signiÖcantly di§erent from 0? Provide the p-value for this test and explain your answer
