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1. You are an analyst at MLB.com who was asked to determine how the temperature

during a home game in.uences attendance. You select a sample of 50 observations of home-

game attendance and the day.s temperature from around the league, and attempt to estimate

the following PRF

Yi = B0 + B1Xi + Ei

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 significant rela-

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

con.dence 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% confidence level? Provide the null and alternative hy-

potheses, 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 = B0 + B1X1i + B2X2i + Ei

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 di¤erence 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 = B0 + B1X1i + B2X2i + B3X3i + Ei

where X3i is the interaction term. Construct this variable in your data, and estimate

the PRF. Is the interaction term (B3) signi.cantly di¤erent from 0? Provide the p-value

for this test and explain your answer.