Question: Suppose you are interested in understanding Coca-Cola profits as a function of temperature, and city-wide promotion data. You have data on Coke profits (sales - costs) in ($1000s) from 300 cities for the month of June 1993, average temperature for that month in degrees Fahrenheit, a variable that is the number of days that month when there were half-page newspaper ads for Coke, and a dummy variable equal to one if the city is in the Southeastern US. You have estimated the following regression:

\[profi{{t}_{i}}=a+b\,s{{d}_{i}}+c\,{{F}_{i}}+d\,F_{i}^{2}+f\,Days{{ & }_{i}}+{{\varepsilon }_{i}}\]

Your OLS estimates are:

Parameter Point Est. Std. Error

a -230 35

b 2000 600

c 10 4

d .0008 .002

f 5 1.5

(a) Does there appear to be a statistically significant increasing marginal effect of temperature on Coke profits?

(b) Does the intercept estimate and standard error indicate that Coke is losing money in the northern US?

(c) How would you add terms to this regression to allow the marginal effect of temperature to be different in the Southeast US from the rest of the country?

(d) If each ad day costs $500 what is probably the expected profit maximizing number of ad days?