Question

Suppose that you have data on restaurant meal sales. You’d like to find out which type of customer group – families or business meetings – generates the most sales. You also have data on which day of the week your observations come, the server who served them, and the drinks that they ordered. How would you write a regression model to test this relationship?

Answer 1

The dependent variable for the regression model is:

y = sales

The independent variables are:

x1 = customer group - familes (1 if true otherwise 0)

x2 = customer group = business meetings (1 if true otherwise 0)

x3,i = Day of the week ( where i stands for the day and takes value 1 if present otherwise 0)

x4,i = Server (where i stands for the server and takes value 1 if present otherwise 0)

x5,i = Drinks (where i stands for the drink and takes value 1 if present otherwise 0)

For the purpose of creating an equation let us assume that there are only 2 servers and 2 drinks and the restaurant runs 4 days a week. So we have:

y = alpha + beta1*x1 + beta2*x2 + beta(3,1)*x(3,1) + beta(3,2)*x(3,2) + beta(3,3)*x(3,3) + beta(3,4)*x(3,4) + beta(4,1)*x(4,1) + beta(4,2)*x(4,2) + beta(5,1)*x(5,1) + beta(5,2)*x(5,2) + error

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