From Chapter 19 - Discussion Question #6, page 574: Sales of a product are influenced by the salesperson’s level of education and gender, as well as consumer income, ethnicity, and wealth.

a. Formulate this statement as a multiple regression model (form only, without parameter estimation).

b. Specify dummy variables.

c. If the effects of consumer income and wealth are not additive alone, and an interaction is expected, specify a new variable to test for the interaction.

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a. The multiple regression model can be formulated as follows:

Sales = β0 + β1*Education + β2*Gender + β3*Income + β4*Ethnicity + β5*Wealth

Here, Sales is the dependent variable, and Education, Gender, Income, Ethnicity, and Wealth are the independent variables. β0, β1, β2, β3, β4, and β5 are the parameters to be estimated.

b. To specify the dummy variables, we need to convert categorical variables (such as Gender and Ethnicity) into binary variables.

For Gender, we can assign one binary variable where 1 represents male and 0 represents female.

For Ethnicity, we can assign multiple binary variables, each representing a specific ethnicity (e.g., Caucasian, African American, Asian, etc.). Each variable will take a value of 1 if the corresponding individual belongs to that ethnicity and 0 otherwise.

c. If an interaction is expected between consumer income and wealth, we can create a new variable to test for this interaction. Let's call this variable Income_Wealth. We can define it as the product of consumer income and wealth:

Income_Wealth = Income * Wealth

Now we can include this new variable in the multiple regression model:

Sales = β0 + β1*Education + β2*Gender + β3*Income + β4*Ethnicity + β5*Wealth + β6*Income_Wealth

The interaction term β6*Income_Wealth captures the joint effect of consumer income and wealth on sales, allowing us to test if the interaction is significant.