Let us adopt the following symbols for the variables:
· Sales: S ($)
· Salesperson's level of education: E (Years of education).
· Gender (M): We use a single dummy variable for two categories. If the observation is male, then the variable M=1, if female then M =0.
· Consumer income: I ($)
· Wealth: W ($)
· Ethnicity: Let us consider three categories Caucasian, Hispanic and Asian. For the three categories we need two dummy variables.
o Asian (A), which takes the value 1, if it is an Asian and 0 otherwise.
o Hispanic (H), which takes the value 1, if it is a Hispanic and 0 otherwise.
b0 is a constant; b1, b2, b3 etc. are coefficients, e is the residual error term.
The general model will be:
S = b0 + b1E + b2M + b3I + b4W + b5A + b6H + e
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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