A university career center collects information on the job status and starting s

Question

A university career center collects information on the job status and starting salary of graduating seniors. Data recently collected over a two-year period included over 900 seniors who had found employment at the time of graduation. The information was used to model starting salary Y as a function of two qualitative independent variables: COLLEGE at four levels {Business, Engineering, Liberal Arts, Nursing} and SEX (male and female).

Define the dummy variables to include college (use Business as your baseline) in a regression model for starting salary Y

Write down the general regression model relating starting salary Y to both college and sex.

How would your model change if students in Engineering have the same starting salary as students in Business? Show the final regression model.

Explanation / Answer

The experiment involves a single factor College, set at 4 levels. Thus, one have completely randomized design with p=4 treatments. The appropraite linear regression model for p=4 is:

y=beta0+beta1x1+beta2x2+beta3x3+e

where, x1=1 if Enginering 0 if not; x2=1 if Liberal Arts 0 if not

x3=1 if Nursing 0 if not; Base level=Business

There are two independent factors-College and sex. Both the variables are qualitative, thus the main effects are represented by dummy variables. The variable College is set at 4 levels, thus one requires three dummy variables for factor College (the number of main effects term is one less than the number of levels for a factor). Consequently the full factorial model is:

y=beta0+beta1x1+beta2x2+beta3x3+beta4x4+beta5x1x4+beta6x2x4+beta7x3x4

where, x1=1 if Enginering 0 if not; x2=1 if Liberal Arts 0 if not

x3=1 if Nursing 0 if not; Base level=Business

x4=1 if male 0 if not, the bolded terms are interaction factor.

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