Question: Write the model. For each of the following situations write a model for µy of the form

µy = β0 + β1x1 + β2x2 +…+βp Xp

where p is the number of explanatory variables. Be sure to give the value of p and, if necessary, explain how each of the x’s is coded.

(a) A model where the explanatory variable is a categorical variable with five possible values.

(b) A model where there are three explanatory variables. One of these is categorized with two possible values; another is categorical with three possible values. Include a term that would model an interaction of the first categorical variable and the third (quantitative) explanatory variable.

(c) A quartic regression, regression where terms up to and including the fourth power of an explanatory variable are included in the model.