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Suppose that we have a categorical variable with 4 types, we use $x_{i1},x_{i2},x_{i3}$ to be predictors that take the value of 1,2,3, and 0 otherwise depending on corresponding type(1 of 4) from categorical variable. Suppose we have a quantitative predictor $x_{i4}$ as well, and we have 100 observations. How would the parallel model look like and how would the nonparallel model look like. And what would the mean functions of each type of the categorical variable look like as well?

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