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I am having some trouble understanding the full context of this question.

Suppose we have a categorical variable T E (1...n) and we observe k observations for Y when T = n. If a regression model holds:

i) Write down Y in terms of dummy variables X1...Xi

ii) What is the design matrix X

iii) what is b?

So what does it mean when it says there are k observations when T = n? A categorical variable is sort of like a dummy variable right? As in using numbers to represent qualitative measurements such as hair colour etc. So does T only take one value from 1 to n or multiple values?

So if T = n, Y would be represented by B1X1 + ... + BnXn in terms of dummy variables?

how can there only be one b?

Thanks.