Variance analysis and regression

[MaxManus]

Homework Statement

Assume a one way variance analysis model on the form:
$$Y_{ij} = \mu + \alpha_{i} + e_{ij}$$

where $$e_{ij}$$ independent with expectation 0 and constant variance

$$z_{ijl} = \left\{ \begin{array}{rcl} 1 & \mbox{for} & 1 \\ 0 & \mbox{else} \end{array}\right$$

show that:
a)
$$Y_{ij} = \mu \sum_{l=1}^I \alpha_l z_{ijl} + e_{ij}$$
and why this can bee seen as a linear regression

b) and why it is possible reduce it to
$$Y_{ij} = \mu \sum_{l=1}^{I-1} \alpha_l z_{ijl} + e_{ij}$$
The last $$\alpha$$ is removed

The Attempt at a Solution

a)
$$Y_{ij} = \mu + \sum_{l=1}^I \alpha_l z_{ijl} + e_{ij} =\mu \alpha_1 z_{1j1} + \alpha_2 z_{ 2j2} + ... + \alpha_I z_{IjI} + e_{ij}$$

Which is on the same form as a multiple linear regression
$$\mu = B_0$$
[tex] \alpha_l = B_l [tex]
$$z_{1j1} = x_{i1}$$

so
$$Y_{ij} = B_0 + B_1 x_i1 + ... + B_I x_{iI} + e_{ij}$$
which is on the form of a multiple regression

b) Don't know

 

[mighty2000]

how to answer this part, as it seems that reducing the number of variables would change the model and the assumptions made. Can you please clarify what you mean by "reduce it to"? Do you mean removing the last alpha term from the model or reducing the number of variables in the model?