Understanding the Relationship Between One-Way ANOVA and Regression Models

[MaxManus]

Homework Statement

Assume a one way anova model:

$$Y_{ij} =\my + \alpha_i + e_{ij}$$

where e are independent, normal distributed with variance sigma and expectation = 0

Define:
$$z_{ijl} = 1$$ if i = l, and 0 else
Show that:

$$Y_{ij} = \mu + \sum_{i=1}^I \alpha_l z_{ijl} + e_{ij}$$

Homework Equations

The Attempt at a Solution

So I have to show that
$$\alpha_i = \sum_{i=1}^I \alpha_l z_{ijl}$$

But how can they be equal when we have a free j?

 

[lippyka]

That is if i = l, then z_{ijl} = 1 and 0 else, but that doesn't help me when j is free.I'm not sure what I'm missing here.