we recently started learning about Neural networks and I would like to get a better grasp of them (or at least make sure I understand correctly);
I'd like to be able to write out the model in explicit form as described in the Title.
We have equations for the hidden layers and for $Y_i$ and when everything is combined and written out we have:
$$Y_i = \beta_0 + \sum_{j=1}^{m-1} \beta_j \alpha_{j,0} + \sum_{j=1}^{m-1} \beta_j \alpha_{j,1} X_{i,1} + ... + \sum_{j=1}^{m-1} \beta_j \alpha_{j,p-1} X_{i,p-1} + e_i $$
So I understand j is the index of the hidden layer, m is the levels associated with the hidden layer and p is the number of inputs (including the intercept). Is this correct?
So I suppose for a network with 3 inputs, 1 hidden layer, and 2 levels in that hidden layer I should have;
$Y_i = \beta_0 + \beta_1\alpha_{10} + \beta_1\alpha_{11}X_{i1} + \beta_1\alpha_{12}X_{i2}$
I guess I'm still having a good bit of trouble with all of this. Something seems off about what I wrote out. Thank you in advance for any help!