IAI Sept 2017 Q5--

[Aditya T.]

Help needed on the 1st part of the question. The linear functions appear to be too tricky and also the estimation of number of parameters. Thanks!

 

[John Lee]

For a variable (ie numerical data that you put in the formula) you do a linear function of it - so it will have 2 parameters
Hence VS which is a variable x would have a formula a +bx with 2 parameters (a and b)

For a factor you assign a parameter to each category.
Hence type of sea would be \(S_i\) with 12 parameters (\(S_1 , S_2, ....., S_{12}\).

 

[Aditya T.]

For a variable (ie numerical data that you put in the formula) you do a linear function of it - so it will have 2 parameters
Hence VS which is a variable x would have a formula a +bx with 2 parameters (a and b)

For a factor you assign a parameter to each category.
Hence type of sea would be \(S_i\) with 12 parameters (\(S_1 , S_2, ....., S_{12}\).

Thanks for your reply, John. But could you explain the number of parameters and the linear predictor for the second, second last and last one?

 

[John Lee]

AA is a variable, so log(AA) we do a linear function of it: \(a+blog(AA)\). Same with \(AA^2\). But recall that when you add covariates you always lose a constant parameter (as two will combine). This gives: \(a+blog(AA)+cAA^2\). You can see there are 3 parameters.

There is a mistake in the second last. It should read: AA + AS + AA.AS
This is equivalent to AA*AS.
Recall that when we do interactive covariates we multiply the formulae together: \(a+blog(AA) * A_i = a_i + b_ilog(AA)\)
Since i here goes from 1 to 15 - there will be 30 parameters.

You should be able to do the last one now.

 

[Aditya T.]

Also, could you let me know how to estimate the residual degrees of freedom? Thanks, A.

 

[John Lee]

For every parameter added, you subtract a degree of freedom.