April 2018 Q4i)

[Sam_actuary_123]

When constructing the matrix X why is it necessary to include the 5th column for age squared?

In general, if age is included as an observation, do we always need to add an extra column for age squared and does this apply to other numeric values.

Thanks

 

[Darren Michaels]

The question says "age of dog will be fitted as a quadratic polynomial".

 

[o.menary11]

Hi,

For part (ii) of this question, how does df1-df2= 2?

from my calcs
df2= 4 observations less 3 parameters (age, size, pre existing condition)
df1= 4 observations less 2 parameters (age, pre existing condition)

Thanks!

 

[Katherine Young]

Age of dog is being modelled using a quadratic, which has 3 parameters (ie y=ax^2+bx+c). But we don't need to include the constant c because we'll already have a constant in the original model.

So by including Age of dog, we'll be using two extra parameters. Hence the change in degrees of freedom is 2.

 

[TIBERIUSNYABIGO]

Age of dog is being modelled using a quadratic, which has 3 parameters (ie y=ax^2+bx+c). But we don't need to include the constant c because we'll already have a constant in the original model.

So by including Age of dog, we'll be using two extra parameters. Hence the change in degrees of freedom is 2.

But why do we look at age of dog yet the factor we want to analyse is size of dog. I dont get that part

 

[Katherine Young]

Quite right, we should have been talking about size of dog, small / medium / large.

One of these is included as a base level, so we have two extra parameters.