In a regression problem whit n40 observations and 4 paramete

In a regression problem whit n=40 observations, and 4 parameters(including the intercept), what is the distribution of a deleted residual?

1- Normal distribution

2-t-distribution with 35 degrees of freedom

3- t-distribution with 36 degrees of freedom

4- None of the above

Solution

The distribution of deleted residual follow t distribution with degree of freedom n-p-1. Where n is the total number of observations and p is number of parameters. So the distribution of a deleted residual will follow t-distribution with n-p-1=40-4-1=35 degree of freedom.

Option 2 is correct.