1. Show algebraically the relationship between R 2 and M S (Res). 2. Show algebraically the relationship between R 2 and C p , and between M S (Res) and C p . 3. Substitute expectations in the...

1. Show algebraically the relationship between R²
and M_S(Res).

2. Show algebraically the relationship between R²
and C_p, and between M_S(Res) and C_p.

3. Substitute expectations in the numerator and denominator of the C_p
statistic and show that C_p
is approximately an estimate of p when the model is correct. (This is approximate because the ratio of expectations is not the same as the expectation of the ratio.)