Hi Guys,
I have some theoretical questions about regression models, I need an answer of true or false for the next few phrases....

1. Leverage values increase when the sample variance increase
2. in a simple model, the residuals ei is dependent with the predicted values of yi
3. when the spread of the X's increase, the the coefficient (beta) decrease and it's variance decrease.
4. if we take 2 models, one with 2 IV X1 and X2, and the other one partial with X1 only, is the significant test for beta1 is equal in both cases, assuming that X1 and X2 are independent ?

In 1 I thought it's false...that it's the other way round...
In 2 I thought it's true
In 4 it's false again.

Am I any near ?

cheers !