Say I have a multiple linear regression model, where two of the variables are positively correlated, and I omit one of these variables from the model.
First question - if I increase the sample size, the estimated errors on the parameters would decrease wouldn't they?
Second question - would increasing the sample size have any effect on the bias of the coefficient? I am thinking that it would have no effect, but I am not sure? (Also, am I right in saying that the bias would have the same sign as the coefficient of the omitted variable?)
Thanks