Let$$s say you are looking at a multiple regression model with two regressors X$1$ and X$2,$ where

both variables are determinants of the dependent variable. You first regress Y on X$1$ only and

$$

find no relationship. However when regressing Y on X$1$ and X$2,$ the slope coefficient $$

$1$ changes

by a large amount. This suggests that your first regression suffers from:

a$.$ heteroskedasticity.

b$.$ perfect multicollinearity.

c$.$ omitted variable bias.

d$.$ dummy variable trap.

$2.$ In a multiple regression model, a control variable:

a$.$ is a regressor to hold constant factors that, if included, could lead the estimated causal effect of

interest to suffer from omitted variable bias

b$.$ should be excluded from the multiple regression since its coefficient is not a parameter of reduce

heteroskedasticity in the error term

c$.$ has a coefficient that always has a causal interpretation, even if it is not of primary interest

d$.$ indicates that it is under the control of the econometrician

$3.$ Extra Credit. In a multiple regression model, the reasons for including control variables are to:

$($Select all that apply.$)$

a$.$ decrease the regression R$2$

$.$

b$.$ make the variables of interest no longer correlated with the error term, once the control variables are

held constant.

c$.$ reduce imperfect multicollinearity.

d$.$ reduce heteroskedasticity in the error term.

e$.$ address the issue of omitted variable bias.

f$.$ increase heteroskedasticity in the error term