Consider the following simple regression model: y = β0 + β1×1 + u(1) and the following multiple regression model: y = β0 + β1×1 +β2×2 + u (2), where x1is the variable of primary interest to explain y.

Consider the following simple regression model: y = β0 + β1×1 + u
(1) and the following multiple regression model: y = β0 + β1×1 +
β2
x2 + u (2), where x1
is the variable of primary interest to
explain y. Which of the following statements is correct?
When drawing ceteris paribus conclusions about how x1
affects y, with model (1), we must assume that x2
, and all
other factors contained in u, are uncorrelated with x1
.
When drawing ceteris paribus conclusions about how x1
affects y, with model (2), because x2
is explicitly in the
model equation, we are able to measure the effect of x1 on
y, holding x2 fixed—assuming all other factors contained in
u, are uncorrelated with x1 and x2
.
With a simple regression model like (1) or a multiple
regression model like (2), if any other factor, not explicitly
in the model equation and, thus contained in u, is correlated
with any independent variable xj
, then the OLS estimator of
the slope parameter βj associated with that variable is
biased.
All of the above.