To determine the relationship between y and x1, Rohit estimated two different OLS models. In the first model, Rohit regressed y on x1 and x2 as given below:
\[
y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + u \quad (1)
\]
In the second model, Rohit regressed y only on x1 as given below:
\[
y = \delta_0 + \delta_1 x_1 + \nu \quad (2)
\]
The estimated coefficients of x1 in the above two models are exactly the same. From this observation we can state conclusively that
\begin{itemize}
\item (i) \( \text{Cov}(x_1, y) = 0 \)
\item (ii) \( \hat{\beta_2} = 0 \)
\item (iii) \( \text{Cov}(x_2, x_1) = 0 \)
\end{itemize}
where \( \hat{\beta_2} \) is the estimated coefficient of x2 in the equation (1).