## Related questions with answers

An economist estimates the following regression model:

$y=\beta_0+\beta_1 x_1+\beta_2 x_2+\varepsilon$

The estimates of the parameters $\beta_1$ and $\beta_2$ are not very large compared with their respective standard errors. But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables. Having obtained these results, the economist strongly suspects the presence of multicollinearity. Since his chief interest is in the influence of $X_1$ on the dependent variable, he decides that he will avoid the problem of multicollinearity by regressing $Y$ on $X_1$ alone. Comment on this strategy.

Solution

VerifiedAn economist estimated the following regression model:

$y=\beta_{0}+\beta_{1}x_1+\beta_{2}x_2+\varepsilon.$

Since his main interest is in the influence of $X_1$ on $Y$ he decides to avoid the potential problem of multicollinearity by regressing $Y$ on $X_1$.

We need to comment on this strategy.

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