An economist estimates the following regression model: y=β0+β1 x1+β2 x2+εThe estimates of the pa

Step 1: Understand the problem of multicollinearity. Multicollinearity occurs when two or more i

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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.

   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.

Statistics for Business and Economics: Global Edition

Newbold P., Carlson… 8th Edition

Chapter 13, Problem 24

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Step 1

Multicollinearity occurs when two or more independent variables in a regression model are highly correlated. This can lead to unreliable and unstable estimates of the regression coefficients, as it becomes difficult to disentangle the individual effects of Show more…

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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.

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