Suppose we estimate the following regression using 48 months of data: Y_t = β₀ + β₁X₁_t+ β₂X₂_t+ β₃X₃_t + β₄X₄_t + ε_t
Using the residuals from this regression,we run another regression of
On the predicted values
_t. From this regression we get an R² of 0.14.Let H₀ be that there is no heteroscedasticity.What can you conclude?

Question

Suppose we estimate the following regression using 48 months of data: Y_t = β₀ + β₁X₁_t+ β₂X₂_t+ β₃X₃_t + β₄X₄_t + ε_t
Using the residuals from this regression,we run another regression of

Suppose we estimate the following regression using 48 months of data: Y<sub>t</sub> = β<sub>0</sub> + β<sub>1</sub>X<sub>1</sub><sub>t</sub><sub> </sub>+ β<sub>2</sub>X<sub>2</sub><sub>t</sub><sub> </sub>+ β<sub>3</sub>X<sub>3</sub><sub>t</sub> + β<sub>4</sub>X<sub>4</sub><sub>t</sub> + ε<sub>t</sub> Using the residuals from this regression,we run another regression of On the predicted values <sub>t.</sub> From this regression we get an R<sup>2</sup> of 0.14.Let H<sub>0</sub> be that there is no heteroscedasticity.What can you conclude? A) Reject H<sub>0</sub> at α = 0.05,but not 0.025 B) Reject H<sub>0</sub> at α = 0.01,but not 0.005 C) Reject H<sub>0</sub> at α = 0.005 D) Unable to reject H<sub>0</sub> at α ≤ 0.10

On the predicted values

_t. From this regression we get an R² of 0.14.Let H₀ be that there is no heteroscedasticity.What can you conclude?

Quizplus · Accepted Answer

Since we have an R² of 0.14, we can conclude that there is heteroscedasticity present. To test for heteroscedasticity, we can use the Breusch-Pagan test. Under H₀, the test statistic follows a chi-squared distribution with k-1 degrees of freedom, where k is the number of predictors in the second regression (in this case, k=1). Since the null hypothesis is that there is no heteroscedasticity, we can reject H₀ at the α=0.01 level if our calculated chi-squared statistic exceeds the 99th percentile of the chi-squared distribution with 1 degree of freedom (since 0.01 is a one-tailed test). This is the same as saying that we cannot reject H₀ at the α=0.005 level, since the 99th percentile of the chi-squared distribution with 1 degree of freedom is 6.634. Therefore, we can conclude that we can reject H₀ at the α=0.01 level, but not at the α=0.005 level. The correct answer is B.

Suppose We Estimate the Following Regression Using 48 Months of Data