Financial Risk Manager Part 1

Explanation

The coefficient estimate β₄ is non-zero but not significant. The fact that the R² value for Model 2 is higher than that for Model 1, but the Adjusted R² value for Model 2 is lower, suggests that the additional variable x₄ in Model 2 is not statistically significant. In other words, it does not have a substantial impact on the dependent variable. This is because the Adjusted R² value takes into account the number of predictors in the model, unlike the R² value. Therefore, even though the coefficient estimate β₄ for the variable x₄ is non-zero, it does not significantly contribute to the prediction of the dependent variable, hence it is not significant.

Choice A is incorrect. The adjusted R² for Model 2 being less than that of Model 1 does not necessarily indicate a mistake by the researcher. The adjusted R² takes into account the number of predictors in the model and penalizes for unnecessary complexity. Therefore, it's possible for a model with more predictors (like Model 2) to have a lower adjusted R² if the additional predictors do not significantly improve the model's predictive power.

Choice B is incorrect. Just because variable x₄'s coefficient estimate β₄ is non-zero, it doesn't automatically mean that variable x₄ is statistically significant. Statistical significance depends on various factors such as sample size, variability in data etc., and cannot be determined solely based on whether or not a coefficient estimate is zero.

Choice D is incorrect. There is sufficient information in the R² and Adjusted R² values to make an inference about the significance of the additional variable.